How does the graph of g(x) = 3x – 2 compare to the graph of f(x) = 3x?

Solution:

Graphs are either compared on the basis of the slope or their intercept.

The graph of both g(x) and f(x) have the same slope, i.e., similar inclination from either axis, but the only difference is in the intercept.

A line with no intercept value always passes through the origin.

The general slope-intercept form of the line is y = mx + c, where m = slope of the line, c = intercept of the line.

Comparing this slope-intercept equation with the g (x) = 3x - 2 and f (x) = 3x, we get:

For g(x): m = 3 , c = -2 

For, f (x): m = 3 , c = 0

Thus, the graph of both g(x) and f(x) has the same slope,  similar inclination from either axis, but the only difference is in the intercept.

How does the graph of g(x) = 3x – 2 compare to the graph of f(x) = 3x?

Summary:

f(x) = 3x passes through the origin, whereas g(x) = 3x -2 passes through the point (0,-2).