Question

Use the table to answer the question.

x y
0 3
1 312

2 4
3 412

Which of the following equations describes the function in the table using function notation?

(1 point)
Responses

f(x)=12x+3
f left parenthesis x right parenthesis equals Start Fraction 1 over 2 End Fraction x plus 3

f(y)=12x+3
f left parenthesis y right parenthesis equals Start Fraction 1 over 2 End Fraction x plus 3

f(y)=3x+12
f left parenthesis y right parenthesis equals 3 x plus Start Fraction 1 over 2 End Fraction

f(x)=3x+12

Answer 1

To determine which equation describes the function in the table, we first need to understand the relationship between \(x\) and \(y\) based on the values given:

- For \(x = 0\), \(y = 3\)
- For \(x = 1\), \(y = 312\)
- For \(x = 2\), \(y = 4\)
- For \(x = 3\), \(y = 412\)

There seems to be some inconsistencies in the table which could be a typographical error (like the value 312 for \(y\)). However, if we focus on the values we have, it appears that the correct pairs are likely:

- \( (0, 3) \)
- \( (2, 4) \)

Assuming a linear relationship, let's try to determine the linear function based on the correct pairs:

Using points \( (0, 3) \) and \( (2, 4) \):

1. Calculate the slope \(m\):
\[
m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{4 - 3}{2 - 0} = \frac{1}{2}
\]

2. Using point-slope form, where \(y - y_1 = m(x - x_1)\) and using the point \( (0, 3) \):
\[
y - 3 = \frac{1}{2}(x - 0)
\]
\[
y = \frac{1}{2}x + 3
\]

In function notation, this can be written as:
\[
f(x) = \frac{1}{2}x + 3
\]

Thus, based on the options provided, the correct response is:
**f(x)=Start Fraction 1 over 2 End Fraction x + 3.**