Question

semester 1: unit 4 exam review
absolute value fct:
given the vertex, identify which equation represents the function?
here is the graph that represents a function.
(the graph is a v - shape opening upward with vertex at (2, -1).)
which equation represents the function?
a. $f(x)=|x - 2| - 1$
b. $g(x)=|x + 2| - 1$
c. $h(x)=|x - 1| + 2$
d. $j(x)=|x| - 1$
○ a
○ b
○ c
○ d

Explanation:

Step1: Recall vertex form of absolute value function

The vertex form of an upward-opening absolute value function is $f(x) = |x - h| + k$, where $(h,k)$ is the vertex.

Step2: Substitute vertex $(2,-1)$ into the form

Substitute $h=2$ and $k=-1$:
$f(x) = |x - 2| + (-1) = |x - 2| - 1$

Step3: Match with given options

Compare the derived equation to the options.

Answer:

A. $f(x) = |x - 2| - 1$