Question

The points (0,2), (1,3), (2,6), and (3,11) are on the graph of a function. Which of the following equations represents that function?

A.h(x)=x^2+2
B.h(x)=0.5x^2+1.5
C.h(x)=2x^2
D.h(x)=x+2

Answer 1

Given:

The points (0,2), (1,3), (2,6), and (3,11) are on the graph of a function.

To find:

The function.

Solution:

In option A,

`h(x)=x^2+2`

Putting x=0, 1, 2, 3 respectively, we get

`h(0)=(0)^2+2=2`

`h(1)=(1)^2+2=3`

`h(2)=(2)^2+2=6`

`h(3)=(3)^2+2=11`

The function passes through the points (0,2), (1,3), (2,6), and (3,11). So,
`h(x)=x^2+2` is the required function.

In option B,

`h(x)=0.5x^2+1.5`

At x=0,

`h(0)=0.5(0)^2+1.5=1.5\\eq 2`

So, option B is incorrect.

In option C,

`h(x)=2x^2`

At x=0,

`h(0)=2(0)^2=0\\eq 2`

So, option C is incorrect.

In option D,

`h(x)=x+2`

At x=2,

`h(2)=(2)+2=4\\eq 6`

So, option D is incorrect.

Therefore, the correct option is A.