the graph of an absolute value function has a vertex at (-2, 3) and passes through the point (-1, 0). using…

Explanation:

Step1: Write the general form of absolute - value function after transformation

The general form of an absolute - value function after translation and dilation is $y = a|x - h|+k$, where $(h,k)$ is the vertex. Given the vertex $(-2,3)$, the function is $y=a|x + 2|+3$.

Step2: Substitute the given point into the function

Substitute the point $(-1,0)$ into $y=a|x + 2|+3$. We get $0=a|-1 + 2|+3$, which simplifies to $0=a\times|1|+3$, or $0=a + 3$.

Step3: Solve for the dilation factor $a$

Solving the equation $0=a + 3$ for $a$, we subtract 3 from both sides to get $a=-3$. Since $|a| = 3>1$, the graph has been dilated by a scale factor other than 1.

Answer:

Yes, the graph has been dilated by a scale factor of 3 (since $a=-3$ and $|a| = 3>1$).