QuestionFind the function $g(x)$ that reflects $f(x)=\frac{1}{2} x-3$ in the $x$ -axis.

Studdy Solution

STEP 1

Assumptions1. The original function is $f(x)=\frac{1}{} x-3$ . We need to reflect this function in the x-axis

STEP 2

A reflection in the x-axis can be achieved by changing the sign of the function. This means that we multiply the entire function by -1.
$g(x) = -f(x)$

STEP 3

Now, plug in the given function $f(x)=\frac{1}{2} x-3$ into the equation.
$g(x) = -(\frac{1}{2} x-3)$

STEP 4

istribute the negative sign to both terms inside the parentheses.
$g(x) = -\frac{1}{2} x +3$ The function $g(x)$ represents the graph of $f(x)$ reflected in the x-axis.

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