Question

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

Answer 1

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

$y = 2x + 1$

Answer 2

Answer:

Option (C) is correct

f(x) = 2x + 1

Step-by-step 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):

$m = \frac{y_2-y_1}{x_2-x_1}$

Substitute the given values we have;

$m = \frac{1-(-1)}{0-(-1)}$

⇒$m = \frac{2}{1} = 2$

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