Question

In Problems 13–32, use the accompanying graph of $y=f\left(x\right)$.

What is the range of $f$?

Short answer

The range is$\left(-\infty ,\infty \right).$

Step-by-step solution

Step. 1 What is range?

Range of a function is the value of the function in the defined domain of that function. We are given with a graph it means all the values of on y-axis we have in our graph is our range.

Step. 2 Calculation of range.

See the interval of [-8,-6),

in this interval the value of f(x) goes from $(0,\infty )$.

Similarly see the interval of $(-6,-4)$,

in this interval the value of f(x) goes from $(-\infty ,2)$.

With the help of only these two intervals we can take union of these intervals and we get

$(-\infty ,2)\cup (0,\infty )=(-\infty ,\infty )$.

Hence, the range of the function is R.