Transformations of graphs

Question 1

What transformation is caused by the following transformation of y = f(x):
y = f(x) + c

Answer 1

Translation c units up

Question 2

What transformation is caused by the following transformation of y = f(x):
y = f(x + d)

Answer 2

Translation d units to the left

Question 3

What transformation is caused by the following transformation of y = f(x):
y = pf(x)

Answer 3

Vertical stretch, scale factor p

Question 4

What transformation is caused by the following transformation of y = f(x):
y = f(qx)

Answer 4

Horizontal stretch, scale factor 1/q

Question 5

What transformation is caused by the following transformation of y = f(x):
y = -f(x)

Answer 5

Reflection in the x-axis

Question 6

What transformation is caused by the following transformation of y = f(x):
y = f(-x)

Answer 6

Reflection in the y-axis

Question 7

What are the 4 steps of transforming a trigonometric graph?

Answer 7

1. Make a substitution (such as A = 2x)
2. Change the interval for x into the interval for A
3. Solve the equation in the usual way
4. Transform the solution back to the original variable

Question 8

In what case can changing the order of 2 transformations affect the final result?

Answer 8

When there are two horizontal or two vertical transformations

Question 9

What is the modulus function?

Answer 9

The function that turns negative numbers into their positive equivalents (but leaves positive numbers alone)

Question 10

How do you sketch the graph of y = |f(x)|?

Answer 10

1. Start with the graph of y = f(x)
2. Reflect any parts that are below the x-axis

Question 11

How else can you write the modulus inequality |x - a|< b?

Answer 11

a - b < x < a + b

Question 12

What must you do when solving a modulus function?

Answer 12

Sketch the graph