Chapter 4: Graphs and Transformations

Question 1

What does it mean if p is a root of the function f(x)?

Answer 1

The graph y = f(x) will either cross or touch the x-axis at (p, 0)

Question 2

What do reciprocal graphs create?

Answer 2

Asymptotes

Question 3

What is an asymptote?

Answer 3

A line which the graph approaches but never reaches

Question 4

What is the graph of y = f(x) + a a translation of?

Answer 4

A translation of the vector (0 a)

Question 5

What is the graph of y = (x + a) a translation of?

Answer 5

A translation of the vector (-a 0)

Question 6

When you translate a function, what happens to the asymptotes?

Answer 6

They are also translated

Question 7

What is the graph of y = af(x) a stretch of?

Answer 7

A stretch by a scale factor of a in the vertical direction

Question 8

What is the graph of y = f(ax) a stretch of?

Answer 8

A stretch by a scale factor of 1/a in the horizontal direction

Question 9

What is the graph of y = -f(x) a reflection of?

Answer 9

A reflection in the x-axis

Question 10

What is the graph of y = f(-x) a reflection of?

Answer 10

A reflection in the y-axis