To describe the graph of the function \( g(x) = 2x + 3 \) in relation to the graph of the function \( f(x) = 2x \), let's analyze the forms of both functions.
1. **Slope**: Both functions have the same slope of 2, which indicates that the graphs of \( f(x) \) and \( g(x) \) will be lines with the same steepness or rate of change.
2. **Y-Intercept**: In the function \( f(x) = 2x \), the y-intercept is 0 (where the line crosses the y-axis). In the function \( g(x) = 2x + 3 \), the y-intercept is \(3\) (where the line crosses the y-axis).
Given these points, we can describe the graph of \( g(x) = 2x + 3 \) as follows:
- The graph of \( g(x) = 2x + 3 \) is a straight line parallel to the graph of \( f(x) = 2x \), because they share the same slope.
- The graph of \( g(x) \) is shifted vertically upward by 3 units compared to the graph of \( f(x) \).
So, the statement that describes the graph of the function \( g \) is:
"The graph of \( g(x) = 2x + 3 \) is a vertical translation of the graph of \( f(x) = 2x \) by 3 units upward."
Which statement describes the graph of function g?
f(x) = 2x
g(x) = 2x + 3
1 answer