Question
Function 1 f(x)= 3/2x +5
Function 2 is a graph with points (-6,1),(0,5),(3,7),(6,9)
Function ___ has a greater rate of change
Function 2 is a graph with points (-6,1),(0,5),(3,7),(6,9)
Function ___ has a greater rate of change
Answers
GPT-4o mini
To determine which function has a greater rate of change, we can calculate the slope of each function.
**Function 1: \( f(x) = \frac{3}{2}x + 5 \)**
The rate of change (slope) of a linear function in the form \( y = mx + b \) is given by the coefficient \( m \).
For Function 1, the slope \( m = \frac{3}{2} = 1.5 \).
**Function 2**: The points given are (-6,1), (0,5), (3,7), and (6,9). To find the overall rate of change, we can calculate the slope between the first and last points (for a broader view):
\[
\text{slope} = \frac{y_2 - y_1}{x_2 - x_1} = \frac{9 - 1}{6 - (-6)} = \frac{8}{12} = \frac{2}{3} \approx 0.67
\]
Now comparing the rates of change (slopes):
- Function 1 slope: \( 1.5 \)
- Function 2 slope: \( \frac{2}{3} \approx 0.67 \)
**Conclusion**: Function 1 has a greater rate of change than Function 2.
**Function 1: \( f(x) = \frac{3}{2}x + 5 \)**
The rate of change (slope) of a linear function in the form \( y = mx + b \) is given by the coefficient \( m \).
For Function 1, the slope \( m = \frac{3}{2} = 1.5 \).
**Function 2**: The points given are (-6,1), (0,5), (3,7), and (6,9). To find the overall rate of change, we can calculate the slope between the first and last points (for a broader view):
\[
\text{slope} = \frac{y_2 - y_1}{x_2 - x_1} = \frac{9 - 1}{6 - (-6)} = \frac{8}{12} = \frac{2}{3} \approx 0.67
\]
Now comparing the rates of change (slopes):
- Function 1 slope: \( 1.5 \)
- Function 2 slope: \( \frac{2}{3} \approx 0.67 \)
**Conclusion**: Function 1 has a greater rate of change than Function 2.