Question

visit www.bigideasmathvideos.com to watch the flipped video instruction for the \try this\ problem(s) below. try this video for extra example 1 - evaluating a piecewise function evaluate the function. \\( f(x)=\

$$\begin{cases}x - 2, & \\text{if } x \\leq 0 \\\\ 2x + 1, & \\text{if } x > 0 \\end{cases}$$

\\) 1. \\( f(-1) \\) 2. \\( f(1) \\)

Explanation:

1. Evaluate \( f(-1) \)

Step1: Determine the applicable function rule

Since \( -1 \leq 0 \), we use the rule \( f(x)=x - 2 \) for \( x\leq0 \).

Step2: Substitute \( x = -1 \) into the rule

Substitute \( x=-1 \) into \( f(x)=x - 2 \), we get \( f(-1)=-1 - 2 \).

Step3: Calculate the result

\( -1-2=-3 \).

Step1: Determine the applicable function rule

Since \( 1>0 \), we use the rule \( f(x)=2x + 1 \) for \( x>0 \).

Step2: Substitute \( x = 1 \) into the rule

Substitute \( x = 1 \) into \( f(x)=2x + 1 \), we get \( f(1)=2(1)+1 \).

Step3: Calculate the result

\( 2(1)+1=2 + 1=3 \).

Answer:

\( f(-1)=-3 \)

2. Evaluate \( f(1) \)