Question

The graph of g(x) is the graph of f(x)=x+6reflected across the x-axis.Which equation describes function g? g(x)=−x+6g(x)=−x−6g(x)=−6x−6g(x)=x−6

Answer 1

We are given the function

$f(x)=x+6$

We are to reflect the function f(x) over the x axis

The rule to reflect a function over x axis is given as

$(x,y)\Rightarrow(x,-y)$

Let f(x) = y

Then

$y=x+6$

Hence for the reflection

x = x, y = -y

Hence, the reflection is

$-y=x+6$

Simplifying this we get

$y=-x-6$

Thereforem the reflection g(x) is

$g(x)=-x-6$