Just as each one has received a gift, use it to serve others,
as good stewards of the varied grace of God.
Peter I 4:10

Audiographs user guide

Important!!!

Before using audiographs, be sure to set audio volume to a low value because the application may produce very high audio frequencies

Quick introduction
User guide
Application shortcuts
List of supported functions

1. Quick introduction

1. Start the application
2. Type x
3. Press Enter

You just heard the audio representation of function f(x) = x

Some useful notes:

1. The application has an autonomous speech synthesizer, for this reason you can disable your screen reader.
For NVDA press NVDA button + s.
If you don't want to disable your screen reader, press F2 to disable audiographs speech synthesizer

2. Every time you want to study a new function press Control + N to start from the beginning.

3. When you start with a new function, audiographs will set a limit from -10 to 10 for both x and y axis. Sound above or below these limits will be clipped.

2. User guide

Here you will find exercises of increasing difficulty that will help you learn the details of the application

Exercise 1. Study function f(x) = 2*x

1. Press Control + N to study a new expression. This is not needed if you just started the application.
2. Press 2 x
3. Press Enter
4. Hear the audio. The audio frequency starts from low and goes high
5. Press F3 to change from continuous sound to musical notes
6. Press Enter again. You will hear musical notes, not a continuous sound
7. Press F4 to use different musical notes for negative values.
8. Press Enter again. You will hear that the sound changes beyond a certain point. Using this way you know if you are in negative or positive values. Note that this feature can be used only when musical notes are selected with F3
9. By pressing Page Up and Page Down, you can explore the function. Press Page Up to go to the right. Press Page Down to go to the left
10. By pressing Home and End buttons, you can go to the starting and the ending point of the function
11. By pressing Control + x, you can hear the x coordinate of the current point
12. By pressing Control + y, you can hear the y coordinate of the current point
13. By pressing Control + ], you can increase the step of the exploration, thus making the exploration faster
14. By pressing Control + [, you can decrease the step of the exploration, thus making the exploration slower
15. By pressing Tab you can explore all the settings of the application
16. Press Tab to reach minimum x setting. This is the starting point of the function. By default is set to -10 when the user edits a new function
16. Press Tab to reach maximum x setting. This is the ending point of the function., By default is set to 10 when the user edits a new function
17. Press Tab to reach minimum y setting. This is the lowest value that will be displayed. Values less than minimum will be clipped and set to minimum. By default is set to -10 when the user edits a new function
18. Press Tab to reach maximum y setting. This is the highest value that will be displayed. Values greater than maximum will be clipped and set to maximum. By default is set to 10 when the user edits a new function
18. Press Tab to reach duration which by default is 15 seconds. Now you can increase duration of the sound or decrease the duration
19. Press Tab to reach minimum frequency. Minimum frequency is the lowest frequency that will be produced by the application. Adjust to the value you prefer.
20. Press Tab to reach maximum frequency. Maximum frequency is the highest frequency that will be produced by the application. Adjust to the value you prefer.
21. Minimum and maximum frequency values are used only when musical notes are not selected. Otherwise the application will override these settings with musical notes frequencies.
22. By pressing F9 you can decrease decimal precision digits
23. By pressing F10 you can increase decimal precision digits
24. Select Reset audio settings to restore default audio settings
25. At any time, press Control + E, to return to the function edit text

Exercise 2. Study function f(x) = x^2

0. Start the application or press Control plus N to start a new expression if you already study an expression
1. Press x power 2
2. Press Enter
3. Listen to audio, the function starts from high, is goes low and then high again
4. Press Home to go to the starting point.
5. Press Control + x to listen to x coordinate. You will hear -10
6. Press Control + y to listen to y coordinate. You will hear 100. So the function starts from the point (-10, 100)
7. Press F3 to switch from continuous sound to audio notes.
8. Press Control + right arrow to go to the next study point.
9. Sound frequency will start decreasing until you hear "local minimum"
10. Press Control + x, you will hear 0.00
11. Press Control + y, you will hear 0.00, so there is a local minimim at (0, 0)
12. Press Control + right arrow
13. Sound frequency will start increasing until you hear "ending point"
14. Press control + x, you will hear 10
15. Press control + y, you will hear 100
16. So the function starts from (-10, 100) goes down to (0, 0) and then up to (10, 100)
17. The values that you will hear from the application depend on the precision digits you have selected. Press F9 to decrease and F10 to increase precision digits

