Question

Which of the following rules could represent the function shown in the table?

x y
-1 -1
0 1
1 3

f(x) = -2x (A)

f(x) = 2x - 1 (B)

f(x) = 2x + 1 (C)

Answer 1

Option (C) is correct

f(x) = 2x + 1

Explanation:

Slope-intercept form:

The equation of line is given by:

`y=mx+b` .....[1]

where, m is the slope and b is the y-intercept.

As per the statement:

Let y = f(x)

Given the table as shown

Let any two points:

(-1, -1) and (0, 1)

Formula for slope(m):

`m = (y_2-y_1)/(x_2-x_1)`

Substitute the given values we have;

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

⇒
`m = (2)/(1) = 2`

Substitute in [1] we have;

y = 2x+b ....[2]

Substitute the point (-1, -1) in [2] we have;

-1 = 2(-1)+b

⇒-1 = -2+b

Add 2 to both sides we have;

1 = b

or

b = 1

then, we get the equation:

y =2x+1

or

f(x) = 2x+1

Therefore, the following rules could represent the function is, f(x) = 2x+1

Answer 2

ANSWER

The rule is given by the relation,


`y = 2x + 1`


EXPLANATION

We need to check and see if there is a constant difference between the y-values.



`1 - - 1 = 2 = 3 - 1`


We can see that, there is a constant difference of 2.

This means that the table represents a linear relationship.


Let the rule be of the form,

`y = mx + c`


Then the points in the table should satisfy the above rule.


So let us plug in



`(0,1)`


This implies that,



`1 =m (0) + c`



`1 = 0 + c`



`c = 1`



Our rule now becomes,



`y = mx + 1 - - (1)`


We again plug in another point say, (-1,-1) in to equation (1) to get,




`- 1 = m( - 1) + 1`

we solve for m now to obtain,


`- m=-1-1`



`- m = - 2`



`m = 2`
We now substitute back in to equation (1) to get


`y = 2x + 1`