Download the App!

Get 24/7 study help with the Numerade app for iOS and Android! Enter your email for an invite.

Get the answer to your homework problem.

Try Numerade free for 7 days

Like

Report

Use the vertical line test to determine if the given graph may represent a function.

Is

Algebra

Chapter 1

Functions and their Applications

Section 2

Basic Notions of Functions

Functions

McMaster University

Idaho State University

Lectures

01:43

In mathematics, a function is a relation between a set of inputs and a set of permissible outputs with the property that each input is related to exactly one output. An example is the function that relates each real number x to its square x^2. The output of a function f corresponding to an input x is denoted by f(x).

03:18

01:22

Use the vertical line test…

01:23

01:30

01:41

01:27

01:44

01:40

01:38

for this problem. We have been asked to use the vertical line test to determine whether are given graph could or could not be a function. So let's review what the vertical line test is and what it shows us well to start with. Let's look at the definition of a function. A function says that every input into the function gets mapped to exactly one output. Inputs are our X values and outputs are y values. So this is saying that every X can Onley matched up toe one y value in order for something to be a function. So when I put a vertical line on my graph that is representing a single X value and my definition, I only wanted to be associated with one. Why, that means I only wanted to cross my graph in one place. If there was a spot that I could move that vertical line where it crossed the graph twice or three times or more, that means that my ex is being mapped to different values of why, and that is contrary to the definition of a function. I could certainly draw that kind of graph, but it would not be a function in that case. So let's take a look at our vertical line as we shift it left and right across our graph, there is nowhere I can put it that will cross the Griff the graph in more than one place. So it does satisfy the vertical line test. And yes, it is ah, function.

View More Answers From This Book

Find Another Textbook

Numerade Educator

03:16

Plot the lines found in Exercise $15$.

03:19

sketch the graph of the given ellipse, labeling all intercepts.$$4 x^{2}…

03:42

Height is a function of age. Suppose at birth the average male is 16 inches …

02:17

Given the function defined by the equation $f(x)=3 x-5,$ determine(a) $f…

01:00

In each of the following, solve the given quadratic equation exactly using t…

01:02

Determine if the function defined by the given equation is odd, even or neit…

05:28

Let $y=f(x)$ describe the upper half of the circle $x^{2}+y^{2}+6 x-10 y+9=0…

02:22

John bikes a distance of 120 miles and then returns over the same route. On …

01:39

Determine the domain of the function defined by the given equation.$f(x)…

01:14

Find the equation of the parabola with focus on the line $y=x$ at $(h, h)$ a…