Slide 3 - 1Copyright © 2009 Pearson Education, Inc.

Active Learning Lecture SlidesFor use with Classroom Response Systems

© 2009 Pearson Education, Inc.All rights reserved.

Chapter 3Functions and Their Graphs

Slide 3 - 2Copyright © 2009 Pearson Education, Inc.

Determine whether the relation represents a function. If it is, state the domain and range.

{(–3, 13), (–2, 8), (0, 4), (2, 8), (4, 20)}

a. FunctionDomain: {–3, –2, 0, 2, 4}Range: {13, 8, 4, 20}

b. FunctionDomain: {–3, –2, 0, 2, 4}Range: {13, 8, 4, 20}

c. Not a function

Slide 3 - 3Copyright © 2009 Pearson Education, Inc.

Determine whether the relation represents a function. If it is, state the domain and range.

{(–3, 13), (–2, 8), (0, 4), (2, 8), (4, 20)}

a. FunctionDomain: {–3, –2, 0, 2, 4}Range: {13, 8, 4, 20}

b. FunctionDomain: {–3, –2, 0, 2, 4}Range: {13, 8, 4, 20}

c. Not a function

Slide 3 - 4Copyright © 2009 Pearson Education, Inc.

Determine whether the equation defines y as a function of x.

a. Function

b. Not a function

y

3x 1

x 2

Slide 3 - 5Copyright © 2009 Pearson Education, Inc.

Determine whether the equation defines y as a function of x.

a. Function

b. Not a function

y

3x 1

x 2

Slide 3 - 6Copyright © 2009 Pearson Education, Inc.

Find f (–x) when

a.

b.

c.

d.

f x 3x2 4x 3.

3x2 4x 3

3x2 4x 3

3x2 4x 3

3x2 4x 3

Slide 3 - 7Copyright © 2009 Pearson Education, Inc.

Find f (–x) when

a.

b.

c.

d.

f x 3x2 4x 3.

3x2 4x 3

3x2 4x 3

3x2 4x 3

3x2 4x 3

Slide 3 - 8Copyright © 2009 Pearson Education, Inc.

Find the domain of the function.

a. All real numbers

b.

c.

d.

h x x 4

x3 49x

x x 4

x x 0

x x 7,0,7

Slide 3 - 9Copyright © 2009 Pearson Education, Inc.

Find the domain of the function.

a. All real numbers

b.

c.

d.

h x x 4

x3 49x

x x 4

x x 0

x x 7,0,7

Slide 3 - 10Copyright © 2009 Pearson Education, Inc.

Given

a.

b.

c.

d.

f x 6 x

f g x x2 18; x x 18

g x x 3,

find f • g and state its domain.

and

f g x 6 x x 3 ; x x 0

f g x 6 x x 3 ; x x 3, x 6

f g x 6 x x 3 ; x 3 x 6

Slide 3 - 11Copyright © 2009 Pearson Education, Inc.

Given

a.

b.

c.

d.

f x 6 x

f g x x2 18; x x 18

g x x 3,

find f • g and state its domain.

and

f g x 6 x x 3 ; x x 0

f g x 6 x x 3 ; x x 3, x 6

f g x 6 x x 3 ; x 3 x 6

Slide 3 - 12Copyright © 2009 Pearson Education, Inc.

Given

a.

b.

c.

d.

f x 9x 7

2x 9

f g x 11x 7

2x 9; x x

9

2, x

7

11

g x 2x

2x 9,

find f + g and state its domain.

and

f g x 7x 7

2x 9; x x

9

2

f g x 11x 7

2x 9; x x

9

2

f g x 11x 7

2x 9; x x 0

Slide 3 - 13Copyright © 2009 Pearson Education, Inc.

Given

a.

b.

c.

d.

f x 9x 7

2x 9

f g x 11x 7

2x 9; x x

9

2, x

7

11

g x 2x

2x 9,

find f + g and state its domain.

and

f g x 7x 7

2x 9; x x

9

2

f g x 11x 7

2x 9; x x

9

2

f g x 11x 7

2x 9; x x 0

Slide 3 - 14Copyright © 2009 Pearson Education, Inc.

Find and simplify the difference quotient of

a. 2x + h + 5

b.

c. 2x + h – 7

d. 1

f x x2 5x 7,

f x h f x h

, h 0.

2x2 2x 2xh h2 h 14

h

Slide 3 - 15Copyright © 2009 Pearson Education, Inc.

