Question

Use the table to answer the question.

Which of the following equations describes the function in the table using function notation?
x 0, 1, 2, 3,
y 3, 3 1/2 ,4 ,4 1/2
(1 point)
Responses

f(x)=3x+12
f of x is equal to 3 x plus 1 half

f(x)=12x+3

f of x is equal to 1 half x plus 3

f(y)=3x+12
f of y is equal to 3 x plus 1 half

f(y)=12x+3

Answer 1

To determine the equation that describes the function in the table using function notation based on the values given:

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

We can observe that the output \( y \) increases by \( 0.5 \) for each increase of \( 1 \) in \( x \). This suggests a linear relationship.

Let's express this in the slope-intercept form \( y = mx + b \).
The slope \( m \) can be calculated as:

\[
m = \frac{\Delta y}{\Delta x} = \frac{0.5}{1} = 0.5
\]

We can use the point (0, 3) to find the y-intercept \( b \):

\[
y = mx + b \\
3 = 0.5(0) + b \\
b = 3
\]

Thus, the equation of the function can be written as:

\[
y = 0.5x + 3
\]

Using function notation, we denote this as:

\[
f(x) = 0.5x + 3
\]

Now, looking at the provided responses, the expression that correctly states this is:

**f of x is equal to 1 half x plus 3.**