Question

the graph shows g(x), which is a translation of f(x) = |x|. write the function rule for g(x).
write your answer in the form a|x - h| + k, where a, h, and k are integers or simplified fractions.
g(x) =

Explanation:

Step1: Identify vertex of $g(x)$

The vertex of $g(x)$ is at $(7, 0)$. For the form $a|x-h|+k$, $h=7$, $k=0$.

Step2: Find $a$ using a point

Use the y-intercept $(0,7)$: substitute $x=0$, $g(x)=7$, $h=7$, $k=0$ into the form:
$7 = a|0-7| + 0$
$7 = 7a$
Solve for $a$: $a = \frac{7}{7}=1$

Step3: Write the function rule

Substitute $a=1$, $h=7$, $k=0$ into $a|x-h|+k$.

Answer:

$g(x) = |x - 7|$