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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

Sagot :

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,

[tex]h(x)=x^2+2[/tex]

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

[tex]h(0)=(0)^2+2=2[/tex]

[tex]h(1)=(1)^2+2=3[/tex]

[tex]h(2)=(2)^2+2=6[/tex]

[tex]h(3)=(3)^2+2=11[/tex]

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

In option B,

[tex]h(x)=0.5x^2+1.5[/tex]

At x=0,

[tex]h(0)=0.5(0)^2+1.5=1.5\neq 2[/tex]

So, option B is incorrect.

In option C,

[tex]h(x)=2x^2[/tex]

At x=0,

[tex]h(0)=2(0)^2=0\neq 2[/tex]

So, option C is incorrect.

In option D,

[tex]h(x)=x+2[/tex]

At x=2,

[tex]h(2)=(2)+2=4\neq 6[/tex]

So, option D is incorrect.

Therefore, the correct option is A.

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