Question

The range of which function includes -4?

Answer 1

Function under A) has range x>0 because we cant calculate square root of negative number (we can if we include imaginery numbers)

B) again x must be greater than 0

C)  x + 5 > 0 which means that x > -5
-4 is withing range so C in correct

D) x - 5 > 0 which means x > 5

Answer is C because only function under C has domain such that it includes -4

Answer 2

Answer: The correct answer is A.

Step-by-step explanation:

Range is defined as the set of 'y' values for which the function is defined.

The graph of $y=\sqrt{x}$ passes through the origin and lies in the first quadrant and in the shape of half parabola. The image is attached below.

The alteration in the 'x' term will transform the graph in the x-direction. In order to find the range we will consider the y-values only. So, we can neglect option C and D.

When we add some constant 'C' in the function, then the graph will shift upward by C-units.

When we subtract some constant 'C' in the function, then the graph will shift downward by C-units.

Therefore, the graph of $y=\sqrt{x}-5$ starts with the point (0,-5) and hence, the graph will lie above this point. The image of the graph is attached below.

As, the range of the function is $y\in {-5,\infty}$, it means that -4 is also included in this range.

Hence, the correct option is A.