Pre-Test Unit 3: Functions KEY

[Pages:32]Pre-Test Unit 3: Functions KEY

No calculator necessary. Please do not use a calculator.

Determine if each of the following is a true function based on the equation or table. Explain how you know. (5 pts; 2 pts for answer only)

1.

2 1 0

1

2

4

1

0

1

4

2.

0

0

1

4

9

16

1

2

3

4

Function, each input has only one output

Not a function, some inputs have more than one output

Evaluate the given function using the given value as inputs. (5 pts; 3 pts for computation error only)

3. 3 2

2 8

4. 3

3 6

Answer the following question in complete sentences. (5 pts; partial credit at teacher discretion)

5. Determine if the following describes a true function or not. Explain why or why not.

Input: Age of an author, Output: Amount of money earned Not a true function, two people could be the same age but make different amounts of money.

6. Give an example of a function in words and explain what the input and output are. Answers will vary. Sample: Input a person's social security number and output their age.

Graph the following functions by filling out the / chart using the inputs ( values) that you think are appropriate. (5 pts; 1 pt for appropriate values, 2 pts for correct table, 2 pts for graph following table)

7. 2

values may vary

2 1 0

1

2

6

3

2

3

6

8.

1

values may vary

8 4

0

4

8

1

0

1

2

3

1

Determine whether the following functions are linear or non-linear and explain how you know. (5 pts; 2 pts for correct answer only)

9. Non-linear because of the exponent on

10.

1

Linear because it's in slope-intercept form.

Answer the following question about different types of functions. (5 pts; 3 pts for correct example with incorrect or missing explanation)

11. Give an example of a linear function in equation form and explain how you know it is linear. Answer will vary. Sample: 2 1 because it's in slope-intercept form.

Identify the rate of change, initial value, independent variable, and dependent variable. Then describe what the rate of change and initial value mean in the context of each situation. Finally, give the equation of the line if necessary. (6 pts; 1 pt for each)

12. The amount of money in dollars a farmer gets paid to leave land fallow for a season based on the acres of land he or she owns is modeled by the following function: 300 50.

Rate of Change:_300_______ Initial Value:____50________ Independent Variable:_____ Dependent Variable:______

Contextual Description of Rate of Change

The farmer gets paid $300 per acre left fallow.

Contextual Description of Initial Value

If the farmer leaves no land fallow he gets charged $50. This may be a $50 fee that he pays regardless.

13. The function relating the cost in dollars of entering a carnival to how many tickets you buy is shown by

the following graph:

Rate of Change:__0.5________

Contextual

Contextual

Initial Value:____3_________

Description of Rate of Change

Description of Initial Value

Independent Variable:_____ The carnival charges The carnival charges

Dependent Variable:_______ $0.50 per ticket. EQ of Line:__ 0.5 3____

a $3 entry fee regardless of the number of tickets purchased.

2

Total cost

bought Tell whether the following linear function is increasing, decreasing, or constant. (3 pts; no partial credit)

14.

7

Decreasing

For the following functions tell where they are increasing and where they are decreasing. Then give the max or min of the function. (5 pts; 3 pts for increasing/decreasing, 2 pts for max/min)

15.

3

16. 3 5

Increasing: 3 and 3 Decreasing: 3 3 Local max: 6 Local min: 6

Increasing: 3 Decreasing: 3 Max: 5

3

Mileage in mpg

Use the following graph showing a function modeling the miles per gallon () a car gets in terms of its speed () to answer the questions. (5 pts; partial credit at teacher discretion) 17. What appears to be the best mileage this car will get and at

what speed does it occur? 35 55

18. What are all the possible speeds this car can drive at? 0 110

Speed in mph

Determine which graph matches the story and explain why. (5 pts; 2 pts for correct answer with no explanation) 19. I started to walk to class, but I realized I had forgotten my notebook, so I went back to my locker and then I went quickly at a constant rate to class.

Graph C

Sketch a graph modeling a function for the following situations. (5 pts; partial credit at teacher discretion) 20. A dog is sleeping when he hears the cat "meow" in the next room. He quickly runs to the next room where he slowly walks around looking for the cat. When he doesn't find the cat, he sits down and goes back to sleep. Sketch a graph of a function of the dog's speed in terms of time.

