Question

evaluating functions
given the function $f(x) = \frac{-5x + 7}{x + 1}$. calculate the following values:
note: round the answer to two decimal places as needed. if the output does not exist, enter dne
$f(-2) = \square$
$f(-1) = \square$
$f(0) = \square$
$f(1) = \square$
$f(2) = \square$
check answer

Explanation:

Step1: Calculate \( f(-2) \)

Substitute \( x = -2 \) into \( f(x)=\frac{-5x + 7}{x + 1} \).
\( f(-2)=\frac{-5(-2)+7}{-2 + 1}=\frac{10 + 7}{-1}=\frac{17}{-1}=-17 \)

Step2: Calculate \( f(-1) \)

Substitute \( x = -1 \) into \( f(x) \). The denominator becomes \( -1 + 1 = 0 \), so the function is undefined here. Thus, \( f(-1)=DNE \)

Step3: Calculate \( f(0) \)

Substitute \( x = 0 \) into \( f(x) \).
\( f(0)=\frac{-5(0)+7}{0 + 1}=\frac{0 + 7}{1}=7 \)

Step4: Calculate \( f(1) \)

Substitute \( x = 1 \) into \( f(x) \).
\( f(1)=\frac{-5(1)+7}{1 + 1}=\frac{-5 + 7}{2}=\frac{2}{2}=1 \)

Step5: Calculate \( f(2) \)

Substitute \( x = 2 \) into \( f(x) \).
\( f(2)=\frac{-5(2)+7}{2 + 1}=\frac{-10 + 7}{3}=\frac{-3}{3}=-1 \)

Answer:

\( f(-2)=-17 \)
\( f(-1)=DNE \)
\( f(0)=7 \)
\( f(1)=1 \)
\( f(2)=-1 \)