1. If a function f (x) is shifted to the left one unit, what function represents the transformation?

A. f (x+1)

B. f (x-1)

C. f (x) + 1

D. f (x) - 1

2. Let g (x) be the reflection of f (x) = x^2+5 in the x-axis. What is a function rule for g (x) ?

A. g (x) = - x^2-5

B. g (x) = x^2+5

C. g (x) = x^2-5

D. g (x) = - x^2+5

3. What transformations change the graph of f (x) to the graph of g (x) ?

4. Write an equation for the following transformation of y=x: a vertical stretch by a factor of 6.

A. y=6x

B. y=x/6

C. y=x+6

D. y=x-6

The correct answers are:

1) A;

2) A;

4) D

3 cannot be done because the graph is not shown.

Explanation:

1) Shifting a graph to the left, we would normally think of subtracting 1 from the function. However, horizontal translations are the opposite; left means adding 1 to x, while right means subtracting 1 from x.

2) A reflection in the x-axis means the y-coordinate will be negated (the opposite sign). This means that g (x) = - f (x) = - (x^2+5=-x^2-5.

4) To perform a vertical stretch of a function, we multiply by the factor; this gives us y=6x.