Unit 2 - Functions Review
1. Go to page 76 in your textbook and complete question #10 in the space below.
Find the following for each function:
a) f (-3)
b) f (x + 1)
c) f (2x)
d) –f (x)
e) even, odd, or neither
f) any local maxima or local minima
2. 𝑓(𝑥) = −2𝑥 3 + 6𝑥
3. 𝑓(𝑥) =
Find the domain of each function. Write in correct domain notation.
4. 𝑓(𝑥) = 𝑥 2 + 2
2𝑥
5. ℎ(𝑥) = 𝑥 2 −9
𝑥 2 −1
𝑥+4
6. 𝑔(𝑥) = √1 − 𝑥
7. 𝑓(𝑥) =
3𝑥−2
√2𝑥−4
For the following functions f and g, find the following new functions:
a) f + g
b) f – g
c) 𝑓 ∙ 𝑔
d)
𝑓
𝑔
8. 𝑓(𝑥) = 2𝑥 + 1 𝑎𝑛𝑑 𝑔(𝑥) = 3𝑥 − 2
9. Find the difference quotient off
𝑓(𝑥+ℎ)−𝑓(𝑥)
ℎ
for the function 𝑓(𝑥) = 𝑥 2 − 5𝑥 − 1
10. Let 𝑔(𝑥) = 𝑥 2 − 2. Find the equation of the secant line containing the points
(-1, g(-1)) and (2, g(2)).
11. An administrator at Southern Illinois University want sot find a function that relates a
student’s college grade point average G to the high school grade point average x. She randomly
selects eight students and obtains the following data:
High School
GPA
2.73
2.92
3.45
3.78
2.56
2.98
3.67
3.10
College
GPA
2.43
2.97
3.63
3.81
2.83
2.81
3.45
2.93
a) Does the relation represent a function?
b) Use your graphing calculator to make a scatter plot of the
data.
c) Find the equation for the line of best fit relating the high
school GPA and college GPA. Express this equation using function
notation.
d) Predict a students’ college GPA if her high school GPA is 3.23
12. David has available 400 yards of fencing and wishes to enclose a rectangular area.
a) Draw a diagram, correctly labeling each side.
b) Express the area A as a function of the width x of the rectangle.
c) For what value of x is the area the largest? What will that area be?