Question

The function f(x) is graphed on the coordinate plane.

What is f(−2) ?
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f(−2)=

Answer 1

The answer is f(-2)=-2, go over -2 units and move vertically -2 units

Answer 2

The value of f(-2) is, -2

Explanation:

The graph which is shown on the coordinate plane passes through the two points i.e, (2,0) and (0, -1).

First find the equation for this line:

Using Point-Slope form for the equation of line:
`y-y_(1)=m(x-x_(1))` ..[1]

where m is the slope given by ;

`m=(y_(2)-y_(1))/(x_(2)-x_(1))`

First find the slope:

`m=(y_(2)-y_(1))/(x_(2)-x_(1))=(-1-0)/(0-2)`

⇒
`m=(-1)/(-2) =(1)/(2)`

Now, substitute the value of m=
`(1)/(2)` ,
`x_(1)`= 2and
`y_(1)`=0 in equation [1];

`y-0=((1)/(2))(x-2)` or

`y=(1)/(2)\cdot (x-2)`

In this graph x represents the input of the process and Y the output of the process and f the function of the variable x i.e, y=f(x)

∴
`y=f(x)=(1)/(2)(x-2)` ....[2]

now, we put the value of x=-2 inequation [2] to solve for f(-2).

`f(-2)=(1)/(2)(-2-2) =(1)/(2) \cdot (-4)`

Simplify we get;

`f(-2)=-2`