Time 4

Speed

Lesson 3.1

Unit 3 Homework Key

Determine if each of the following is a true function based on the equation or table. Explain how you know.

1.

2 1 0

1

2

4

1

0

1

4

Function, one input gives only one output

2. 25

4

3

0

3

4

3

4

5

4

3

Not a function, one input gives more than one output

3. 5

5 4 1

4

11

0

1

2

3

4

Function, one input gives only one output

4.

5

4

2

0

2

4

4

8

0

8

4

Function, one input gives only one output

5. 100

6. 2 5

8 6

0

6

8

6 8 10 8 6

2

1

0

1

2

1

3

5

7

9

Not a function, one input gives more than one output Function, one input gives only one output

7.

8. 2 1

0 0

1

4

9

25

1

2

3

5

2 1

0

1

2

7

1

1

1

7

Not a function, one input gives more than one output Function, one input gives only one output

9. 9

5

3

3

5

4

0

0

4

Not a function, one input gives more than one output

10.

1

2

0

2

0

4

0

Not a function, one input gives more than one output

11.

4 2

0

2

4

2

1

0

1 2

Function, one input gives only one output

12.

2 1

1

2

1 2

2

1

Function, one input gives only one output

13. Explain how to determine whether or not an

equation models a function. If there is an exponent on the it is not a function.

14. Explain how to determine whether or not a table models a function.

If there is more than one output for an input, it's not.

5

Determine if the following descriptions of relationships represent true functions. Explain why they do or why they do not.

15. Input: Time elapsed, Output: Distance run around the track. Not a function, in 2 minutes you could run a single lap and the next time in 2 minutes run only half a lap. 16. Input: Store's name, Output: Number of letters in the name. Function, the number of letters is constant meaning inputting "Wal-Mart" will always give only one output of 7. 17. Input: Person's age, Output: Yearly salary. Not a function, two 45 year olds could be making very different salaries. 18. Input: Amount of food eaten, Output: A dog's weight. Not a function, the same dog could eat the same amount of food each day and weight different amounts. 19. Input: Person's name/identity, Output: That person's birthday. Function, a person only has one birthday. 20. Input: Person's age, Output: Height. Not a function, the same age has different heights. 21. Input: Name of a food, Output: Classification of that food (such as meat, dairy, grain, fruit, vegetable). Function, a tomato is always a fruit and only a fruit. 22. Input: Time studied for test, Output: Test score. Not a function, you could study for 30 minutes and get different scores.

Evaluate the given function using the given input.

23. 4

= -2 = -8

24.

=

+3

= 10

=8

25. = + 2

= -3 = 11

26. = + 75

= 100 = 175

27. = -4

= -3 = 12

28.

=

-3

= -8

= -5

29. = - 6

= -2 = -2

30. = - 85

=40 = -45

31. = 2 + 5

=5 = 15

32.

=

-

+

2

=9

= -1

33. = 2 + 1

=3 = 19

34. = + 55

= 70 = 125

6

Lesson 3.2

Graph the following functions by filling out the x/y chart using the given inputs (x values).

1. = - 7

2 1 0

1

2

3 6 7 6 3

2.

2

6 3

0

3

6

0

1

2

3

4

3. 9

9 8 5 0

7

0

1

2

3

4

4. 2 1

2 1

0

1

2

7

1

1

1

7

5.

2

10 5 0

0

1

2

5

10

3

4

6. 7

7 6 3

2

9

0

1

2

3

4

7

Graph the following functions by filling out the x/y chart using the inputs (x values) that you think are appropriate.

7. = 2 8

2 1 0

1

2

0 6 8 6 0

8.

4

6 3

0

3

6

8 6 4 2

0

9.

4

4 2 0

2

4

6 5 4 3 2

10. 8

8 7 4

1

8

0

1

2

3

4

11. 7

7 6 3 2

9

0 1 2 3 4

12. 4

2 1

0

1

2

0

3

4

3

0

8

 ................
................

In order to avoid copyright disputes, this page is only a partial summary.

Google Online Preview   Download