Exercise 3. Study function f(x) = -x^2 - 1

0. Start the application or press Control plus N to start a new expression if you already study an expression
1. Press minus x power 2 minus 1
2. Press F3 to choose continuous sound or musical notes depending on your preferences
3. Press Enter. Listen to audio, the function starts from low, it goes high and then low again
4. Press Home to go to the starting point.
5. Press Control + x to listen to x coordinate. You will hear -10
6. Press Control + y to listen to y coordinate. You will hear -100. So the function starts at the point (-10, -101)
7. Press Control + right arrow to go to the next study point.
8. Sound frequency will start increasing until you hear "local maximum"
10. Press Control + x, you will hear 0.00
11. Press Control + y, you will hear -1.00, so there is a local maximum at (0, -1)
12. Press Control + right arrow
13. Sound frequency will start decreasing until you hear "ending point"
14. Press control + x, you will hear 10
15. Press control + y, you will hear -101
16. So the function starts from (-10, -101) goes up to (0, -1) and then down to (10, -101)
17. The values that you will hear from the application depend on the precision digits you have selected. Press F9 to decrease and F10 to increase precision digits

Exercise 4. Study function f(x) = x^2 - 8x + 8

0. Start the application or press Control plus N to start a new expression if you already study an expression
1. Press x power 2 minus 8 x plus 8
2. Press Enter. Listen to audio, the function starts from high, it goes low and then high again
3. Press F3 and make sure "use notes" is checked
4. Press F4 and make sure "use different notes for negative values" is checked. This setting can only be used when "use notes" is checked. It cannot be used with continuous sound. Now we will hear different sounds when the function has negative values.
5. Press Enter. You will hear the function starting from high, going low. At some point the sound will change. This means the function has negative values. Then it goes up again. It changes to normal sound. This means the function has positive values and continues to go up
6. Press Home. You will hear that we are in starting point.
7. Press Ctrl + x, You will hear -10.00
8. Press Ctrl + y, You will hear 188
9. Press Control + right arrow to go to the next study point. You will hear "local minimum". You will hear different sound because we are below zero.
10. Press Control + x, You will hear 4
10. Press Control + y, You will hear -8. So the function has a local minimum at (4, -8)
11. Press Control + right, You will hear "ending point"
12. Press Control + x, You will hear 10
13. Press Control + y, You will hear 27.98
14. So the function starts from (-10, 188) goes down to (4, -8) and then up to (10, 27.98)
15. Press Home. We are at the start again.
16. Press Control + 1. Now we can here the first derivative of the function.
17. Press Control + right. You hear negative values till you reach the local minimum. This means that the function is decreasing
17. Press Control + right. You hear positive values till you reach the ending point. This means that the function is increasing
18. Press Home again. We are at the start again.
19. Press Control + 2. Now we can here the second derivative of the function.
20. Press Control + right. You will positive values till you reach the local minimum.
21. Press Control + right. You will positive values till you reach the ending point. This means that the function has positive curvature
22. Press Control + 0 if you want to leave the derivative mode and return to normal mode.

