1. Unit 3 Functions and Graphs
PreCalculus 3-R

2. Evaluate the function f (x) = x2 + 6x at f (8).
Evaluate the function at f (6).
f (6) = 28
Review Problems 1

3. Review Problems 2 f (1) = 1, f (3) = 18, f (7) = 50
Evaluate the following piecewise defined function at f (1), f (3), and f (7).
f (1) = 1,
f (3) = 18,
f (7) = 50
Determine whether the equation defines y as a function of x
Yes
Review Problems 2

4. Use the function f (x) = x2 + 1 to evaluate the following expressions and simplify.
f (x + 5) and f (x) + f (5)
For the function , find .
Review Problems 3

5. Review Problems 4 What is the domain of the function

6. Sketch the graph of the piecewise defined function
Review Problems 5

7. Sketch the graph of the piecewise defined function
Review Problems 6

8. Sketch the graph of the piecewise defined function
Review Problems 7

9. Determine whether the equation defines y as a function of x.
Consider a family of functions.
How does the value of c affect the graph?
The graphs are obtained by shifting the graph of upward c units,
Review Problems 8

10. The graph of g is given. Sketch the graph of the function
Review Problems 9

11. Review Problems 10 f (x) = x 2
The function f (x) is reflected in the x-axis and then shifted up 5 units and the graph of g (x) = 5 – x 2 is obtained. What is f (x)?
f (x) = x 2
Review Problems 10

12. The graph of f is given. Sketch the graph of the function y = –f(x) + 3.
Review Problems 11

13. Review Problems 12 Express the function in the form
Find the inverse function of
Review Problems 12

14. Use the given graphs of f and g to evaluate g (f (5)).3
Review Problems 13

15. For find
Find the inverse function of
Review Problems 14

16. Review Problems 15 A function f is given.
 Sketch the graph of f. Use the graph of f to sketch the graph of Find
Review Problems 15

17. Review Problems 16 –5 f –1(x) = x – 8
Assume f is a one-to-one function.
If f (x) = 3 – 6x, find f –1 (33). –5
Use the Property of Inverse Functions to find the inverse function of f(x) = x + 8
f –1(x) = x – 8
Review Problems 16

18. Review Problems 17 Find the inverse function of

19. Review Problems 18 Express the function in the form -2
evaluate f(g(–1)). -2
Review Problems 18

20. Use the given graphs of f and g to evaluate g (f (5))3
Review Problems 19

21. Review Problems 20 Find the domain of
Suppose that g(x) = 5x + 3 and h(x) = 25x2 + 30x Find a function f, such that f(g(x)) = h(x).
f(x) = x
Review Problems 20

22. Review Problems 21 A function f is given
Sketch the graph of f. Use the graph of f to sketch the graph of Find
Review Problems 21

23. Review Problems 22 A one-to-one function is given
Find the inverse of the function. Graph both the function and its inverse on the same screen to verify that the graphs are reflections of each other in the line y=x.
Review Problems 22

24. Review Problems 23 A one-to-one function is given
Find the inverse of the function. Graph both the function and its inverse on the same screen to verify that the graphs are reflections of each other in the line y=x.
Review Problems 23

25. Assume f is a one-to-one function. If f (x) = 3 – 6x, find f –1 (33).-5
Use the Property of Inverse Functions to find the inverse function of f(x) = x + 8.
f –1(x) = x – 8
Review Problems 24

26. Review Problems 25 Find the inverse function of

27. Review Problems 26 x + y – 2 = 0 3x – y – 2 = 0
Find an equation of the line that satisfies the given conditions
Through (-2, 4); slope – 1
y-intercept = - 2; slope 3
x + y – 2 = 0
3x – y – 2 = 0
Review Problems 26

28. Find an equation of the line that satisfies the given conditions
Through (4, 5); parallel to the x-axis
Through (4, 5); parallel to the y-axis
y = 5
x = 4
Review Problems 27

29. Review Problems 28 5x – 2y + 1 = 0 x – y + 6 = 0
Find an equation of the line that satisfies the given conditions
Through (–1, –2); perpendicular to the line x + 5y + 8 = 0
Through (1, 7); parallel to the line passing through (2, 5) and (– 2, 1)
5x – 2y + 1 = 0
x – y + 6 = 0
Review Problems 28

30. A taxi company charges $3
A taxi company charges $3.00 for the first mile (or part of a mile) and 30 cents for each succeeding tenth of a mile (or part). Express the cost C (in dollars) of a ride as a function of the distance x traveled (in miles) for 0 < x < 2
Review Problems 29

31. Answers 3 Yes f (x) = x 2 No f (6) = 28 f (8) = 112 f (1) = 1,
The graphs are obtained by shifting the graph of upward c units,
f (8) = 112
f (6) = 28
f (1) = 1,
f (3) = 18,
f (7) = 50
Yes
f (x) = x 2 3
Answers

32. Answers 3 f(x) = x 2 + 10 –5 f –1(x) = x – 8 -5 -2 f –1(x) = x – 8
x + y – 2 = 0
3x – y – 2 = 0
f(x) = x
y = 5
x = 4
5x – 2y + 1 = 0
x – y + 6 = 0
Answers