Question

what is the domain of the graph?
what is the range of the graph?
true or false: this is a one-to-one function?
the function $f(x) = |x|$ is transformed to $f(x) = 5|x|$. which statement describes the graph of the transformed function?
a) the graph was translated up 5 units.
b) the graph was translated down 5 units.
c) the graph was compressed by a factor of 5.
d) the graph was stretched by a factor of 5

Explanation:

Step1: Identify domain (x-values)

The graph has a closed dot at $x=-5$, an open dot at $x=3$, and covers all x-values between them.
Domain: $-5 \leq x < 3$

Step2: Identify range (y-values)

The graph's lowest y-value is $-7$, highest y-value is $0$, and covers all y-values between them.
Range: $-7 \leq y \leq 0$

Step3: Test one-to-one property

A one-to-one function passes the horizontal line test; this graph fails (a horizontal line would intersect it twice).
Result: False

Step4: Analyze function transformation

For $f(x) = |x|$ transformed to $f(x)=5|x|$, a coefficient $a>1$ outside the parent function causes a vertical stretch by factor $a$.
Result: Option d is correct.

Answer:

1. Domain: $\boldsymbol{-5 \leq x < 3}$
2. Range: $\boldsymbol{-7 \leq y \leq 0}$
3. False
4. d) The graph was stretched by a factor of 5