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Review for Exam #1 (Practice Problems)
Function Basics (notation, how to evaluate a function, how to read the graph of a function, identify domain and range)
Linear and Quadratic Functions (find equations of, identify intercepts, slopes of lines, vertices of parabolas, applications)
Piecewise Functions (notation, how to evaluate, how to graph, applications)
Transformations (shifting, stretching, reflecting)
2x 5
.
x3
e) h(a-3)
f) the domain of each function
1. Find the following given f ( x) 2 x 2 3x 2 and g ( x) x 5 and h( x)
a) g(14)
b) f(7)
c) h(-2)
2. Determine if S is a function:
a) S = {(1, 2), (2, 3), (4, 5), (1, 3)}
d) f(5a)
b) S = {(-3, 7), (-1, 7), (3, 9), (6, 7), (10, 0)}
3. Determine if the following real world relations are functions:
a) People assigned to their telephone numbers.
b) People assigned to their birthdays.
4. The graph of the left is of y = f(x) and on the right is of y = g(x). Use the graphs to answer the following questions:
a) What are the domains of the functions?
b) What are the ranges of the functions?
c) Find g(2), g(4), g(-2).
d) Find f(2), f(1), f(-2).
e) Find any x values such that f(x) = 2.
f) Find any x values such that g(x) = 2.
g) Find the vertex of the parabola.
h) Find the equation of the parabola.
y
y
x
x
5. Write a symbolic representation (equation) for a function that calculates the given quantity:
a) The number of quarters in x dollars.
b) The number of dollars in x dimes.
c) The monthly long distance bill in dollars for using x minutes of airtime at 10 cents per minute plus a flat fee of $5.
f ( x h) f ( x )
.
h
6. For f ( x) 5x 4 , find f ( x h) and then the difference quotient,
7. Find the equation of a line with slope ½ and a point (4, 5).
8. Find the equation of a line containing the points (1, 4) and (5, 3).
9. In 1998 there were 47 million people worldwide who had been infected with HIV. At that time the infection rate was 5.8
million people per year. Write a function for a linear function f that models the total number of people in millions who were
infected with HIV x years after 1998. Then estimate the number of people who may have been infected by the year 2007.
10. Use the piecewise function defined on the right for a – d:
a) Determine the domain of p.
b) Evaluate p(-2), p(3), p(0), and p(-1).
c) Graph p
d) Is p continuous on its domain?
3 if 4 x 1
p( x) x 2 if 1 x 2
1x
if 2 x 6
2
11. Write a piecewise function for a monthly electric bill based on the following description. The customer is charged a flat
fee of $30 for the use of 400 kilowatthours or less and 6 cents for each kilowatt hour used over 400 kilowatt hours.
12. Find the equation corresponding to each of the following graphs:
y
x
y
x
y
x
13. Find the vertex and write the quadratic function in vertex form: a) f ( x) x 2 10 x 7
b) g ( x) 2 x 2 4 x 5
14. Find the x- and y-intercepts of f ( x) 3x 2 5 x 2 .
15. One day in November, the town of Coldwater was hit by a sudden winter storm that caused temperatures to plummet.
During the storm, the temperature (in degrees Fahrenheit) could be modeled in the first 12 hours by the function
T (h) 0.8h 2 16 h 60 , where h is the number of hours since the storm began.
a) What was the temperature as the storm began? What was the temperature 2 hours into the storm?
b) When was the temperature 0˚F? When was the temperature -10˚F?
c) What was the coldest temperature recorded during this storm?
16. A bagel factory finds that its profit is related to the number of bagels produced as given in the function,
f ( x) x 2 70 x where x is the number of hundreds of bagels produced daily and y is the daily profit in dollars. How many
bagels must be produced daily to maximize the profit? What would the maximum profit be?
17. Use the graph of y f (x) to sketch a graph of each equation:
a) y = f(x) + 2
b) y = f(x – 3)
c) y = f(-x)
d) y = f(x + 1) – 2
e) y = 3f(x)
f) y = f(2x)
y
x
18. In words, describe the transformation of the graph f from the one of the very basic functions:
c) f ( x) 2 x 1
b) f ( x) x 5
a) f ( x) ( x 2) 2 3
d) f ( x) 2 x
19. Write the equation of the graph (there have been no horizontal or vertical stretches/shrinks):
y
x
x
y
y
x
20. Given the tables for the following functions f and h; write a table for g and k.
a. Let g ( x) f ( x) 10
x
f(x)
0
-5
5
11
b. Let k ( x) h( x 2)
10
21
15
32
20
47
x
h(x)
-4
5
-2
8
0
10
21. Given the equation 5x 2y 6 , algebraically find
a) the slope
b) y-intercept
c) Use the slope and y-intercept to graph the line.
2
7
4
3
