Question

Piecewise and Absolute Value FunctionsSelect the correct answer.Which function is represented by this graph?

Answer 1

Notice that the given graph is the graph of the function g(x)=|x| reflected over the x-axis, translated 1 unit to the right, and translated 1 unit up.

Now, recall that:

1) The function represented by the graph of the function h(x) reflected over the x-axis is:

`-h(x)\text{.}`

2) The function represented by the graph of the function h(x) translated n units to the right is:

`h(x-n)\text{.}`

3) The function represented by the graph of the function h(x) translated m units up is:

`h(x)+m`

Therefore, the function that is represented by the graph of g(x)=|x| reflected over the x-axis, translated 1 unit to the right, and then translated 1 unit up is:

`f(x)=-|x-1|+1.`

Answer: Second option.