Name _________________________________ Period _____ Date ________________
College Algebra
Chapter 2
Functions and Their Graphs
TEST RETAKE
A calculator MAY be used on this test. Show all work and reasoning to receive full credit.
7) Consider the function 𝑓(𝑥) = 3𝑥 2 − 10𝑥 − 8 .
(a) Determine the value(s) of x so that f (x) = – 11. Write your answer as a point(s) on the graph. (4 points)
(b) Determine all 𝑥 − 𝑖𝑛𝑡𝑒𝑟𝑐𝑒𝑝𝑡𝑠 of f(x). Write your answer(s) as point(s) on the graph. (4 points)
(c) Determine the 𝑦 − 𝑖𝑛𝑡𝑒𝑟𝑐𝑒𝑝𝑡 of f(x). Write your answers as a point on the graph. (2 points)
8) Determine and simplify the difference quotient,
f ( x  h)  f ( x)
, for the function f ( x)  4 x 2  6 x  9 .(4 points)
h
9) For 𝑓(𝑥) = 5𝑥 2 − 2𝑥 − 4 and 𝑔(𝑥) = 8𝑥 2 − 11, determine the following and simplify fully. (3 points each)
(a) f  g
(b) f  g
(c) 𝑓(4 + 𝑥)
10) Consider the function f ( x)  2 x3  3x2  7 .
(a) Determine the average rate of change as x changes from -5 to 3. (4 points)
(b) Determine any local maxima and local minima. (2 points)
11) Given the function 𝑓(𝑥) = 4𝑥 2 − 𝑥, write an equation of the secant line containing the points  1, f (1) 
and  3, f (3)  . (4 points)
12) A marketing firm wishes to find a function that relates the sales S of a product and A, the amount spent on
advertising the product. The data are obtained from past experience. Advertising ad sales are measured in
thousands of dollars:
Advertising Expenditures (A)
Sales (s)
20 22 22.5
335 339 338
24
343
24
341
27
350
28.3
351
(a) Determine the best-fit linear function for the data (round answers to the nearest thousandths). (2points)
(b) Use the linear function to predict the number of sales if advertising expenditures are $25,000. (2 points)
13) A farmer has 2000 yards of fencing to enclose a rectangular field. One side will be against a river, and will
therefore not need any fencing. The length of the field is represented by the side parallel to the river.
(a) Draw a diagram. (1 points)
(b) Express the area A of the field as a
function of the length l. (3points)
(c) What length will maximize the area
of the garden? (2 points)
(d) What width will maximize the area
of the garden? (2 points)
(e) What is the maximum possible area? (2 points)
.