Question

Which statement is true? A.The function is only increasing when x ≥ −8. B.The function is only increasing when x ≥ 0. C.The function is always decreasing. D.The function is always increasing.

Answer 1

The correct statement is B. The function is only increasing when x ≥ 0.

Step-by-step explanation:

The correct statement is B. The function is only increasing when x ≥ 0.

To determine if a function is increasing or decreasing, we look at its derivative. If the derivative is positive, the function is increasing. If the derivative is negative, the function is decreasing.

In this case, we have no information about the derivative, so we can only determine if the function is increasing or decreasing by looking at specific values of x. Since the function is only increasing when x ≥ 0, statement B is true.

Answer 2

The graph of the function is only increasing when x ≥ 0.

The graph of an exponential function.

An exponential function takes the form f(x) = aˣ ; where (a) is the base (constant) and (x) is the exponent (variable). The graph of an exponential function is usually an upward curve or a downward curve. This depends on the given function if it is an even function or an odd function.

An even function is a function whose coefficient of the leading term is positive. An odd function has a negative coefficient in their leading term.

Given the function:

f(x) = 3√x+8

Using GeoGebra online calculator to plot the graph, we can see that function on the graph is always increasing and it starts from the origin (x) = 0,y = 8.

Thus, the function is only increasing when x ≥ 0.

The complete question.

The graph of f(x)=3√x+8 is shown. Which statement is true? A The function is only increasing when x ≥ −8 B The function is only increasing when x ≥ 0 C The function is always decreasing D The function is always increasing.