Question

Write a function in any form that would match the graph shown below

Answer 1

Answer: The most common graphs name the input value  

x

and the output value  

y

, and we say  

y

is a function of  

x

, or  

y

=

f

(

x

)

when the function is named  

f

. The graph of the function is the set of all points  

(

x

,

y

)

in the plane that satisfies the equation  

y

=

f

(

x

)

. If the function is defined for only a few input values, then the graph of the function is only a few points, where the x-coordinate of each point is an input value and the y-coordinate of each point is the corresponding output value. For example, the black dots on the graph in the graph below tell us that  

f

(

0

)

=

2

and  

f

(

6

)

=

1

. However, the set of all points  

(

x

,

y

)

satisfying  

y

=

f

(

x

)

is a curve. The curve shown includes  

(

0

,

2

)

and  

(

6

,

1

)

because the curve passes through those points.

Graph of a polynomial.

The vertical line test can be used to determine whether a graph represents a function. A vertical line includes all points with a particular  

x

value. The  

y

value of a point where a vertical line intersects a graph represents an output for that input  

x

value. If we can draw any vertical line that intersects a graph more than once, then the graph does not define a function because that  

x

value has more than one output. A function has only one output value for each input value.

Three graphs visually showing what is and is not a function.

HOW TO: GIVEN A GRAPH, USE THE VERTICAL LINE TEST TO DETERMINE IF THE GRAPH REPRESENTS A FUNCTION.

Inspect the graph to see if any vertical line drawn would intersect the curve more than once.

If there is any such line, the graph does not represent a function.

If no vertical line can intersect the curve more than once, the graph does represent a function.

Step-by-step explanation: