Math 135 Functions: Examples Worksheet. 1. The constant function: f(x) = c, c R. Domain (, ) Range Intervals of Increase Intervals of Decrease none

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1 Math 135 Functions: Eamples Worksheet 1. The constant function: f() = c, c R. Domain (, ) c} Intervals of Increase Intervals of Decrease Turning Points Local Maima Global Maima = c Global Minima = c 2. The linear function: f() = a + b; a, b R. Domain (, ) b}, a = 0; (, ), a 0., a 0; Intervals of Increase (, ), a > 0. Intervals of Decrease Turning Points Local Maima Global Maima Global Minima, a 0; b, a = 0., a 0; b, a = 0. Universit of Hawai i at Mānoa 62 R Spring

2 Math 135 Functions: Eamples Worksheet 3. The square function: f() = 2. Domain (, ) Intervals of Increase [0, ) Intervals of Decrease (, 0] Turning Points =0 Local Maima = 0 Global Maima Global Minima = 0 4. The cube function: f() = 3. Domain Intervals of Increase (, ) Intervals of Decrease Turning Points Local Maima Global Maima Global Minima Universit of Hawai i at Mānoa 63 R Spring

3 Math 135 Functions: Eamples Worksheet 5. The inverse function: f() = 1. Domain Intervals of Increase Intervals of Decrease (, 0) (0, ) Turning Points Local Maima Global Maima Global Minima 6. The inverse square function: f() = 1 2. Domain (, 0) (0, ) Intervals of Increase Intervals of Decrease Turning Points Local Maima Global Maima Global Minima Universit of Hawai i at Mānoa 64 R Spring

4 Math 135 Functions: Eamples Worksheet 7. The square root function: f() =. Domain [0, ) [0, ) Intervals of Increase Intervals of Decrease Turning Points Local Maima Global Maima Global Minima 8. The cube root function: f() = 3. Domain Intervals of Increase Intervals of Decrease Turning Points Local Maima Global Maima Global Minima Universit of Hawai i at Mānoa 65 R Spring

5 Math 135 Functions: Eamples Worksheet 9. The absolute value function: f() =. Domain Intervals of Increase [0, ) Intervals of Decrease (, 0] Turning Points = 0 Local Maima Global Maima Global Minima Sample Midterm 15 A B C D 20 A B C D 24 A B C D 25 A B C D Sample Final Universit of Hawai i at Mānoa 66 R Spring

6 Math 135 Functions: Eamples Solutions 1. The constant function: f() = c, c R. Domain (, ) c} Intervals of Increase Intervals of Decrease Turning Points Local Maima c, = c c, = c Global Maima c, = c Global Minima c, = c -ais ( 2, c) (1, c) = c Universit of Hawai i at Mānoa 67 R Spring

7 Math 135 Functions: Eamples Solutions 2. The linear function: f() = a + b; a, b R. Domain (, ) b}, a = 0; (, ), a 0., a 0; Intervals of Increase (, ), a > 0., a 0; Intervals of Decrease (, ), a < 0. Turning Points, a 0; Local Maima b, a = 0., a 0; b, a = 0., a 0; Global Maima b, a = 0., a 0; Global Minima b, a = 0., a 0; -ais, a = 0. = (0, 2) (0, 1) ( 1 2, 0) ( 2 3, 0) = Universit of Hawai i at Mānoa 68 R Spring

8 Math 135 Functions: Eamples Solutions 3. The square function: f() = 2. Domain (, ) [0, ) Intervals of Increase [0, ) Intervals of Decrease (, 0] Turning Points = 0 Local Maima = 0 Global Maima Global Minima = 0 -ais (2, 4) = 2 (1, 1) (0, 0) Universit of Hawai i at Mānoa 69 R Spring

9 Math 135 Functions: Eamples Solutions 4. The cube function: f() = 3. Domain (, ) (, ) Intervals of Increase (, ) Intervals of Decrease Turning Points Local Maima Global Maima Global Minima origin = 3 (1, 1) (0, 0) ( 1, 1) Universit of Hawai i at Mānoa 70 R Spring

10 Math 135 Functions: Eamples Solutions 5. The inverse function: f() = 1. Domain (, 0) (0, ) (, 0) (0, ) Intervals of Increase Intervals of Decrease (, 0) (0, ) Turning Points Local Maima Global Maima Global Minima origin = 0 (1, 1) = 0 = 1 ( 1, 1) Universit of Hawai i at Mānoa 71 R Spring

11 Math 135 Functions: Eamples Solutions 6. The inverse square function: f() = 1 2. Domain (, 0) (0, ) (0, ) Intervals of Increase (, 0) Intervals of Decrease (0, ) Turning Points Local Maima Global Maima Global Minima -ais = 0 ( 1, 1) (1, 1) = 0 = 1 2 Universit of Hawai i at Mānoa 72 R Spring

12 Math 135 Functions: Eamples Solutions 7. The square root function: f() =. Domain [0, ) [0, ) Intervals of Increase [0, ) Intervals of Decrease Turning Points Local Maima = 0 Global Maima Global Minima = 0 (4, 2) = (1, 1) (0, 0) Universit of Hawai i at Mānoa 73 R Spring

13 Math 135 Functions: Eamples Solutions 8. The cube root function: f() = 3. Domain (, ) (, ) Intervals of Increase (, ) Intervals of Decrease Turning Points Local Maima Global Maima Global Minima origin (1, 1) = 3 (0, 0) ( 1, 1) Universit of Hawai i at Mānoa 74 R Spring

14 Math 135 Functions: Eamples Solutions 9. The absolute value function: f() =. Domain (, ) [0, ) Intervals of Increase [0, ) Intervals of Decrease (, 0] Turning Points = 0 Local Maima = 0 Global Maima Global Minima = 0 -ais = ( 1, 1) (1, 1) (0, 0) Universit of Hawai i at Mānoa 75 R Spring