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You are reading an older version of this FlexBook® textbook: CK-12 Texas Instruments Algebra I Student Edition Go to the latest version.

This activity is intended to supplement Algebra I, Chapter 1, Lesson 5.

Definition

A function is a relation in which each input is paired with exactly one output.

For every value that goes into a function, the function outputs one unique result.

Problem 1 – Graphical

At time t = 0, Marty is at position d = 2.

1. Can the graph to the right describe Marty’s position as a function of time? Explain.

2. What would have to happen for this graph to occur?

3. Redraw the dashed lines to make the graph a function.

Problem 2 – Set of Ordered Pairs

The first element of each ordered pair is the input value.

4. Which sets below describe a function? Explain why.

A. \left \{(0, 1), (1, 4), (2, 7), (3, 6) \right \}

B. \left \{(-2,2), (-1, 1), (0, 0), (1, 3), (2, 4) \right \}

C. \left \{(3, 2), (3, 4), (5, 6), (7, 8) \right \}

D. \left \{(2, 3), (3, 2), (1, 4), (4, 1) \right \}

Marty flies to Mars, where the acceleration of gravity is 0.375 of what it is on Earth. So with a = 12ft/s^2, use the distance formula d = \frac{1}{2}at^2 to compute the output when given the input.

5. Use the formula to compute d. Give the set or ordered pairs (t, d) when the input t is the set \left \{0, 1, 2, 6 \right \}.

6. Use the formula to compute t. Give the set of ordered pairs (d, t) if the input is d. The input set for d is \left \{0, \frac{2}{3}, 6 \right \}.

7. Which of the two solutions sets from Questions 5 and 6 is a function? Why?

8. From solutions sets above, which is true?

A. d is a function of t

B. t is a function of d

C. both

D. neither

Problem 3 – Function Notation

If f is a function of x this can be written as f(x).

For example, f(x) = x^2. So f(3) = 9.

To use the function ability of your graphing calculator, press Y= and enter x^2 - 2x + 3.

Return to the Home screen.

To enter different values for x and observe what f(x) equals, press VARS, arrow right to the Y-VARS menu, select Function and then choose Y1. Then enter (#), replacing # with the x-value.

Press 2^{nd} [ENTER] to recall the last entry.

9. For f(x) = x^2 - 2x + 3, find f(4) using the graphing calculator, then by substitution showing your work below.

10. For f(x) = 3x^2 + 5x + 3, find f(2) using the graphing calculator, then by substitution showing your work below.

Problem 4 – Function Machine

Run the program MACHINE and select option 1. The program will return an output for the input entered.

11. What is the input for the function f(x) that gives an output of 8.5?

12. What is the unknown function?

Now select option 2.

13. What is the input for the function f(x) that gives an output of 6?

14. What is the unknown function?

Now select option 3.

15. What is the input for the function f(x) that gives an output of 83?

16. What is the unknown function?

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Date Created:

Feb 22, 2012

Last Modified:

Oct 31, 2014
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TI.MAT.ENG.SE.1.Algebra-I.2.1

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