Question

for questions 16 - 19, use the functions ( f(x)=dots ) to find each function value.

1. ( f(-4)-f(1) )

( f(-4)= -(-4)^2 + 8\times(-4)-11 )
( f(-4)= -16 - 32 - 11 )
( f(1)= -1^2 + 8\times1 - 11 )
( f(1)= -1 + 8 - 11 )
( f(-4)-f(1)= dots )
17.
18.

Explanation:

First, the full function is inferred as $f(x) = -x^2 + 8x - 11$ from the handwritten work.

Step1: Calculate $f(-4)$

Substitute $x=-4$ into $f(x)$:

$$\begin{align*} f(-4)&=-(-4)^2 + 8(-4) - 11\\ &=-16 - 32 - 11\\ &=-59 \end{align*}$$

Step2: Calculate $f(1)$

Substitute $x=1$ into $f(x)$:

$$\begin{align*} f(1)&=-(1)^2 + 8(1) - 11\\ &=-1 + 8 - 11\\ &=-4 \end{align*}$$

Step3: Compute $f(-4)-f(1)$

Subtract the two results:

$$ f(-4)-f(1)=-59 - (-4) = -59 + 4 $$

Answer:

$-55$