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 …

Question

asked Oct 10, 2022 204k views

1 Answer

John Laffoon · Answer 1 · 2022-10-15T02:36:25+0000

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,
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.