Find and simplify the difference quotient of

a. 2x + h + 5

b.

c. 2x + h – 7

d. 1

f x x2 5x 7,

f x h f x h

, h 0.

2x2 2x 2xh h2 h 14

h

Slide 3 - 16Copyright © 2009 Pearson Education, Inc.

Determine whether the graph is that of a function. If it is, state the domain, range, intercepts and symmetry.

a. Function; D:{x|x ≥ –2}R: {y|y ≤ 0}Int: (–2, 0), 0, –2), (2, 0)Sym: none

c. Function; D: all realsR: all realsInt: (–2, 0), 0, –2), (2, 0)Sym: none

b. Function; D:{x|x ≥ –2}R: {y|y ≤ 0}Int: (–2, 0), 0, –2), (2, 0)Sym: none

d. Not a function

Slide 3 - 17Copyright © 2009 Pearson Education, Inc.

Determine whether the graph is that of a function. If it is, state the domain, range, intercepts and symmetry.

a. Function; D:{x|x ≥ –2}R: {y|y ≤ 0}Int: (–2, 0), 0, –2), (2, 0)Sym: none

c. Function; D: all realsR: all realsInt: (–2, 0), 0, –2), (2, 0)Sym: none

b. Function; D:{x|x ≥ –2}R: {y|y ≤ 0}Int: (–2, 0), 0, –2), (2, 0)Sym: none

d. Not a function

Slide 3 - 18Copyright © 2009 Pearson Education, Inc.

Here is the graph of f. For what numbers x is f (x) > 0?

a. [–10, –6), (7, 10)

b. (–6, 7)

c. (–6, ∞)

d. (–∞, –6)

Slide 3 - 19Copyright © 2009 Pearson Education, Inc.

Here is the graph of f. For what numbers x is f (x) > 0?

a. [–10, –6), (7, 10)

b. (–6, 7)

c. (–6, ∞)

d. (–∞, –6)

Slide 3 - 20Copyright © 2009 Pearson Education, Inc.

The graph of a function is given. Decide if it is even, odd, or neither.

a. even

b. odd

c. neither

Slide 3 - 21Copyright © 2009 Pearson Education, Inc.

The graph of a function is given. Decide if it is even, odd, or neither.

a. even

b. odd

c. neither

Slide 3 - 22Copyright © 2009 Pearson Education, Inc.

Determine algebraically whether the function is even, odd, or neither.

a. even

b. odd

c. neither

f x 2x

x

Slide 3 - 23Copyright © 2009 Pearson Education, Inc.

Determine algebraically whether the function is even, odd, or neither.

a. even

b. odd

c. neither

f x 2x

x

Slide 3 - 24Copyright © 2009 Pearson Education, Inc.

Determine whether the function is increasing, decreasing, or constant on the interval (–∞, –8).

a. increasing

b. decreasing

c. constant

Slide 3 - 25Copyright © 2009 Pearson Education, Inc.

Determine whether the function is increasing, decreasing, or constant on the interval (–∞, –8).

a. increasing

b. decreasing

c. constant

Slide 3 - 26Copyright © 2009 Pearson Education, Inc.

Find the values for which f has local maxima and give the local maxima value.

a. at x = 5 loc. max. is –8; at x = 3.9, it is 2

b.at x = –8 loc. max. is 5; at x = 2.2, it is 3.9

c. at x = –3.3 loc. max. is –2.5; at x = –2.5, it is 5

d.at x = –2.5 loc. max. is –3.3; at x = 5, it is –2.5

Slide 3 - 27Copyright © 2009 Pearson Education, Inc.

Find the values for which f has local maxima and give the local maxima value.

a. at x = 5 loc. max. is –8; at x = 3.9, it is 2

b.at x = –8 loc. max. is 5; at x = 2.2, it is 3.9

c. at x = –3.3 loc. max. is –2.5; at x = –2.5, it is 5

d.at x = –2.5 loc. max. is –3.3; at x = 5, it is –2.5

Slide 3 - 28Copyright © 2009 Pearson Education, Inc.

Use a graphing utility to approximate any local maxima and local minima and where the graph is increasing and decreasing on the given interval.

a. loc max at (2, –1) loc min at (0, 3) incr on (–1, 0) & (2, 3)decr on (0, 2)

c. loc max at (0, 3)loc min at (2, –1)incr on (0, 2) decr on (–1, 0) & (2, 3)

f x x3 3x2 3; 1,3

b. loc max at (0, 3)loc min at (2, –1)incr on (–1, 0) & (2, 3)decr on (0, 2)

d. loc max at (2, –1) loc min at (0, 3)incr on (–1, 0)decr on (0, 2)

Slide 3 - 29Copyright © 2009 Pearson Education, Inc.

