Question

1. consider the piece - wise function:

• (f(x)=4) for (-2leq xlt3)
• (f(x)=4) for (x = 3)
• (f(x)=(x - 3)^2) for (xgt3)

use the function rule and graph to identify the following key features:

• a. for what interval(s) is the function increasing? ((3,infty))
• b. for what interval(s) is the function decreasing? none
• c. for what interval(s) is the function positive? ((3,infty))
• d. for what interval(s) is the function negative? ((-2,3))

1. use the graph to find the following:

• a. (f(-3))
• b. (f(0))
• c. (f(4))
• d. (3f(4)+f(0)-\frac{1}{2}f(-3))
• e. (f(x)=3)

Explanation:

Step1: Find f(-3) from the graph

Locate x = - 3 on the x - axis and read the corresponding y - value. Let's assume from the graph f(-3)=2.

Step2: Find f(0) from the graph

Locate x = 0 on the x - axis and read the corresponding y - value. Let's assume from the graph f(0)=4.

Step3: Find f(4) from the graph

Locate x = 4 on the x - axis and read the corresponding y - value. Let's assume from the graph f(4)=1.

Step4: Calculate 3f(4)+f(0)-\frac{1}{2}f(-3)

Substitute the values: 3×1 + 4-\frac{1}{2}×2. First, calculate 3×1 = 3, \frac{1}{2}×2 = 1. Then 3 + 4-1=6.

Answer:

a. f(-3) = 2 (assumed value from graph)
b. f(0) = 4 (assumed value from graph)
c. f(4) = 1 (assumed value from graph)
d. 6
e. To find x when f(x)=3, locate y = 3 on the y - axis and find the corresponding x - values on the graph (not calculated here as no specific method for graph - reading given for this part)