Question

to produce g, function f was reflected over the x - axis and shifted up 5 units. function g can be defined as
options:
g(x) = f(x) + 5
g(x) = f(x - 1) + 4
g(x) = f(x + 1) - 4
g(x) = f(x + 5)

Explanation:

Step1: Recall reflection over x-axis

A reflection of $f(x)$ over the x-axis gives $-f(x)$.

Step2: Recall vertical shift up 5 units

Shifting $-f(x)$ up 5 units adds 5 to the function: $-f(x) + 5$.

Step3: Match to given options

The transformed function matches the first option.

Answer:

$g(x) = -f(x) + 5$