Question

A student graphed f(x) = x and g(x) = 1/2x on the same coordinate grid. How does the graph of f(x) compare to the graph of g(x)?

a) f(x) is a horizontal line.
b) f(x) is steeper than g(x).
c) f(x) is a vertical line.
d) f(x) and g(x) have the same slope.

Answer 1

The slope of f(x) is greater than that of g(x), making f(x) steeper. Thus, the correct comparison between the two graphs is that f(x) is steeper than g(x).

Step-by-step explanation:

When comparing the graphs of the functions f(x) = x and g(x) = 1/2x on the same coordinate grid, it is important to understand the concept of slope. The slope of a linear function in the form y = mx + b is represented by the coefficient m, which shows the steepness of the line on the graph. f(x) has a slope of 1 as the coefficient of x is 1, meaning for every increase of 1 unit in x, y also increases by 1 unit. On the other hand, g(x) has a slope of 1/2, indicating that for every increase of 1 unit in x, y increases by only 1/2 unit.

Since the slope of f(x) is greater than the slope of g(x), f(x) is steeper than g(x).

Therefore, the correct answer to the student's question is: b) f(x) is steeper than g(x).