Question

1. $y = 3|x - 2| + 3$

Explanation:

Step1: Find vertex of the function

The vertex form of an absolute value function is $y=a|x-h|+k$, where $(h,k)$ is the vertex. For $y=3|x-2|+3$, $h=2$, $k=3$. So vertex is $(2, 3)$.

Step2: Find point for $x>2$

Let $x=3$, substitute into the function:
$y=3|3-2|+3=3(1)+3=6$
Point: $(3, 6)$

Step3: Find point for $x<2$

Let $x=1$, substitute into the function:
$y=3|1-2|+3=3(1)+3=6$
Point: $(1, 6)$

Step4: Find y-intercept ($x=0$)

Substitute $x=0$:
$y=3|0-2|+3=3(2)+3=9$
Point: $(0, 9)$

Step5: Plot and connect points

Plot the vertex $(2,3)$, $(3,6)$, $(1,6)$, $(0,9)$, then draw two straight lines from the vertex through the other points to form the V-shape.

Answer:

The graph is a V-shaped absolute value function with vertex at $(2, 3)$, passing through points $(1, 6)$, $(3, 6)$, and $(0, 9)$, opening upwards with a slope of $3$ for $x>2$ and $-3$ for $x<2$.