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Math  /  Algebra

QuestionFind f(−3)f(-3) for this piecewise-defined function. f(x)={73x−1 if x≤0x+8 if x>0f(x)=\left\{\begin{array}{ll} \frac{7}{3} x-1 & \text { if } x \leq 0 \\ x+8 & \text { if } x>0 \end{array}\right.
Write your answer as an integer or as a fraction simplest form. f(−3)=f(-3)=

Studdy Solution

STEP 1

1. We are given a piecewise-defined function: $ f(x) = \begin{cases} \frac{7}{3}x - 1 & \text{if } x \leq 0 \\ x + 8 & \text{if } x > 0 \end{cases} \]
2. We need to find \( f(-3) \).

STEP 2

1. Determine which piece of the piecewise function to use for x=−3 x = -3 .
2. Substitute x=−3 x = -3 into the appropriate piece of the function.
3. Simplify the expression to find f(−3) f(-3) .

STEP 3

Determine which piece of the function to use for x=−3 x = -3 .
Since −3≤0 -3 \leq 0 , we use the first piece of the function: f(x)=73x−1 f(x) = \frac{7}{3}x - 1

STEP 4

Substitute x=−3 x = -3 into the chosen piece of the function:
f(−3)=73(−3)−1 f(-3) = \frac{7}{3}(-3) - 1

STEP 5

Simplify the expression:
f(−3)=7×(−3)3−1 f(-3) = \frac{7 \times (-3)}{3} - 1 f(−3)=−213−1 f(-3) = \frac{-21}{3} - 1 f(−3)=−7−1 f(-3) = -7 - 1 f(−3)=−8 f(-3) = -8
The value of f(−3) f(-3) is:
−8 \boxed{-8}

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