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.
1 answer