Which graph represents a function? How do you know?

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fap4er fap4er

21-12-2017
Mathematics

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Which graph represents a function? How do you know?

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ardni313 ardni313 · Answer 1 · 2019-08-12T05:40:21+02:00

The graph which is a function is graph D

Further explanation

Set A to set B is said to be a function if each member of set A pairs is exactly one member of set B

So, one value of x is only assigned to one value of y

A function can be expressed in the form of a cartesian diagram, sequential pairs, or arrow diagram

If y is a function of x, then y = f (x)

where x is the independent variable and y is the dependent variable

x is the domain and y is the result area or range

There are several forms of function including:

1. linear function
2. quadratic function

3. trigonometric functions

4. polynomial function

5. fraction function etc.

One of the features mentioned above is that the function graph must map each domain member (x value) with one codomain member value y

So the graph is not a function if a graph that has one or more domain members is paired with more than one member of the codomain

If we look at graphs A, B and C, for the same x value has a different y value

So that it can be concluded that the graph which is a function is graph D

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AkhileshT AkhileshT · Answer 2 · 2019-08-22T06:21:31+02:00

The graph in the [tex]\fbox{\begin\\\ \bf option D\\\end{minispace}}[/tex] represents a function.

Further explanation:

A function is defined as a relation between the independent variable and the dependent variable.

In a function of the form [tex]y=f(x)[/tex] the independent variable is represented by [tex]x[/tex] and the dependent variable is represented by [tex]y[/tex].

The ordered pair of the form [tex](x,y)[/tex] represent the set of pairs which defines the function.

The set of all the values of [tex]x[/tex] is called the domain of the function and the set of all the value of [tex]y[/tex] is called the range of the function.

A function is a relation between the elements of the domain set and range set in such a way that every element in the range set has a unique pre-image in the domain set.

This implies that for one value of [tex]y[/tex] there is a unique value of [tex]x[/tex].

In order to test if a given curve represents a function or not we use the vertical line test.

Vertical line test: If any vertical line intersects a curve at more than one point then the curve does not represents the function.

Option A:

In option A the curve represents a parabola facing towards the negative side of [tex]x[/tex]-axis.

From figure 1 (attached in the end) it is observed that as a vertical line is drawn which intersects with the curve at two points.

So, as per the concept of vertical line test the curve given in the option A is incorrect.

Option B:

In option B the curve represents a circle with origin as its center.

From figure 2 (attached in the end) it is observed that as a vertical line is drawn it intersects with the curve at two points.

So, as per the concept of vertical line test the curve given in the option B is incorrect.

Option C:

In option C the curve represents a vertical line.

From the given figure in option C it is observed that the curve is a vertical line which means that for single value of [tex]x[/tex] there are multiple values of [tex]y[/tex]. This implies that the curve does not satisfies the definition of function so, it does not represent a function.

So, option C is incorrect.

Option D:

From figure 3 (attached in the end) it is observed that as a vertical line is drawn it intersects with the curve at only one point.

This implies that for one value of [tex]x[/tex] there is a unique value of [tex]y[/tex].

So, as per the concept of vertical line test the curve given in the option D is correct.

Therefore, the graph in the [tex]\fbox{\begin\\\ \bf option D\\\end{minispace}}[/tex] represents a function.

Learn more:

1. A problem on greatest integer function https://brainly.com/question/8243712

2. A problem to find radius and center of circle https://brainly.com/question/9510228

3. A problem to determine intercepts of a line https://brainly.com/question/1332667

Answer details:

Grade: High school

Subject: Mathematics

Chapter: Functions

Keywords: Functions, curve, range, domain, co-domain, vertical line test, variable, ordered pair, parabola, circle, set, image, pre-image, dependent variable, independent variable.