Exercise 5. Study function f(x) = 1 - sqrt(x)/2

0. Start the application or press Control plus N to start a new expression if you already study an expression
1. Press 1 minus s q r t ( x ) / 2
2. Press F3 and make sure "use notes" is checked
3. Press F4 and make sure "use different notes for negative values" is checked.
4. Press Enter. You will hear noise. This means that the function is not defined at that point. At some point you will hearing the sound for the points that the function is defined.
5. Press Home. You will hear that we are in starting point.
6. Press Ctrl + x. You will hear -10.00
7. Press Ctrl + y. You will hear "not defined". This means that the function is not defined at this point
8. Press Control + right arrow to go to the next study point. You will hear noise and after that you will hear "maximum after undefined point".
10. Press Control + x. You will hear 0.00
10. Press Control + y. You will hear 1. So the function is not defined at (-10,0). It starts from (0,1) where there is a maximum.
11. Press Control + right. You will hear different notes meaning we are going below zero. Finally you will hear "ending point".
12. Press Control + x. You will hear 10
13. Press Control + y. You will hear -0.58
14. So the function is not defined at (-10,0). It starts from (0, 1) and goes down to (10, -0.58)
15. Press Home. We are at the start again.
16. Press Shift + right arrow. You will hear "maximum after undefined point". Shift + right takes you to the next study point without having to hear any sound. Shift + left takes you to the previous study point. So shift plus arrows is a very fast way to explore the function.
17. Press Control + x. As before you will hear 0.00 because we are the maximum point, where the function starts.
18. Press Control + y. You will hear 1.00
19. Press Page Up. You have moved a little bit to the right.
19. Press Page Down. You have moved a little bit to the left. Using Page Up and Page Down you can explore the function in great detail.
20. At any point you can hear where you are using Control + x and Control + y. You can use Home button and End button to go the start and to the end of the function
21. Press Control + [. You will hear that you decreased the value of the step when you are exploring. Control + [ makes the navigation more slow but more accurate.
22. Press Control + ]. You will hear that you increased the value of the step when you are exploring. Control + ] makes the navigation faster but less accurate.

Exercise 6. Study function f(x) = 1/x

0. Start the application or press Control plus N to start a new expression if you already study an expression
1. Press 1 / x
2. Press Enter. You will hear the audio generated for this function.
3. Press Home. You will hear that we are in starting point.
4. Press Ctrl + x. You will hear -10.00.
5. Press Ctrl + y. You will hear -0.10.
6. Press Control + right arrow to go to the next study point. You will hear the function going low till it reaches a minimum.
7. Press Control + x. You will hear 0.00.
8. Press Control + y. You will hear -500.
9. Press Control + right. You will immediately reach maximum.
10. Press Control + x. You will hear 0.00.
11. Press Control + y. You will hear 500. The function cannot have both minimum and maximum at the same point. Let's see what is going on
12. Press Control + left to go the previous point. You will hear "minimum before undefined point".
13. Press F10 to increase precision digit points to 5.
14. Press Control + x. You will hear -0.002.
15. Press Control + y. You will hear -500.
16. Press Control + left. You will hear "maximum after undefined point".
17. Press Control + x. You will hear 0.002.
18. Press Control + y. You will hear 500. So the function has a discontinuity point at 0. From the left of zero it goes to minus infinity and from the right of zero it goes to positive infinity
19. Press Control + right. You will hear the function going down till you reach ending point.
20. Press Control + x. You will hear 9.998
21. Press Control + y. You will hear 0.10002.
22. So the function starts from -0.1 goes down to minus infinity at zero and then starts from positive infinitive at zero to go down to 0.1.

Exercise 7. Study function f(x) = 1/(x-8)^2

0. Start the application or press Control plus N to start a new expression if you already study an expression
1. Press 1 / ( x - 8 ) ^ 2
2. Press Enter. You will hear the audio generated for this function.
3. Press Home. You will hear that we are in starting point.
4. Press Ctrl + x. You will hear -10.00.
5. Press Ctrl + y. You will hear 0.00.
5. Press F10 to increase precision digit points to 3.
5. Press Ctrl + y. You will hear 0.003.
6. Press Control + right arrow to go to the next study point. You will hear the function going up till it reaches maximum.
7. Press Control + x. You will hear 7.998.
8. Press Control + y. You will hear 250000.
9. Press Control + right. You will immediately reach maximum.
10. Press Control + x. You will hear 8.002.
11. Press Control + y. You will hear 250000. So the function has a discontinuity point at 8. From the left of 8 it goes to positive infinity and from the right of 8 it goes to positive infinity again.
19. Press Control + right. You will hear the function going down till you reach ending point.
20. Press Control + x. You will hear 9.998
21. Press Control + y. You will hear 0.251.
22. So the function starts from 0.003 goes up to infinity at 8 and then starts from positive infinitive at 8 to go down to 0.251.

