2015
Name ___________________________________________
Precalculus with Trig – Review 3.1 to 3.4
1. Determine whether the given function is linear without using a graphing
calculator. If it is linear, determine the average rate of change and write the
equation of the line.
x
f(x)
-1
-2
0
3
1
8
2
13
3
18
2. Suppose 𝑓(𝑥) = 3𝑥 − 5 and 𝑔(𝑥) = −2𝑥 + 10.
a. Solve 𝑓(𝑥) = 0
b. Solve 𝑓(𝑥) < 𝑔(𝑥)
c. Solve 𝑓(𝑥) = 𝑔(𝑥)
d. Solve 𝑓(𝑥) ≥ 𝑔(𝑥)
e. If you were to graph 𝑓(𝑥) and 𝑔(𝑥), describe where on the graph you
would find the solution to 𝑓(𝑥) = 𝑔(𝑥)
3. Use the given the graph of 𝑓(𝑥) to answer the following
a. Solve 𝑓(𝑥) = 1
b. Solve 𝑓(𝑥) ≥ 3
c. Solve 1 < 𝑓(𝑥) < 5
4. Given the graph of 𝑓(𝑥) and 𝑔(𝑥), answer the following:
a. Solve the equation: 𝑓(𝑥) = 𝑔(𝑥)
b. Solve the inequality: 𝑓(𝑥) < 𝑔(𝑥)
5. Suppose that a company has just purchased a new machine for its manufacturing
facility for $120,000. The company chooses to depreciate the machine using the
straight-line method over 10 years.
a. Write a linear model that expresses the book value V of the machine as a
function of x.
b. What is the implied domain of the function found in part a?
c. What is the book value of the machine after 4 years?
d. When will the machine have a book value of $72,000?
6. Suppose the quantity supplied S and the quantity demanded D of cellular
telephones each month are given by the following functions:
𝑆(𝑝) = 60𝑝 − 900
𝐷(𝑝) = −15𝑝 + 2850
Find the equilibrium price.
7. The following data represent the weight (in grams) of a box of raisins and the
number of raisins in the box..
a. Use a graphing utility to draw a scatter diagram
b. Use a graphing utility to find the line of best fit
that models the relation between the weight
of a box and number of raisins in the box
c. Use the linear model to predict the number
of raisins in a box that weighs 42 grams
8. Graph the quadratic function by finding its vertex, axis of symmetry, y-intercepts
and x-intercepts, if any. State the domain and range.
𝑓(𝑥) = 𝑥 2 − 4𝑥 + 6
Vertex: ________________
Axis of Symmetry: ________________
x-intercepts: _________________
y-intercepts: _________________
Domain: ___________________
Range: ___________________
9. Write the quadratic function in vertex form by completing the square. Then
sketch the graph using transformations.
𝑓(𝑥) = 2𝑥 2 + 12𝑥 + 13
10. Write and equation for a parabola in standard form with x-intercepts at -5 and 7
with a vertical stretch by a factor of 2 and a reflection across the x-axis.
11. Write the equation of a parabola in standard form with a vertex at (-1, 2) and
that passes through the point (1, 6).
12. Suppose that 𝑓(𝑥) = 3𝑥 2 − 13𝑥 − 10
a. What are the x-intercepts of f ?
b. Solve 𝑓(𝑥) = −10 for x. What are the point(s) on the graph of f ?
13. The price p (in dollars) and the quantity x sold of a certain product obey the
demand equation
1
𝑝 = − 𝑥 + 150
10
a.
b.
c.
d.
Express the revenue R as a function of x (Remember 𝑅 = 𝑥𝑝)
What is the revenue if 100 units are sold?
What quantity x maximizes revenue? What is the maximum revenue?
What price should the company charge to maximize revenue?
14. A farmer has 40 yards of fencing to enclose a rectangular pen for his pig Sir
Oinks-A-Lot.
a. Express the area A of the rectangle as a function of x, where x is the width
of the rectangle
b. For what value of x is the area the largest.
c. What is the maximum area?
d. Shoot! The farmer changed his mind and wants to build the pig pen up
against his barn, so the farmer does not need fencing on the side along the
barn. Redo parts a through c for his new plan