Section 9A Practice

What is the purpose of a function?

• A function describes how inputs and outputs are affected by machines.

• A function describes an operation, such as multiplication or division.

• A function describes how one variable depends on another.

• A function describes how a domain and a range interact with one another.

What does the fact that the Dow Jones Industrial Average (DJIA) changes from day to day say?

• The DJIA is a function of time because time, the dependent variable changes with respect to the DJIA, the independent variable.

• Time is a function of the DJIA because time, the dependent variable, changes with respect to the DJIA, the independent variable.

• Time is a function of the DJIA because the DJIA, the dependent variable, changes with respect to time, the independent variable.

• The DJIA is a function of time because the DJIA, the dependent variable, changes with respect to time, the independent variable.

Which variable is plotted on the vertical axis when a graph of the function z = f (w) is created?

• z is plotted on the vertical axis because the horizontal axis is used for the dependent variable and the vertical axis is used for the independent variable.

• w is plotted on the vertical axis because the horizontal axis is used for the independent variable and the vertical axis is used for the dependent variable.

• z is plotted on the vertical axis because the horizontal axis is used for the independent variable and the vertical axis is used for the dependent variable.

• f is plotted on the vertical axis because the horizontal axis is used for the dependent variable and the vertical axis is used for the independent variable.

Consider a function that describes how a particular car's gas mileage depends on its speed. What would an appropriate domain for this function be?

• An appropriate domain would be times from 0 to 10 minutes because the time is the dependent variable of the function, and the domain consists of all reasonable values of the dependent variable.

• An appropriate domain would be 0 to 50 miles per gallon because the gas mileage is the independent variable of the function, and the domain consists of all reasonable values of the independent variable.

• An appropriate domain would be 0 to 100 miles per hour because the speed is the independent variable of the function, and the domain consists of all reasonable values of the independent variable.

What is a mathematical model?

• Mathematical models are based on relationships between quantities that remain constant and can only be described by a graph.

• Mathematical models are based on relationships between quantities that change and are described by very complicated functions that can only be understood using supercomputers.

• Mathematical models are based on relationships between quantities that change and are described by mathematical tools called functions.

• Mathematical models are based on relationships between quantities that remain constant and are described by mathematical tools called functions.

What are the three basic ways to represent a function?

• The three basic ways to represent a function are a table, a graph, and an expression.

• The three basic ways to represent a function are an ordered pair, a graph, and an expression.

• The three basic ways to represent a function are a table, a graph, and an equation.

• The three basic ways to represent a function are a table, an ordered pair, and an equation.

Graph the points on the same axes.

A(4, 2 ), B( − 7, 3 ),

C(1, 0 ), D( − 3, − 1 )

In the following situation, state whether two variables are related in a way that might be described by a function.

You make a list of 5 friends'/ families' names and all 17 of their e-mail addresses.

• The situation cannot be described by a function

• The situation can be described by a function. The dependent variable is your friends'/ families' names and the independent variable is the e-mail addresses.

• The situation can be described by a function. The dependent variable is the e-mail addresses

  and the independent variable is your friends'/ families' names.

• The situation can be described by a function. There is a dependent variable, but no independent variable. The dependent variable is your friends'/ families' names.

In the following situation, state whether two variables are related in a way that might be described by a function.

You run an electronic store and want to know how the quantity of TVs you sell depends on the price you charge per TV.

• The situation cannot be described by a function.

• The situation can be described by a function. There is a dependent variable, but no independent variable. The dependent variable is TVs sold.

• The situation can be described by a function. The dependent variable is the TVs sold and the independent variable is the price.

• The situation can be described by a function. The dependent variable is the price and the independent variable is the TVs.

Write a short statement that expresses a possible relationship between the variables.

(volume of gas tank, cost to fill the tank)

• As the volume of a gas tank increases, the cost to fill the tank increases.

• As the cost to fill a gas tank increases, the volume of a gas tank decreases.

• As the volume of a gas tank increases, the cost to fill the tank decreases.

• As the cost to fill a gas tank increases, the volume of a gas tank increases.