Question

1. use the graph of the piecewise function to evaluate the function:
2. $f(-1)$
3. $f(0)$
4. $f(-3)$
5. $f(-2)$
6. $f(1)$

Explanation:

Step1: Find \( f(-1) \)

Locate \( x = -1 \) on the graph. The \( y - \)value at \( x=-1 \) is \( 1 \).

Step2: Find \( f(0) \)

Locate \( x = 0 \) on the graph. The \( y - \)value at \( x = 0 \) is \( 0 \).

Step3: Find \( f(-3) \)

Locate \( x=-3 \) on the graph. The \( y - \)value at \( x=-3 \) is \( 1 \).

Step4: Find \( f(-2) \)

Locate \( x=-2 \) on the graph. The \( y - \)value at \( x=-2 \) is undefined (open - circle), but if we consider the left - hand side (since for \( x\lt - 2\) the function is a horizontal line), we note that the function value for \( x\lt - 2\) is \( 1 \).

Step5: Find \( f(1) \)

Locate \( x = 1 \) on the graph. The \( y - \)value at \( x = 1 \) is \( 3 \).

Answer:

1. a. \(1\)
2. c. \(0\)
3. a. \(1\)
4. a. \(1\) (assuming the left - hand limit as the function is not defined at \(x = - 2\) in the proper sense, but if we consider the piece for \(x\lt - 2\))
5. e. \(3\)