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RyanTurley43
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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)

Verified Answer :

kudzordzifrancis

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:

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

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