Questions: Consider the following piecewise function: f(x) = -x^2 - 5x + 4 if x ≤ -2 9x - 8 if x > -2 Evaluate (-4), (2), and (1).

Transcript text: Consider the following piecewise function: \[ f(x)=\left\{\begin{array}{ll} -x^{2}-5 x+4 & x \leq-2 \\ 9 x-8 & x>-2 \end{array}\right. \] Evaluate $(-4),(2)$, and ( $(1)$.

Solution

Solution Steps

Step 1: Evaluate $ f(-4) $

For $ x = -4 $, we use the first piece of the piecewise function since $ -4 \leq -2 $.

\[ f(x) = -x^2 - 5x + 4 \]

Substitute $ x = -4 $:

\[ f(-4) = -(-4)^2 - 5(-4) + 4 = -16 + 20 + 4 = 8 \]

Step 2: Evaluate $ f(2) $

For $ x = 2 $, we use the second piece of the piecewise function since $ 2 > -2 $.

\[ f(x) = 9x - 8 \]

Substitute $ x = 2 $:

\[ f(2) = 9(2) - 8 = 18 - 8 = 10 \]

Step 3: Evaluate $ f(1) $

For $ x = 1 $, we use the second piece of the piecewise function since $ 1 > -2 $.

\[ f(x) = 9x - 8 \]

Substitute $ x = 1 $:

\[ f(1) = 9(1) - 8 = 9 - 8 = 1 \]

Final Answer

\[ \boxed{f(-4) = 8} \] \[ \boxed{f(2) = 10} \] \[ \boxed{f(1) = 1} \]

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