<img src="https://d5nxst8fruw4z.cloudfront.net/atrk.gif?account=iA1Pi1a8Dy00ym" style="display:none" height="1" width="1" alt="" />
Dismiss
Skip Navigation
Our Terms of Use (click here to view) and Privacy Policy (click here to view) have changed. By continuing to use this site, you are agreeing to our new Terms of Use and Privacy Policy.

2.1: Back in Time?

Difficulty Level: At Grade Created by: CK-12

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. {(0,1),(1,4),(2,7),(3,6)}

B. {(2,2),(1,1),(0,0),(1,3),(2,4)}

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

D. {(2,3),(3,2),(1,4),(4,1)}

Marty flies to Mars, where the acceleration of gravity is 0.375 of what it is on Earth. So with a=12ft/s2, use the distance formula d=12at2 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 {0,1,2,6}.

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 {0,23,6}.

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)=x2. So f(3)=9.

To use the function ability of your graphing calculator, press Y= and enter x22x+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 xvalue.

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

9. For f(x)=x22x+3, find f(4) using the graphing calculator, then by substitution showing your work below.

10. For f(x)=3x2+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?

My Notes/Highlights Having trouble? Report an issue.

Color Highlighted Text Notes
Show More

Image Attributions

Show Hide Details
Description
Subjects:
Grades:
Date Created:
Feb 22, 2012
Last Modified:
Oct 31, 2014
Save or share your relevant files like activites, homework and worksheet.
To add resources, you must be the owner of the section. Click Customize to make your own copy.
Please wait...
Please wait...
Image Detail
Sizes: Medium | Original
 
TI.MAT.ENG.SE.1.Algebra-I.2.1
Here