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Math  /  Algebra

QuestionQuestion 26 of
Evaluate the piecewise function at the given values of the independent variable. g(x)={x+3 if x≥−3−(x+3) if x<−3g(x)=\left\{\begin{array}{ll} x+3 & \text { if } x \geq-3 \\ -(x+3) & \text { if } x<-3 \end{array}\right. a. g(0)g(0) b. g(−6)g(-6) c. g(−3)g(-3) a. g(0)=g(0)= □\square b. g(−6)=g(-6)= □\square c. g(−3)=g(-3)= □\square

Studdy Solution

STEP 1

1. We are given a piecewise function g(x) g(x) .
2. The function has two cases: - g(x)=x+3 g(x) = x + 3 if x≥−3 x \geq -3 - g(x)=−(x+3) g(x) = -(x + 3) if x<−3 x < -3
3. We need to evaluate the function at specific values: g(0) g(0) , g(−6) g(-6) , and g(−3) g(-3) .

STEP 2

1. Evaluate g(0) g(0) using the appropriate case of the piecewise function.
2. Evaluate g(−6) g(-6) using the appropriate case of the piecewise function.
3. Evaluate g(−3) g(-3) using the appropriate case of the piecewise function.

STEP 3

Determine which case of the piecewise function to use for g(0) g(0) .
Since 0≥−3 0 \geq -3 , use the case g(x)=x+3 g(x) = x + 3 .

STEP 4

Substitute x=0 x = 0 into the equation g(x)=x+3 g(x) = x + 3 :
g(0)=0+3 g(0) = 0 + 3 g(0)=3 g(0) = 3

STEP 5

Determine which case of the piecewise function to use for g(−6) g(-6) .
Since −6<−3 -6 < -3 , use the case g(x)=−(x+3) g(x) = -(x + 3) .

STEP 6

Substitute x=−6 x = -6 into the equation g(x)=−(x+3) g(x) = -(x + 3) :
g(−6)=−(−6+3) g(-6) = -(-6 + 3) g(−6)=−(−3) g(-6) = -(-3) g(−6)=3 g(-6) = 3

STEP 7

Determine which case of the piecewise function to use for g(−3) g(-3) .
Since −3≥−3 -3 \geq -3 , use the case g(x)=x+3 g(x) = x + 3 .

STEP 8

Substitute x=−3 x = -3 into the equation g(x)=x+3 g(x) = x + 3 :
g(−3)=−3+3 g(-3) = -3 + 3 g(−3)=0 g(-3) = 0
The evaluated values are:
a. g(0)=3 g(0) = \boxed{3}
b. g(−6)=3 g(-6) = \boxed{3}
c. g(−3)=0 g(-3) = \boxed{0}

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