Question

Find the range of the following piecewise function.

Answer 1

Given:

The piecewise function is

$f(x)=\begin{cases}x+4 & \text{ if } -4\leq x$

To find:

The range of given piecewise function.

Solution:

Range is the set of output values.

Both functions $f(x)=x+4$ and $f(x)=2x-1$ as linear functions.

Starting value of $f(x)=x+4$ is at x=-4 and end value is at x=3.

Starting value: $f(-4)=-4+4=0$

End value: $f(3)=3+4=7$

Starting value of $f(x)=2x-1$ is at x=3 and end value is at x=6.

Starting value: $f(3)=2(3)-1=5$

End value: $f(6)=2(6)-1=11$

Least range value is 0 at x=-4 and 0 is included in the range because -4 is included in the domain.

Largest range value is 11 at x=6 and 11 is not included in the range because 6 is not included in the domain.

So, the range of the given piecewise function is [0,11).

Therefore, the correct option is A.