11.1.A.1Multiple Choice
Each ordered pair is (input, output). Which relation is a function?
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 1–12 cover 1.1.A; questions 13–20 cover 1.1.B.
Each ordered pair is (input, output). Which relation is a function?
Select A, B, C, or D to check your answer.
The table shows a function. State its domain and its range.
| x | −3 | −1 | 0 | 2 |
| y | 4 | 4 | 1 | 6 |
A bakery's cost C(n), in dollars, depends on the number of cupcakes n it bakes, where n is a whole number from 0 to 200. Which statement is correct?
Select A, B, C, or D to check your answer.
Let f(x) = x² − 9 and g(x) = (x − 3)(x + 3), both defined for all real numbers. Let h(x) = (x² − 9)/(x − 3), defined for x ≠ 3. Which statement is true?
Select A, B, C, or D to check your answer.
Use the table to find the image of 2 and the preimage of 5.
| x | 0 | 1 | 2 | 3 | 4 |
| f(x) | 5 | 8 | 3 | 5 | 11 |
For f(x) = 2x² − 3x, what is the image of −2?
Select A, B, C, or D to check your answer.
For g(x) = x² + 1, what is the preimage of 10?
Select A, B, C, or D to check your answer.
A function is described in words: “multiply the input by 3, then subtract 2.” Which equation represents it?
Select A, B, C, or D to check your answer.
Based on the table, on which interval of inputs is f increasing?
| x | 0 | 1 | 2 | 3 | 4 | 5 |
| f(x) | 8 | 5 | 3 | 4 | 7 | 12 |
Select A, B, C, or D to check your answer.
Use the definition of an increasing function to show that f(x) = 5x + 2 is increasing for all real numbers.
The function f is given by f(x) = x² − 6x + 5. On which interval is f decreasing?
Select A, B, C, or D to check your answer.
The graph shows g(x) = −x² + 4x. Describe how g(x) varies as x increases from 0 to 4.
The graph shows a hiker's elevation, in feet, t hours after starting. Over which time interval is the elevation decreasing?
Select A, B, C, or D to check your answer.
A table of values for a function is shown. Which statement best describes the function over these inputs?
| x | 0 | 1 | 2 | 3 | 4 | 5 |
| f(x) | 10 | 6 | 4 | 5 | 8 | 13 |
Select A, B, C, or D to check your answer.
Water flows into a tank at one constant rate for 5 minutes, and then at a faster constant rate for the next 3 minutes. Which graph best shows the volume of water in the tank as a function of time?
Select A, B, C, or D to check your answer.
A cup of hot coffee is left on a table in a cool room. Describe a graph of the coffee's temperature (output) as a function of time (input).
The table gives values of y at equally spaced inputs. Which statement describes the graph over these inputs?
| x | 0 | 1 | 2 | 3 | 4 |
| y | 20 | 12 | 7 | 4 | 2.5 |
Select A, B, C, or D to check your answer.
The table shows the percent P of a task completed t minutes after starting. Which statement describes the graph?
| t (min) | 0 | 5 | 10 | 15 | 20 |
| P (%) | 0 | 40 | 70 | 90 | 100 |
Select A, B, C, or D to check your answer.
What are the zeros of f(x) = x² − 2x − 8?
Select A, B, C, or D to check your answer.
The graph of g(x) = x³ − 4x is shown. (a) Find the zeros of g. (b) Using g(−1) and g(1), describe how g varies between x = −1 and x = 1. (c) Use the average rates of change of g over [1, 2] and [2, 3] to decide whether the graph is concave up or concave down on [1, 3].