Exercise 8. Study the curvature of function f(x) = x^2

0. Start the application or press Control plus N to start a new expression if you already study an expression
1. Press x ^ 2
2. Press F3 and make sure "use notes" is checked
3. Press F4 and make sure "use different notes for negative values" is checked.
4. Press Control + 2 to select second derivative mode .
5. Press Enter. You will hear the audio generated for this function. You will notice that the sound generated corresponds to positive values. This means that the function has positive curvature for the interval (-10, 10)

Exercise 9. Study the curvature of function f(x) = 1/x

0. Start the application or press Control plus N to start a new expression if you already study an expression
1. Press 1 / x
2. Press F3 and make sure "use notes" is checked
3. Press F4 and make sure "use different notes for negative values" is checked.
4. Press Control + 2 to select second derivative mode .
5. Press Enter. You will hear the audio generated for this function. You will notice that the second derivative has negative values and then positive values.
6. Press Home to go to the start.
7. Press Control + right. The application will produce sound for negative values, till it reaches minimum.
8. Press Control + x. You will hear 0.00. So the function has negative curvature at the interval (-10,0).
9. Press Control + right. You will hear that the second derivative has positive values, meaning that the curvature is positive, till we reach ending point. So the function has positive curvature at the interval (0, 10).

Exercise 10. Study the curvature of function f(x) = sqrt(abs(x))

0. Start the application or press Control plus N to start a new expression if you already study an expression
1. Press s q r t ( a b s ( x ) )
2. Press F3 and make sure "use notes" is checked
3. Press F4 and make sure "use different notes for negative values" is checked.
4. Press Control + 2 to select second derivative mode .
5. Press Enter. You will hear the audio generated for this function. You will notice that the second derivative has negative values during the interval (-10, 10). This means that the function has negative curvature at the interval (-10, 10).

Exercise 11. Study the curvature of function f(x) = -x^3

0. Start the application or press Control plus N to start a new expression if you already study an expression
1. Press - x ^ 3
2. Press F3 and make sure "use notes" is checked
3. Press F4 and make sure "use different notes for negative values" is checked.
4. Press Control + 2 to select second derivative mode .
5. Press Enter. You will hear the audio generated for this function. You will notice that the second derivative has positive values and then negative values.
6. Press Home to go to the start.
7. Press Control + right arrow. You will hear positive values till you reach inflection point. Curvature changes at an inflection point.
8. Press Control + x. You will hear 0.00
9. Press Control + y. You will hear 0.00. So the point (0, 0) is an inflection point.
10. Press Control + right arrow. You will hear negative values till you reach ending point.
11. So the function has positive curvature till it reaches 0.00 and then the function has negative curvature till it reaches the ending point.

Exercise 12. Study function f(x) = x^(2/3)

0. Start the application or press Control plus N to start a new expression if you already study an expression
1. Don't use the ^ operand. ^ operand in the form of x^(a/b) may not produce correct result. Use instead the powint function. Press p o w i n t ( x , 2 , 3 )
2. Press Enter. You will hear the function going down and then going up.
3. Press Home. You will hear that you are at the starting point.
4. Press Control + x. You will hear -10.00
5. Press Control + y. You will hear 4.64
6. Press Control + right. You will reach local minimum.
7. Press Control + x. You will hear 0.00
8. Press Control + y. You will hear 0.00
9. Press Control + right. You will reach ending point.
10. Press Control + x. You will hear 10.00
11. Press Control + y. You will hear 4.64
12. So the function starts at (-10, 4.64) goes to a minimum at (0,0) and then goes up to (10, 4.64)

3. Application shortcuts

Help dialog - F1

New expression - Ctrl + N

Set focus on expression - Ctrl + E

Play sound - Enter

Previous point - Page down

Next point - Page up

X Coordinate - Ctrl + X

Y Coordinate - Ctrl + Y

Derivative - Ctrl + D

Previous point of interest - Ctrl + Left

Next point of interest - Ctrl + Right

Previous point (fast) - Shift + Left

Next point (fast) - Shift + Right

First point - Home

Last point - End

Decrease step - Ctrl + [ left bracket

Increase step - Ctrl + ] right bracket

Decrease precision - F9

Increase precision - F10

Normal mode - Ctrl + 0

First derivative mode - Ctrl + 1

Second derivative mode - Ctrl + 2

Self voice - F2

Use notes - F3

Use different notes for negative values - F4

Recent function expressions - Alt + 1 to 9

3. List of supported functions

Audiographs uses C++ Mathematical Expression Library.
For more information visit http://www.partow.net/programming/exprtk/