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Find the range of the following piecewise function.

[0,11)
(-4,6]
(0,11]
[-4,6)

Find the range of the following piecewise function. [0,11) (-4,6] (0,11] [-4,6)-example-1

1 Answer

3 votes

Given:

The piecewise function is


f(x)=\begin{cases}x+4 &amp; \text{ if } -4\leq x<3 \\ 2x-1 &amp; \text{ if } 3\leq x<6 \end{cases}

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.

User Jeeyoung
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