02 Graphs And Transformations Flashcards

1
Q

When does a cubic graph look like this?

A

When all 3 roots are the same (positive).

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2
Q

When does a cubic graph look like this?

A

When you have 3 different roots. (Positive)

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3
Q

When does a cubic graph look like this?

A

When you have 1 repeated root and one different root. (Positive)

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4
Q

When does a cubic graph look like this?

A

All 3 roots are the same (negative).

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5
Q

When does a cubic graph look like this?

A

3 different roots (negative).

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6
Q

When does a cubic graph look like this?

A

One repeated root and one different.

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7
Q

What is an a^x graph called?

A

An exponential function

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8
Q

What does an exponential graph look like (y = a^x)?

A
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9
Q

What type of graph is y = k/x (or y=k/x^2)?

A

A reciprocal graph

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10
Q

What type of graph is this?

A

Reciprocal (y=k/x)

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11
Q

Where are the asymptotes on a reciprocal graph?

A

X=0 and y=0

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12
Q

What is an asymptote?

A

A line which the graph approaches but never reaches.

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13
Q

What type of graph is this?

A

A reciprocal graph (y=k/x^2)

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14
Q

What type of graph is this?

A

A reciprocal graph (y=k/x^2)

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15
Q

How do you sketch a modulus graph?

A

Sketch the graph without the modulus, then reflect any sections of the graph below the x-axes.

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16
Q

What type of graph is this?

A

Modulus.

17
Q

|-5| =

A

5

18
Q

|5| =

A

5

19
Q

Explain this translation.
Y =f(x) —> y = f(x) + a

A

Translation by the vector (0 a)

20
Q

Explain this translation Y = f(x) —> y = f(x + a)

A

Translation by the vector (-a 0).

21
Q

How is x awkward in translation?

A

Change the sign.

22
Q

Explain this stretch.
Y = f(x) —> y = a f(x)

A

Stretch by a scale factor a in the y direction.

23
Q

Explain the stretch.
Y = f(x) —> y = f(ax)

A

Stretch by a scale factor of 1/a in the x direction.

24
Q

Why is x awkward in stretched graphs?

A

Use the reciprocal for the scale factor.

25
Q

Explain the reflection
Y = f(x) —> y = -f(x)

A

Reflection in the x axis. (y = 0)

26
Q

Explain the reflection
Y = f(x) —> y = f(-x)

A

Reflection in the y axis. (x = 0)

27
Q

How do you reflect a graph vertically?

A

Multiply the function by -1 ‘outside the function’.

28
Q

How do you reflect a graph horizontally?

A

Multiply the function by -1 ‘inside’ the function.