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

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:

3< x< 5

step-by-step explanation:

|x - 4| < 1

there are two solutions, one positive and one negative.   remember to flip the inequality when taking the negative solution

x-4 < 1       x-4 > -1

add 4 to each side

x-4+4 < 1+4       x-4+4 > -1+4

x< 5                 x> 3

3< x< 5

-3

step-by-step explanation:

a drawing really does here:

so i draw the horizontal line y=2 and the vertical line x=-2 at this intersection i put b (this is where my right angle is going to be).   so point b is at (-2,2).   point a is 5 units long and is also on y=2 so this point has to be (3,2) or (-7,2) -doesn't matter i will go with (3,2).

now we know c is at (-2,y) we don't know the y yet bet we know that c is on x=-2.

we have the area of the triangle is .5bh=12.5

we know the base length is 5 (ab)

we have the height is (2-y) if you look at your

plug in

.5(5)(2-y)=12.5

solve for y to get the y-coordinate for c

2.5(2-y)=12.5

divide both sides by 2.5 giving:

2-y=5

now subtract 2 on both sides

-y=3

y=-3