Question

Suppose f(x) = 1/3x + 1. Describe how the following function compares to it.

h(x) = (1/4)x + f(x)

a) The two functions are equal.
b) The function h(x) has a steeper slope than f(x).
c) The function h(x) has a shallower slope than f(x).
d) The relationship between the two functions cannot be determined.

Answer 1

The function h(x) = (1/4)x + f(x) has a steeper slope than f(x) = 1/3x + 1.

Step-by-step explanation:

To determine how the function h(x) = (1/4)x + f(x) compares to f(x) = 1/3x + 1, we can compare their slopes. The slope of f(x) is 1/3, which means for every 1 unit increase in x, the value of y increases by 1/3.

The slope of h(x) is 1/4 + 1/3 = 7/12, which means for every 1 unit increase in x, the value of y increases by 7/12. Since 7/12 is greater than 1/3, the function h(x) has a steeper slope than f(x).

Therefore, the correct answer is b) The function h(x) has a steeper slope than f(x).