Fuentes Stewart
08/24/2024 · Middle School
For questions \( 16-19 \), use the fur to find each function value. 16. \( f(-4)-f(1) \) \( -(-4)^{2}+8(-4)-11 \)
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Tutor-Verified Answer
Step-by-step Solution
To find the value of \( f(-4) - f(1) \), we need to substitute the given values into the function \( f(x) \) and then calculate the result.
Given function: \( f(x) = -x^2 + 8x - 11 \)
1. Substitute \( x = -4 \) into the function:
\( f(-4) = -(-4)^2 + 8(-4) - 11 \)
2. Substitute \( x = 1 \) into the function:
\( f(1) = -(1)^2 + 8(1) - 11 \)
3. Calculate the values of \( f(-4) \) and \( f(1) \).
4. Subtract \( f(1) \) from \( f(-4) \) to find the final result.
Let's calculate the values step by step.
Calculate the value by following steps:
- step0: Calculate:
\(-\left(-4\right)^{2}+8\left(-4\right)-11\)
- step1: Multiply the numbers:
\(-\left(-4\right)^{2}-32-11\)
- step2: Evaluate the power:
\(-16-32-11\)
- step3: Subtract the numbers:
\(-59\)
Calculate or simplify the expression \( -(1)^2 + 8(1) - 11 \).
Calculate the value by following steps:
- step0: Calculate:
\(-1^{2}+8\times 1-11\)
- step1: Evaluate the power:
\(-1+8\times 1-11\)
- step2: Multiply:
\(-1+8-11\)
- step3: Calculate:
\(-4\)
Calculate or simplify the expression \( -59 - (-4) \).
Calculate the value by following steps:
- step0: Calculate:
\(-59-\left(-4\right)\)
- step1: Remove the parentheses:
\(-59+4\)
- step2: Add the numbers:
\(-55\)
The value of \( f(-4) - f(1) \) is -55.
Quick Answer
The value of \( f(-4) - f(1) \) is -55.
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