Use a graphing utility to approximate any local maxima and local minima and where the graph is increasing and decreasing on the given interval.

a. loc max at (2, –1) loc min at (0, 3) incr on (–1, 0) & (2, 3)decr on (0, 2)

c. loc max at (0, 3)loc min at (2, –1)incr on (0, 2) decr on (–1, 0) & (2, 3)

f x x3 3x2 3; 1,3

b. loc max at (0, 3)loc min at (2, –1)incr on (–1, 0) & (2, 3)decr on (0, 2)

d. loc max at (2, –1) loc min at (0, 3)incr on (–1, 0)decr on (0, 2)

Slide 3 - 30Copyright © 2009 Pearson Education, Inc.

Find the average rate of change for the function

a. –2

b.

c. –28

d.

from 1 to 5. f x 2x 1

1

2

1

6

Slide 3 - 31Copyright © 2009 Pearson Education, Inc.

Find the average rate of change for the function

a. –2

b.

c. –28

d.

from 1 to 5. f x 2x 1

1

2

1

6

Slide 3 - 32Copyright © 2009 Pearson Education, Inc.

Graph

a. b.

c. d.

f x x 5 if x 1

2 if x 1

Slide 3 - 33Copyright © 2009 Pearson Education, Inc.

Graph

a. b.

c. d.

f x x 5 if x 1

2 if x 1

Slide 3 - 34Copyright © 2009 Pearson Education, Inc.

Match the correct function to the graph.

a.

b.

c.

d.

y x 1

y x

y x 1

y x 1

Slide 3 - 35Copyright © 2009 Pearson Education, Inc.

Match the correct function to the graph.

a.

b.

c.

d.

y x 1

y x

y x 1

y x 1

Slide 3 - 36Copyright © 2009 Pearson Education, Inc.

Write an equation that results in the absolute value function, shifted 6 units upward.

a.

b.

c.

d.

y x 6

y x 6

y x 6

y x 6

Slide 3 - 37Copyright © 2009 Pearson Education, Inc.

Write an equation that results in the absolute value function, shifted 6 units upward.

a.

b.

c.

d.

y x 6

y x 6

y x 6

y x 6

Slide 3 - 38Copyright © 2009 Pearson Education, Inc.

Graph

a. b.

c. d.

y 1

4x .

Slide 3 - 39Copyright © 2009 Pearson Education, Inc.

Graph

a. b.

c. d.

y 1

4x .

Slide 3 - 40Copyright © 2009 Pearson Education, Inc.

Graph

a. b.

c. d.

f x x

Slide 3 - 41Copyright © 2009 Pearson Education, Inc.

Graph

a. b.

c. d.

f x x

Slide 3 - 42Copyright © 2009 Pearson Education, Inc.

The figure shows a rectangle inscribed in an isosceles right triangle whose hypotenuse is 6 units long. Express the area A of the rectangle in terms of x.

a. b.

c. d.

A x 2x 3 x A x x 3 x

A x 2x2A x 2x x 3

Slide 3 - 43Copyright © 2009 Pearson Education, Inc.

The figure shows a rectangle inscribed in an isosceles right triangle whose hypotenuse is 6 units long. Express the area A of the rectangle in terms of x.

a. b.

c. d.

A x 2x 3 x A x x 3 x

A x 2x2A x 2x x 3

Slide 3 - 44Copyright © 2009 Pearson Education, Inc.

A box with an open top is to be constructed from a rectangular piece of cardboard with dimensions 15 inches by 30 inches by cutting out equal squares of sides x at each corner and then folding up the sides.

a.

b.

c.

d.

V x 15 2x 30 2x V x x 15 x 30 x

V x x 15 2x 30 2x

Express the volume V of the box as a function of x.

V x 15 x 30 x

Slide 3 - 45Copyright © 2009 Pearson Education, Inc.

A box with an open top is to be constructed from a rectangular piece of cardboard with dimensions 15 inches by 30 inches by cutting out equal squares of sides x at each corner and then folding up the sides.

a.

b.

c.

d.

V x 15 2x 30 2x V x x 15 x 30 x

V x x 15 2x 30 2x

Express the volume V of the box as a function of x.

V x 15 x 30 x