Section 3.2 Graphing a Function Page 1 of 20
Example 1:
Sketch the graph of the function ( ) .fx x
=
Solution to Example 1:
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Solutions to examples and exercises on graphing functions. It includes step-by-step solutions for various functions and exercises that require finding the domain, range, and function values. The document also includes exercises for determining if equations define a function and graphing piecewise-defined functions.
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Pre 2010
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Example 1:
Sketch the graph of the function f ( ) x = x.
Solution to Example 1:
Example 2:
2
Sketch the graph of the function f ( ) x = x +1.
Solution to Example 2:
Example 4:
Solution to Example 4:
Example 5:
Example 6:
Solution to Example 6:
Example 7:
Solution to Example 7:
Example 9:
Solution to Example 9:
Exercise Set 3.2: Functions and Graphs
11. The graph of y = g ( x ) is shown below.
(a) Find the domain of the function.
(b) Find the range of the function.
(c) Find the following function values:
g ( โ 2 ); g ( 0 ); g ( 2 ); g ( 3 ); g ( 6 )
(d) Which is greater, g (โ 2 )or g ( 3 )?
12. The graph of y = f ( x )is shown below.
(a) Find the domain of the function.
(b) Find the range of the function.
(c) Find the following function values:
f ( โ 3 ); f (โ 2 ); f (โ 1 ); f ( 1 ); f ( 4 )
(d) Which is smaller, f^ (^0 )or^ f^ (^3 )?
For each of the following functions:
(a) State the domain of the function.
(b) Graph the function.
2
f x = โ^3 x +
3
fx = 2 x โ
15. h ( x )= 3 x โ 5 ,โ 1 โค x < 3
16. h ( x )= โ 2 x ,โ 3 < x โค 2
17. g ( x )= x โ 3
18. g ( x )= x โ 4
19. f ( x )= x โ 3
20. f ( x )= 5 โ x
21. F ( x ) x 4 x
2 = โ
2 Gx = x โ +
3 fx = x +
4 fx = x โ
x
g x
x
h x
Determine whether each of the following equations
defines y as a function of x. (Do not graph.)
27. 3 x โ 5 y = 8
28. 2 x โ 9 = 6 y + 2
2 x + 3 = y
2 x + y =
31. 3 x 2 xy 5 x
4 โ =
4 x โ y =
x
y
f
x
y
g
Exercise Set 3.2: Functions and Graphs
2 2 x + y =
34. 2 y 3 x 8 x
2 2 โ =
3 xy โ y =
36. x โ 3 y = 5
37. x 5 y
3
38. y 7 x
3 =โ
39. y โ 2 = x
40. x + 3 y = 4
Graph the following piecewise-defined functions.
3 ,if 1 5
2 4 ,if 2 1 ( ) x x
x x fx
4 3 ,if 0
2 ,if 3 0 ( )^3
1
x x
x x fx
5 ,if 2
3 ,if 2 ( ) x
x fx
2 ,if 1 3
4 ,if 5 1 ( ) x
x fx
1 ,if 0
4 ,if 0 ( ) 2 x x
x fx
3 ,if 1
3 ,if 1 ()
2
x
x x fx
4 ,if 2
,if 3 2
,if 3
2
x
x x
x x
fx
2 ,if 3
1 ,if 0 3
5 ,if 0
()
2
x x
x
x x
fx