Questions: Evaluate the piecewise-defined function. f(x)= 4x if x<0 7-x if 0 ≤ x<4 x if x ≥ 4 (a) f(-0.5)= (b) f(0)= (c) f(4)=

Transcript text: Evaluate the piecewise-defined function. \[ f(x)=\left\{\begin{array}{ll} 4 x & \text { if } x<0 \\ 7-x & \text { if } 0 \leq x<4 \\ |x| & \text { if } x \geq 4 \end{array}\right. \] (a) $f(-0.5)=$ $\square$ (b) $f(0)=$ $\square$ (c) $f(4)=$ $\square$

Solution

Solution Steps

To evaluate the piecewise-defined function $ f(x) $ at specific points, we need to determine which condition each point satisfies and then apply the corresponding function rule.

(a) For $ f(-0.5) $, since $ -0.5 < 0 $, we use the rule $ f(x) = 4x $.

(b) For $ f(0) $, since $ 0 \leq x < 4 $, we use the rule $ f(x) = 7 - x $.

Step 1: Evaluate $ f(-0.5) $

For $ f(-0.5) $, since $ -0.5 < 0 $, we use the rule $ f(x) = 4x $: \[ f(-0.5) = 4 \times (-0.5) = -2.0 \]

Step 2: Evaluate $ f(0) $

For $ f(0) $, since $ 0 \leq x < 4 $, we use the rule $ f(x) = 7 - x $: \[ f(0) = 7 - 0 = 7 \]

Step 3: Evaluate $ f(4) $

For $ f(4) $, since $ x \geq 4 $, we use the rule $ f(x) = |x| $: \[ f(4) = |4| = 4 \]