the graph shows $g(x)$, which is a translation of $f(x) = |x|$. write the function rule for $g(x)$.\nwrite…

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

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

Answer

Explanation:

Step1: Identify the vertex of the graph

The vertex $(h, k)$ is the lowest point of the V-shape. From the graph, the vertex is at $(2, 0)$. $$h = 2, k = 0$$

Step2: Determine the vertical stretch factor

Pick another point on the graph, such as $(3, 1)$, and substitute into $g(x) = a|x - h| + k$. $$1 = a|3 - 2| + 0$$

Step3: Solve for the constant a

Simplify the equation to find the value of $a$. $$1 = a|1| \implies a = 1$$

Step4: Write the final function rule

Substitute $a = 1$, $h = 2$, and $k = 0$ into the general form. $$g(x) = 1|x - 2| + 0$$

Answer:

g(x) = |x - 2|