Question

2 looking at the parent function of $f(x) = |x|$ how would the graph of $g(x) = |x| + 5$ be different? graph using the drawing tools.

Explanation:

Step1: Identify vertical shift rule

For $g(x)=f(x)+k$, shift up by $k$.

Step2: Apply rule to parent function

Here $f(x)=|x|$, $k=5$, so $g(x)=|x|+5$ shifts $f(x)$ up 5 units.

Step3: Find vertex of $g(x)$

Vertex of $f(x)$ is $(0,0)$. New vertex: $(0,0+5)=(0,5)$.

Step4: Define rays for $g(x)$

For $x\geq0$: $g(x)=x+5$, ray from $(0,5)$ through $(3,8)$.
For $x\leq0$: $g(x)=-x+5$, ray from $(0,5)$ through $(-3,8)$.

Answer:

The graph of $g(x)=|x|+5$ is the graph of the parent function $f(x)=|x|$ shifted 5 units vertically upward. The vertex of $g(x)$ is at $(0,5)$, with one ray extending from $(0,5)$ through positive $x$-values (e.g., $(3,8)$) and another ray extending from $(0,5)$ through negative $x$-values (e.g., $(-3,8)$).