Question

Without graphing, compare the slopes and the intercepts of the graphs of the functions f(x) = x + 1 and g(x) = f(2x).

A. Same slope, different intercepts.
B. Different slope, same intercepts.
C. Same slope, same intercepts.
D. Different slope, different intercepts.

Answer 1

The slopes are the same but the intercepts are different.

Step-by-step explanation:

The slope of a linear function determines how steep the line is, while the y-intercept represents the point where the line intersects the y-axis. For the function f(x) = x + 1, the slope is 1 and the y-intercept is 1. On the other hand, for the function g(x) = f(2x), the slope remains the same at 1, but the y-intercept changes to 2 because 2x is substituted for x in the function. Therefore, the slopes are the same but the intercepts are different, so the correct answer is A. Same slope, different intercepts.