QuestionDefine the function $g(x)$ based on the graph of $f(x)=|x|$ shifted left 1 unit and down 9 units.

Studdy Solution

STEP 1

Assumptions1. The function $f(x)=|x|$ is the absolute value function, which gives the distance of a number from zero on the number line. . The function $g(x)$ is a transformation of $f(x)$ , shifted one unit to the left and nine units down.

STEP 2

The general form of the equation for a function that is shifted horizontally and vertically is $g(x) = f(x - h) + k$ where $h$ is the horizontal shift and $k$ is the vertical shift.

STEP 3

In this case, the function is shifted one unit to the left and nine units down. So, $h =1$ (left shift is positive) and $k = -9$ (down shift is negative).

STEP 4

Substitute $h =1$ and $k = -9$ into the general form of the equation.
$g(x) = f(x -1) -9$

STEP 5

Since the original function $f(x)$ is the absolute value function, we can replace $f(x -1)$ with $|x -1|$ .
$g(x) = |x -1| -9$ So, the equation for the function whose graph is the graph of $f(x)=|x|$ , but shifted one unit to the left and nine units down is $g(x) = |x -1| -9$ .

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