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) $f(x) = |x - 2| + 2$

matching boxes: 9 to (-3, 3), 10 to (0, -4), 11 to (-1, -4), 12 to (2, 2); bottom has extra vertex options like (0,3), (-3,2), etc.

Explanation:

Step1: Recall vertex form of absolute value function

The general form of an absolute value function is \( f(x) = |x - h| + k \), where \((h, k)\) is the vertex.

Step2: Analyze function 9: \( f(x)=|x + 3|+ 3 \)

Rewrite \( |x + 3| \) as \( |x - (-3)| \). So, \( h=-3 \), \( k = 3 \). Vertex is \((-3, 3)\).

Step3: Analyze function 10: \( f(x)=|x| - 4 \)

Rewrite as \( f(x)=|x - 0|+(-4) \). So, \( h = 0 \), \( k=-4 \). Vertex is \((0, -4)\).

Step4: Analyze function 11: \( f(x)=|x + 1|-4 \)

Rewrite \( |x + 1| \) as \( |x - (-1)| \). So, \( h=-1 \), \( k = -4 \). Vertex is \((-1, -4)\).

Step5: Analyze function 12: \( f(x)=|x - 2|+ 2 \)

Here, \( h = 2 \), \( k = 2 \). Vertex is \((2, 2)\).

Answer:

1. \((-3, 3)\)
2. \((0, -4)\)
3. \((-1, -4)\)
4. \((2, 2)\)