12.2.A.1Multiple Choice
Which statement correctly compares the linear function f(x) = b + mx with the arithmetic sequence an = a0 + dn?
Select A, B, C, or D to check your answer.
Directions: Work each problem on your own paper first. For multiple choice, select A, B, C, or D. You will see right away whether you are correct. If you miss, you will see the most likely reason, and you can try again. For short response, type your answer, then compare it with the model solution. Questions 1–10 cover 2.2.A; questions 11–20 cover 2.2.B (question 20 uses both). In every problem, the first term of a sequence is the term at n = 0.
Which statement correctly compares the linear function f(x) = b + mx with the arithmetic sequence an = a0 + dn?
Select A, B, C, or D to check your answer.
The arithmetic sequence an = 8 − 5n is given. (a) Write the matching linear function f(x). (b) Find a3 and f(3). (c) Find f(0.4), and say whether a0.4 exists.
A linear function f has slope 3 and satisfies f(2) = 5. Which expression gives f(x)?
Select A, B, C, or D to check your answer.
A linear function has slope −4 and passes through the point (5, 1). (a) Write f(x) in point form. (b) Rewrite it in the form b + mx. (c) Find f(8).
The geometric sequence gn = 7·2n is given. Which exponential function matches it?
Select A, B, C, or D to check your answer.
A culture starts with 400 cells and doubles every hour. (a) Write the sequence gn for whole hours and the function f(t) for any time t. (b) Find the number of cells at 3 hours. (c) Find f(2.5), and explain why g2.5 does not exist.
An exponential function is given by f(x) = 10·2x − 3. When it is rewritten in the form f(x) = a·2x, what is a?
Select A, B, C, or D to check your answer.
An exponential function has ratio 0.5 and passes through the point (4, 5). (a) Write f(x) in point form. (b) Find the initial value a. (c) Find f(6).
The graph shows the linear function f(x) = 5 + 2x as a line, and the arithmetic sequence an = 5 + 2n as dots. Which statement is true?
Select A, B, C, or D to check your answer.
Let gn = 6·2n be a sequence and f(x) = 6·2x the matching function. (a) State the domain of each. (b) Evaluate each at −1, 3, and 1.5, or say that the value is not defined. (c) Describe how the graphs differ.
The table gives values of a function. Which statement is correct?
| x | 0 | 3 | 6 | 9 |
| f(x) | 4 | 10 | 16 | 22 |
Select A, B, C, or D to check your answer.
The table gives values of a function at equally spaced inputs. Show that the function is exponential, state the ratio, write f(x), and find f(4).
| x | 0 | 1 | 2 | 3 |
| f(x) | 81 | 27 | 9 | 3 |
The table shows a function whose inputs are not evenly spaced. Which statement is correct?
| x | 1 | 2 | 3 | 5 | 6 |
| f(x) | 4 | 8 | 16 | 64 | 128 |
Select A, B, C, or D to check your answer.
Which statement about f(x) = b + mx and g(x) = abx is correct?
Select A, B, C, or D to check your answer.
For which value of b is f(x) = 5·bx NOT an exponential function?
Select A, B, C, or D to check your answer.
Account A starts at $300 and adds $25 each month. Account B starts at $300 and grows by 5% each month. (a) Write a model for each. (b) Find each balance after 12 months. (c) Find the first whole month in which B is larger than A.
An exponential function f has f(1) = 10 and f(4) = 80. (a) Find the ratio b. (b) Write f(x) in the form a·bx. (c) Find f(0) and f(6).
A linear function f has f(3) = 11 and f(7) = 27. Which expression gives f(x)?
Select A, B, C, or D to check your answer.
The values f(0) = 5 and f(2) = 45 are known. (a) Find the linear function through both points. (b) Find the exponential function through both points. (c) Find each function's value at x = 3. If a third measurement gives f(3) = 135, which model fits?
Two functions are given by tables at equally spaced inputs. (a) Classify h and k as linear or exponential, giving the constant change or ratio. (b) Write a function for each. (c) Find each function's value at x = 2.5 and say which is larger.
| x | 0 | 1 | 2 | 3 | 4 |
| h(x) | 3 | 6 | 12 | 24 | 48 |
| k(x) | 3 | 7 | 11 | 15 | 19 |