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bazaltina [42]
2 years ago
5

Find the range of the following piecewise function.

Mathematics
1 answer:
Anna11 [10]2 years ago
5 0

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.

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