Question

1. given the function $f(x) = 2x + a$, what value of $a$ will result in a vertical translation down 3?

a. -3
b. 3
c. 5
d. -5
e. cannot be determined

1. the parent function $f(x) = |x|$ is transformed to $g(x) = -3|x|$. which of the following describes the transformation from $f(x)$ to $g(x)$?

a. vertical stretch by a factor of 3
b. vertical stretch by a factor of 3 and reflection in the $x$-axis
c. vertical shrink by a factor of one - third
d. vertical shrink by a factor of one - third and reflection in the $x$-axis
e. cannot be determined

Explanation:

Problem 9

Step1: Recall vertical translation rule

For $f(x)=mx+a$, $a$ shifts vertically.

Step2: Downward shift means negative $a$

A downward shift of 3 gives $a=-3$.

Problem 10

Step1: Analyze coefficient sign

Negative coefficient reflects over $x$-axis.

Step2: Analyze coefficient magnitude

$|k|=3>1$ means vertical stretch by 3.

Step3: Combine transformations

Reflection + vertical stretch by 3.

Answer:

1. A. -3
2. B. vertical stretch by a factor of 3 and reflection in the x-axis