Question

Which statement is true about the function f(x)= - square root of x?

Answer 1

Answer:

It has the same range but not the same domain as the function $f(x) = - \sqrt{-x}$.

Step-by-step explanation:

Recall the domain of the function is all x values which input into the function and give an output. The outputs or y values are called the range. To find the domain and range, graph the function and look at where it is on the coordinate plane.

$f(x) = \sqrt{x}$ starts at (0,0) and curves upward and towards the right. Its domain is $x\geq 0$ and its range is $y\geq 0$.

$f(x) = - \sqrt{x}$ starts at (0,0) and curves downward to the right. Its domain is $x\geq 0$ still but its range is negative numbers or $y\leq 0$.

$f(x) = - \sqrt{-x}$ starts at (0,0) and curves downward to the left. Its domain is negative x values or $x\leq 0$ and its range is negative values or $y\leq 0$.

This means the two functions have the same range but different domains.