UA · Unit 4 review

1. 1.

   The mapping { (1, 4), (2, 4), (3, 5) } — is it a function?

   Answer. yes

   Each input appears once.

2. 2.

   A function is f(x) = 3x + 7. Find f(4).

   Answer. 19

   f(4) = 3(4) + 7 = 19.

3. 3.

   f(x) = 2x and g(x) = 5x. Which function has the greater rate of change?

   Answer. g

   Rate of change is the slope: 5 > 2.

4. 4.

   A car travels at a steady speed, then brakes to a stop. Speed vs. time?

   Answer. A horizontal segment, then a decreasing segment to 0.

   A horizontal segment, then a decreasing segment to 0.

5. 5.

   The mapping { (2, 1), (2, 7), (3, 8) } — is it a function? Write a complete answer — Theo will compare with a partner.

   Answer. no

   Input 2 is paired with two outputs.

6. 6.

   A function is f(x) = 6x + 3. Find f(5). Then Mei needs 3 of that amount. What is the total they need?

   Answer. 99

   f(5) = 6(5) + 3 = 33. Then multiply by 3: 99.

7. 7.

   f(x) = 5x and g(x) = 6x. Which function has the greater rate of change? Write a complete answer — Elena will compare with a partner.

   Answer. g

   Rate of change is the slope: 6 > 5.

8. 8.

   A car travels at a steady speed, then brakes to a stop. Speed vs. time? Then Ava needs 2 of that amount. What is the total they need?

   Answer. A horizontal segment, then a decreasing segment to 0.

   A horizontal segment, then a decreasing segment to 0. Then multiply by 2: A horizontal segment, then a decreasing segment to 0..

9. 9.

   The mapping { (1, 4), (2, 4), (3, 5) } — is it a function? Write a complete answer — Jonah will compare with a partner.

   Answer. yes

   Each input appears once.

10. 10.

    A function is f(x) = 5x + 6. Find f(7). Then Theo needs 3 of that amount. What is the total they need?

    Answer. 123

    f(7) = 5(7) + 6 = 41. Then multiply by 3: 123.

11. 11.

    Think

    Jonah tried this problem:
    f(x) = 5x and g(x) = 6x. Which function has the greater rate of change?
    Jonah wrote g (check this). That is not correct. What is the right answer?

    Answer. g

    Jonah’s answer g (check this) is off. Rate of change is the slope: 6 > 5.

12. 12.

    Think

    Theo tried this problem:
    A car travels at a steady speed, then brakes to a stop. Speed vs. time?
    Theo wrote A horizontal segment, then a decreasing segment to 1.. That is not correct. What is the right answer?

    Answer. A horizontal segment, then a decreasing segment to 0.

    Theo’s answer A horizontal segment, then a decreasing segment to 1. is off. A horizontal segment, then a decreasing segment to 0.

Original extra practice. Keys are computed from the items, not guessed.