Milestones - Functions

Which of the following statements must be true of a function?

• Every output value corresponds to only one input value.

• Every input value corresponds to only one output value.

• No input values are repeated.

• No output values are repeated.

Each of the tables below shows a relation. Which relation is a function?

• Input: 1, 5, 5, 7, 9 | Output: 2, 8, 9, 13, 21

• Input: 7, 8, 9, 8, 11 | Output: 3, 5, 7, 6, 9

• Input: 3, 7, 6, 10, 15 | Output: 0, 0, 0, 0, 0

• Input: 1, 1, 1, 1, 1 | Output: 2, 3, 4, 5, 6

Pia registered for an account on the website of a national magazine. The magazine charges $5 as a setup fee and $17 per month for access to the website. What is the initial value of the function that represents Pia's cost for access to the magazine's website over time?

• $0

• $5

• $17

• $22

Ibrahim drew the graph below. Which of the following statements best describes the graph?

• The graph represents a relation but not a function.

• The graph represents both a relation and a function.

• The graph represents neither a relation nor a function.

• There is no relationship between the x and y values in the graph.

André paid a $65 annual fee to register with a car rental company. The company charges $8.50 for each hour a car is rented. What is the rate of change of the function that represents André's cost for renting a car over the course of a year?

• $8.50 per hour

• $65 per year

• $73.50 per hour

• $73.50 per year

Which of the following is the equation of a nonlinear function?

• y = 25

• y = x - 3/4

• y = 10x

• y = x^2 + 15

The graph below shows the relationship between time and speed for a 300-mile journey. Which of the following statements is the best description of the functional relationship between the two quantities in the graph?

• The graph shows a decreasing, nonlinear function. As the time of the journey increases, the speed decreases.

• The graph shows an increasing, nonlinear function. As the speed increases, the time of the journey increases.

• The graph shows a decreasing, linear function. As the time of the journey increases, the speed decreases.

• The graph shows an increasing, linear function. As the speed increases, the time of the journey increases.

Which of these graphs does not represent a function?

• Graph A

• Graph B

• Graph C

• Graph D

Which of the following statements is true regarding the rate of change for Function A and Function B?

• A. The rate of change for Function A is twice the rate of change for Function B.

• B. The rate of change for Function A is four times the rate of change for Function B.

• C. The rate of change for Function B is twice the rate of change for Function A.

• D. The rate of change for Function B is one-tenth the rate of change for Function A.

Orhan studied the relationship between temperature and sales of refreshments at the concession stands inside the football stadium. He wrote an equation for the linear function that relates temperature (x) and refreshment sales (y). Which of the following could be Orhan’s equation?

• y = 3x + 25

• y = 15x + 40

• y = 11x - 55

• y = x/3 + 135