Question

Select the correct answer.
Which statement is true about the function shown in the graph?

Answer 1

The function is increasing

Answer 2

A statement that is true about the function shown in the graph above is: A. The function is strictly increasing.

For any given function, y = f(x), if the output value (range) is increasing when the input value (domain) is increased, then, the function is generally referred to as an increasing function.

Generally speaking, a function is considered as a strictly increasing function when the graph of the function is always rising from left to right and the first derivative f'(x) is greater than 0 for the domain of f(x);

f'(x) > 0

By taking the first derivative of this square root function above, we have:

`f(x)=2√(x+4) \\\\f'(x)=2(d(√(x+4) ))/(dx) \\\\f'(x)=2 \cdot (1)/(2) (x+4)^{-(1)/(2) }\\\\f'(x)= (x+4)^{-(1)/(2) }\\\\f'(x)=(1)/(√(x+4) )`

Since the domain of f(x) is x ≥ -4 and f'(x) > 0 for all values of x, we can logically conclude that f(x) is a strictly increasing function for all x-values in the domain.