QuestionFind the equation of the graph after reflecting $y=f(x)$ across the $x$ -axis and translating it up 2 units: $y=$

Studdy Solution

STEP 1

Assumptions1. The original function is $y=f(x)$ . . The function is reflected across the $x$ -axis.
3. The function is then translated up by units.

STEP 2

When a function is reflected across the $x$ -axis, the $y$ value of each point on the graph is negated. This means that the new function after the reflection will be $y=-f(x)$ .

STEP 3

When a function is translated up by $k$ units, the $y$ value of each point on the graph is increased by $k$ . In this case, the function is translated up by2 units, so the new function after the translation will be $y=-f(x)+2$ .
Therefore, the new graph will have the equation $y=-f(x)+2$ .

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