Question

identify the transformations that occurred from the parent function $f(x)=|x|$.
$g(x)=\frac{5}{2}|x-3|+4$
the function select an answer reflected over the x-axis.
the function was select an answer vertically by a factor of $square$
the function was shifted select an answer $square$ units.
the function was shifted select an answer $square$ units.

Explanation:

Step1: Check reflection

The parent function $f(x)=|x|$ has a positive coefficient, and $g(x)=\frac{5}{2}|x-3|+4$ also has a positive coefficient for the absolute value term, so there is no reflection over the x-axis.

Step2: Identify vertical stretch

The coefficient of $|x-3|$ is $\frac{5}{2}>1$, so this is a vertical stretch by a factor of $\frac{5}{2}$.

Step3: Identify horizontal shift

For $|x-h|$, when $h=3$, the graph shifts right 3 units.

Step4: Identify vertical shift

The constant term $+4$ at the end means the graph shifts up 4 units.

Answer:

The function was not reflected over the x-axis.
The function was stretched vertically by a factor of $\boldsymbol{\frac{5}{2}}$.
The function was shifted right $\boldsymbol{3}$ units.
The function was shifted up $\boldsymbol{4}$ units.