Question

Use the table to answer the question.
x y
0 3
1 3 1/2
2 4
3 4 1/2

Which of the following equations describes the function in the table using function notation?
(1 point)
Responses

f(y)=3x+1/2

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

Answer 1

To determine the equation that describes the function in the table, we begin by analyzing the provided values:

- When \( x = 0, y = 3 \)
- When \( x = 1, y = 3.5 \)
- When \( x = 2, y = 4 \)
- When \( x = 3, y = 4.5 \)

The change in \( y \) corresponds to the change in \( x \). Observing the table:

- From \( x=0 \) to \( x=1 \): \( y \) changes from 3 to 3.5 (increase of 0.5)
- From \( x=1 \) to \( x=2 \): \( y \) changes from 3.5 to 4 (increase of 0.5)
- From \( x=2 \) to \( x=3 \): \( y \) changes from 4 to 4.5 (increase of 0.5)

This indicates that for every increase of 1 in \( x \), \( y \) increases by 0.5, suggesting a linear relationship. This can be expressed as:

\[
y = 0.5x + b
\]

To find \( b \), we can use one of the points. Let's use the point \( (0, 3) \):

\[
3 = 0.5(0) + b \implies b = 3
\]

Thus, the equation becomes:

\[
y = 0.5x + 3
\]

In function notation:

\[
f(x) = \frac{1}{2}x + 3
\]

Therefore, the correct function from the options provided is:

**f(x) = \frac{1}{2} x + 3**