Question

1. does the following relationship represent a function?

{(1,0),(2,3),(4,5),(9,0)}
a. yes, there is only one y for each x
b. yes, there is only one y for each x
c. no, there is not only one y for each x
d. no, there is not only one x for each y

1. identify the domain of the graph

a. -5,3 or -5≤x≤3
b. (-5,3) or -5<x<3
c. -2,2 or -2≤x≤2
d. (-2,2) or -2<x<2

1. identify the dependent variable in the following situation:

the number of miles to school and the time it takes to get to school
a. number of miles
b. time
c. neither

Explanation:

4.

Step1: Recall function definition

A relation is a function if for each input value \(x\) (first - element of each ordered pair), there is exactly one output value \(y\) (second - element of each ordered pair).
In the relation \(\{(1,0),(2,3),(4,5),(9,0)\}\), the input values are \(1\), \(2\), \(4\), and \(9\). Each of these \(x\) - values has only one corresponding \(y\) - value.

Step1: Identify domain on graph

The domain of a graph is the set of all \(x\) - values for which the graph is defined.
Looking at the graph, the left - most \(x\) - value is \(x=-5\) (a closed - circle, so included) and the right - most \(x\) - value is \(x = 3\) (a closed - circle, so included).
The domain is the interval \([-5,3]\) or \(-5\leq x\leq3\).

Step1: Recall dependent variable concept

The dependent variable is the variable whose value depends on another variable.
The time it takes to get to school depends on the number of miles to school. As the number of miles changes, the time changes. So, the time is the dependent variable.

Answer:

a. yes, there is only one y for each x

5.