Question

Consider two functions

f(x)=x^2
and the function
g(x) shown in the graph...
Select each true statement:
A. f(x) and g(x) are both increasing.
B. f(x) increases at a faster rate than g(x) does on the interval (0, infinite).
C. g(x) has a greater y-intercept than f(x) does.
D. f(x) is greater than g(x) on the interval (0,1).

Answer 1

The question involves comparing two functions, f(x) = x^2 and g(x), which is represented by a graph. Without the graph of g(x), definitive conclusions about the true statements cannot be made, although the nature of the quadratic function f(x) provides some insights.

Step-by-step explanation:

The student is asked to consider two functions, f(x) = x^2 and g(x), which is represented by a graph not provided in the question. Selections of various true statements about these functions must be made based on their characteristics.

Without the graph of g(x), a precise answer to each statement cannot be provided. Nevertheless, given the nature of the function f(x) = x^2:

• Statement A: f(x) is increasing for x > 0, but we need the graph to evaluate g(x).
• Statement B: f(x) increases at a faster rate as x becomes larger, but without seeing g(x), we cannot determine the comparison.
• Statement C: f(x) has a y-intercept of 0. If g(x) has a greater y-intercept, this statement would be true.
• Statement D: For f(x) = x^2, on the interval (0,1), f(x) values are between 0 and 1. Without g(x), it's unclear if f(x) is greater on this interval.