Question

match the vertex to each absolute value function.

1. $f(x) = |x + 3| + 3$ 10) $f(x) = |x| - 4$ 11) $f(x) = |x + 1| - 4$ 12) $f(x) = |x - 2| + 2$

(vertex options: (0,3), (-3,2), (3,2), (2, -3), (2,2), (-2, 2), (-1,4), (-1, -4), (-4, -1), (3,3), (3, -3), (-3, 3), (4,0), (-4,0), (0, -4))

Explanation:

Step1: Recall vertex form of absolute value function

The general form of an absolute value function is \( f(x) = |x - h| + k \), where the vertex is \( (h, k) \). If the function is \( f(x)=|x + a|+b \), we can rewrite \( x + a \) as \( x - (-a) \), so the vertex is \( (-a, b) \).

Step2: Find vertex for \( f(x)=|x + 3|+3 \)

For \( f(x)=|x + 3|+3 \), comparing with \( f(x)=|x - h|+k \), we have \( h=-3 \) and \( k = 3 \). So the vertex is \( (-3, 3) \).

Step3: Find vertex for \( f(x)=|x|-4 \)

For \( f(x)=|x|-4 \), we can rewrite it as \( f(x)=|x - 0|+(-4) \). So \( h = 0 \) and \( k=-4 \), and the vertex is \( (0, -4) \).

Step4: Find vertex for \( f(x)=|x + 1|-4 \)

For \( f(x)=|x + 1|-4 \), rewrite \( x + 1 \) as \( x-(-1) \). So \( h=-1 \) and \( k = -4 \), and the vertex is \( (-1, -4) \).

Step5: Find vertex for \( f(x)=|x - 2|+2 \)

For \( f(x)=|x - 2|+2 \), we have \( h = 2 \) and \( k = 2 \). So the vertex is \( (2, 2) \).

Answer:

1. \( f(x)=|x + 3|+3 \) matches with vertex \( (-3, 3) \)
2. \( f(x)=|x|-4 \) matches with vertex \( (0, -4) \)
3. \( f(x)=|x + 1|-4 \) matches with vertex \( (-1, -4) \)
4. \( f(x)=|x - 2|+2 \) matches with vertex \( (2, 2) \)