Question

name: christopher perez alvarez date: 10/11/25 block: a2 precalculus analysis of a graph use the graph of f(x) to answer the following questions. 1. what is f(-1)? 2. what is f(4)? 3. where does f(x)=4? 4. f(x) has an absolute maximum value of _ that occurs when x = _? 5. f(x) has an absolute minimum value of _ that occurs when x = _? 6. where does f(x)=0? 7. state the set of x - values where f(x) is increasing? 8. state the set of x - values where f(x) is decreasing? 9. state the domain of f(x) in either set notation or interval notation. 10. state the range of f(x) in either set notation or interval notation.

Explanation:

Step1: Find the y - value at x = - 1

Locate x=-1 on the x - axis and find the corresponding y - value on the graph of f(x).

Step2: Find the y - value at x = 4

Locate x = 4 on the x - axis and find the corresponding y - value on the graph of f(x).

Step3: Find x - values for y = 4

Locate y = 4 on the y - axis and find the x - values where the graph of f(x) intersects the line y = 4.

Step4: Identify absolute maximum

Find the highest point on the graph of f(x) to determine the absolute maximum value and its corresponding x - value.

Step5: Identify absolute minimum

Find the lowest point on the graph of f(x) to determine the absolute minimum value and its corresponding x - value.

Step6: Find x - values for y = 0

Locate y = 0 (the x - axis) and find the x - values where the graph of f(x) intersects the x - axis.

Step7: Determine increasing intervals

Find the intervals on the x - axis where the graph of f(x) is rising.

Step8: Determine decreasing intervals

Find the intervals on the x - axis where the graph of f(x) is falling.

Step9: Find the domain

Determine all the x - values covered by the graph of f(x).

Step10: Find the range

Determine all the y - values covered by the graph of f(x).

Answer:

1. f(-1) = 6
2. f(4) = 2
3. f(x)=4 at x=-3 and x = 2
4. f(x) has an absolute maximum value of 7 that occurs when x=-2
5. f(x) has an absolute minimum value of - 3 that occurs when x = 6
6. f(x)=0 at x=-8,x=-5,x = 7
7. f(x) is increasing on the intervals (-8,-2) and (6,9)
8. f(x) is decreasing on the intervals (-2,6)
9. Domain: [-8,9]
10. Range: [-3,7]