Question

Begin by graphing the absolute value function, f(x)= |x|. Then use the transformations of this graph to graph the given function g(x)= |x+7|What transformations are needed in order to obtain the graph of g(x) from the graph of f(x)? Select all that apply

Answer 1

The absolute value of x means that all negative values are transformed into positive values.

Graphing the absolute value function, we have:

Then, in order to graph the function g(x) = |x + 7|, let's first calculate some points that are solutions to this equation:

`\begin{gathered} x=-6\colon \\ g(-6)=|-6+7|=1 \\ \\ x=-7\colon \\ g(-7)=|-7+7|=0 \\ \\ x=-8\colon \\ g(-8)=|-8+7|=1 \end{gathered}`

Graphing g(x), we have:

The transformation needed to graph g(x) from f(x) is a translation (horizontal shift) of 7 units left.

Therefore the correct option is D.