Question

complete the following for the piece - wise - defined function f(x) = {4 if x<1; - 2 if x≥1}. a. find f(-2), f(0), and f(5). b. sketch the graph of y = f(x). c. find the domain of f. d. find the range of f.

Explanation:

Step1: Evaluate f(-2)

Since -2 < 1, use f(x)=4. So f(-2)=4.

Step2: Evaluate f(0)

Since 0 < 1, use f(x)=4. So f(0)=4.

Step3: Evaluate f(5)

Since 5 ≥ 1, use f(x)= - 2. So f(5)= - 2.

Step4: Sketch the graph

For x < 1, the graph is a horizontal line y = 4 (a dashed - line at x = 1 as x is not included in this part). For x ≥ 1, the graph is a horizontal line y=-2 (a solid - line at x = 1 as x is included in this part).

Step5: Find the domain

The domain of a piece - wise function is the set of all real numbers. So the domain is (-∞,∞).

Step6: Find the range

The function takes on two values, 4 and -2. So the range is {-2,4}.

Answer:

a. f(-2)=4, f(0)=4, f(5)= - 2
b. Graph: For x < 1, y = 4 (dashed - line at x = 1), for x ≥ 1, y=-2 (solid - line at x = 1)
c. Domain: (-∞,∞)
d. Range: {-2,4}