Pre Calc Checkup 3
Name:
Date:
Graded Assignment
Checkup: Graphing Polynomial Functions
Answer the following questions using what you've learned from this unit. Write your responses in the space provided, and turn the assignment in to your instructor.
For problems 1 – 5, state the x- and y-intercepts for each function.
1.
x-intercept: (0, 0), (-4, 0), (0, 0)
y-intercept: (0, 0)
2.
x-intercept: (1, 0) (0, 0) (-4, 0)
y-intercept: (0, 4)
3.
x-intercept: (-1, 0) (0, 0) (0, 0)
y-intercept: (0, 0)
4.
x-intercept: (0, 0) (0, 0) (-25, 0)
y-intercept: (0, 0)
5.
x-intercept: (5, 0) (0, 0) (3, 0)
y-intercept: (0, -15)
For problems 6 – 10, describe the end behavior for each of the functions by writing a limit expression.
6.
lim f(x) = (infinity) x -> (infinity)
7.
lim f(x) = - (infinity) x -> (infinity)
8.
lim f(x) = - (infinity) x -> (infinity)
9.
lim f(x) = (infinity) x -> (infinity)
10. lim f(x) = - (infinity) x -> (infinity)
For problems 11 – 13, use the graphs to state the zeros for each polynomial function. State the multiplicity of any roots if the multiplicity is 2 or higher.
11.
Zeros: x = 0, x = 2
Multiplicity of 0 is 2.
12.
Zeros: x = -2, x = 2
Multiplicity of 2 is 2.
13.
Zeros: x = -0.5, x = 0, x = 0.5
No multiplicity higher than 1.
For problems 14 – 16, identify the extrema for each function. Classify each as a relative (local) or absolute (global) maximum or minimum value.
14.
Relative Max: 15, occurring when x = 0
Absolute Max: None
Relative Min: -1, occurring when x = 2
Absolute Min: None
15.
Relative Max: 9.4, occurring when x = 2.2
Absolute Max: None
Relative Min: -4.16, occurring when x = 0.3
Absolute Min: None
16.
Relative Max: 7.3, occurring when x = 3.19
Absolute Max: None
Relative Min: -3.6, occurring when x = 1.25
Absolute Min: None
For problems 17 – 20, sketch a graph of each function.
17.
18.
19.
20.
Date:
Graded Assignment
Checkup: Graphing Polynomial Functions
Answer the following questions using what you've learned from this unit. Write your responses in the space provided, and turn the assignment in to your instructor.
For problems 1 – 5, state the x- and y-intercepts for each function.
1.
x-intercept: (0, 0), (-4, 0), (0, 0)
y-intercept: (0, 0)
2.
x-intercept: (1, 0) (0, 0) (-4, 0)
y-intercept: (0, 4)
3.
x-intercept: (-1, 0) (0, 0) (0, 0)
y-intercept: (0, 0)
4.
x-intercept: (0, 0) (0, 0) (-25, 0)
y-intercept: (0, 0)
5.
x-intercept: (5, 0) (0, 0) (3, 0)
y-intercept: (0, -15)
For problems 6 – 10, describe the end behavior for each of the functions by writing a limit expression.
6.
lim f(x) = (infinity) x -> (infinity)
7.
lim f(x) = - (infinity) x -> (infinity)
8.
lim f(x) = - (infinity) x -> (infinity)
9.
lim f(x) = (infinity) x -> (infinity)
10. lim f(x) = - (infinity) x -> (infinity)
For problems 11 – 13, use the graphs to state the zeros for each polynomial function. State the multiplicity of any roots if the multiplicity is 2 or higher.
11.
Zeros: x = 0, x = 2
Multiplicity of 0 is 2.
12.
Zeros: x = -2, x = 2
Multiplicity of 2 is 2.
13.
Zeros: x = -0.5, x = 0, x = 0.5
No multiplicity higher than 1.
For problems 14 – 16, identify the extrema for each function. Classify each as a relative (local) or absolute (global) maximum or minimum value.
14.
Relative Max: 15, occurring when x = 0
Absolute Max: None
Relative Min: -1, occurring when x = 2
Absolute Min: None
15.
Relative Max: 9.4, occurring when x = 2.2
Absolute Max: None
Relative Min: -4.16, occurring when x = 0.3
Absolute Min: None
16.
Relative Max: 7.3, occurring when x = 3.19
Absolute Max: None
Relative Min: -3.6, occurring when x = 1.25
Absolute Min: None
For problems 17 – 20, sketch a graph of each function.
17.
18.
19.
20.