Question

Select the correct answer.Which function is represented in this graph?A. f(x) = |x − 1| − 5B. f(x) = |x − 5| − 1C. f(x) = |x + 5| − 1D. f(x) = |x + 1| − 5

Answer 1

The graph of the function shown is obtained by a transformation of the function:

`f(x)=\lvert x\rvert`

which graph is shown below:

From the graph of the parent function, we notice that the graph of the function given is obtained by translating the graph of the parent function five units to the left and one unit down. The table shown below gives us the algebraic rules to perform these transformations:

From the table and the translations we know we need to perform we conclude that the expression for the function shown is:

`f(x)=\lvert x+5\rvert-1`

Therefore, the answer is C.