Question

If the points (0, 0), (-1, 1), and (-2, 2) lie on the graph of function h, then which of the following rules could represent the function?

A. h(x) = x 2
B. h(x) = |x|
C. h(x) = -2x

Answer 1

We can plug in the values:
A ) 0 = 0² , 1 = ( - 1 )², 2 ≠ ( -2)²
B ) 0 = | 0 |, 1 = | -1 |, 2 = | - 2 |
C ) 0 = - 2 · 0, 1 ≠ - 2 · ( -1 ), 2 ≠ - 2 · ( - 2 )
Answer: B ) h ( x ) = | x |

Answer 2

Option B is correct

The function h(x) = |x|

Explanation:

Given the points (0, 0) , (-1 , 1) and (-2 , 2)

The absolute value of x i,e |x| will always gives the positive value of y

i.e y = |x|

For x = 0

y=|x| =|0| = 0

For x =-1

y= |-1| = 1

For x = -2

y = |x| = |-2| = 2

As you can see that for every value of x , we get the positive value of y;

therefore, the function which represents the condition is: y=h(x)=|x|

Hence, the given points lie on the graph of the function h(x) = |x|