Slide Copyright © 2009 Pearson Education, Inc. Active Learning Lecture Slides For use with Classroom Response Systems © 2009 Pearson Education, Inc. All rights reserved. Chapter 3 Functions and Their Graphs

Slide Copyright © 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.Function Domain: {–3, –2, 0, 2, 4} Range: {13, 8, 4, 20} b.Function Domain: {–3, –2, 0, 2, 4} Range: {13, 8, 4, 20} c.Not a function

Slide Copyright © 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.Function Domain: {–3, –2, 0, 2, 4} Range: {13, 8, 4, 20} b.Function Domain: {–3, –2, 0, 2, 4} Range: {13, 8, 4, 20} c.Not a function

Slide Copyright © 2009 Pearson Education, Inc. Determine whether the equation defines y as a function of x. a.Function b.Not a function

Slide Copyright © 2009 Pearson Education, Inc. Determine whether the equation defines y as a function of x. a.Function b.Not a function

Slide Copyright © 2009 Pearson Education, Inc. Find f (–x) when a. b. c. d.

Slide Copyright © 2009 Pearson Education, Inc. Find f (–x) when a. b. c. d.

Slide Copyright © 2009 Pearson Education, Inc. Find the domain of the function. a. All real numbers b. c. d.

Slide Copyright © 2009 Pearson Education, Inc. Find the domain of the function. a. All real numbers b. c. d.

Slide Copyright © 2009 Pearson Education, Inc. Given a. b. c. d. find f g and state its domain. and

Slide Copyright © 2009 Pearson Education, Inc. Given a. b. c. d. find f g and state its domain. and

Slide Copyright © 2009 Pearson Education, Inc. Given a. b. c. d. find f + g and state its domain. and

Slide Copyright © 2009 Pearson Education, Inc. Given a. b. c. d. find f + g and state its domain. and

Slide Copyright © 2009 Pearson Education, Inc. Find and simplify the difference quotient of a.2x + h + 5 b. c. 2x + h – 7 d.1

Slide Copyright © 2009 Pearson Education, Inc. Find and simplify the difference quotient of a.2x + h + 5 b. c. 2x + h – 7 d.1

Slide Copyright © 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 reals R: all reals Int: (–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 Copyright © 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 reals R: all reals Int: (–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 Copyright © 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 Copyright © 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 Copyright © 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 Copyright © 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 Copyright © 2009 Pearson Education, Inc. Determine algebraically whether the function is even, odd, or neither. a.even b.odd c.neither

Slide Copyright © 2009 Pearson Education, Inc. Determine algebraically whether the function is even, odd, or neither. a.even b.odd c.neither

Slide Copyright © 2009 Pearson Education, Inc. Determine whether the function is increasing, decreasing, or constant on the interval (–∞, –8). a.increasing b.decreasing c.constant

Slide Copyright © 2009 Pearson Education, Inc. Determine whether the function is increasing, decreasing, or constant on the interval (–∞, –8). a.increasing b.decreasing c.constant

Slide Copyright © 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 Copyright © 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 Copyright © 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) 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 Copyright © 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) 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 Copyright © 2009 Pearson Education, Inc. Find the average rate of change for the function a.–2 b. c.–28 d. from 1 to 5.

Slide Copyright © 2009 Pearson Education, Inc. Find the average rate of change for the function a.–2 b. c.–28 d. from 1 to 5.

Slide Copyright © 2009 Pearson Education, Inc. Graph a.b. c.d.

Slide Copyright © 2009 Pearson Education, Inc. Graph a.b. c.d.

Slide Copyright © 2009 Pearson Education, Inc. Match the correct function to the graph. a. b. c. d.

Slide Copyright © 2009 Pearson Education, Inc. Match the correct function to the graph. a. b. c. d.

Slide Copyright © 2009 Pearson Education, Inc. Write an equation that results in the absolute value function, shifted 6 units upward. a. b. c. d.

Slide Copyright © 2009 Pearson Education, Inc. Write an equation that results in the absolute value function, shifted 6 units upward. a. b. c. d.

Slide Copyright © 2009 Pearson Education, Inc. Graph a.b. c.d.

Slide Copyright © 2009 Pearson Education, Inc. Graph a.b. c.d.

Slide Copyright © 2009 Pearson Education, Inc. Graph a.b. c.d.

Slide Copyright © 2009 Pearson Education, Inc. Graph a.b. c.d.

Slide Copyright © 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.

Slide Copyright © 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.

Slide Copyright © 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. Express the volume V of the box as a function of x.

Slide Copyright © 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. Express the volume V of the box as a function of x.