Question

Please Help....

Which of the following rules represents the function graphed?


A) f(x)=1/2x

B) f(x)=x

C) f(x)=x+2

Answer 1

B

Explanation:

To figure out equation of a line, we need two points.

If you look at the graph, one point is
`(0,0)` and another point let's take
`(1,1)`.

The equation of the line is given by
`y=mx+b`

Where m is the slope with formula
`m=(y_(2)-y_(1))/(x_(2)-x_(1))` and
`(x_(1),y_(1))` is point 1 and
`(x_(2),y_(2))` is point 2.

Solving for m, we have:

`m=(1-0)/(1-0)\\m=(1)/(1)\\m=1`

Thus we have
`y=1x+c`

To solve for c [the y-intercept] we plug in any point into x and y of this equation. Let's use the point
`(0,0)`. We have:

`0=1(0)+c\\0=0+c\\c=0`

Thus we can write
`y=1x+0` or simply
`y=x`

In function notation, we replace
`y` with
`f(x)`

So we have
`f(x)=x`

Answer choice B is right.