Mathematics, 31.01.2020 16:55, Mrdwarf7163

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

a. the domain of the graph is all real numbers.
b. the range of the graph is all real numbers.
c. the domain of the graph is all real numbers less than or equal to 0.
d. the range of the graph is all real numbers less than or equal to 0.

question 2 has a graph

the function f(x) = - square root of x is shown on the graph.

which statement is correct?

a. the domain of the function is all real numbers less than or equal to −1.
b. the range of the function is all real numbers greater than or equal to 0.
c. the range of the function is all real numbers less than or equal to 0.
d. the domain of the function is all real numbers less than or equal to 0.

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

Answers: 2

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Answers

answered: george6871

The correct answers are:

Question 1: C. The domain of the graph is all real numbers less than or equal to 0. ; and Question #2: C. The range of the function is all real numbers less than or equal to 0.

Explanation:

For Question #1:

We cannot use real numbers to take the square root of a negative number. This means if we are to have a real number value for this, we can only use values of x that are negative; this will make it the square root of a "negative negative," which makes it the square root of a positive. This means the domain, or list of all possible x values, would be real numbers less than or equal to 0.

For Question #2:

We can see in the graph that the domain, or set of x values, goes from 0 towards positive infinity. We can also see that the range, or set of y values, starts at 0 and decreases; this means that the range is all real numbers less than or equal to 0.

answered: jocejay83681

(1). The correct option is $\boxed{\bf option C}$ .

(2). The correct option is $\boxed{\bf option C}$ .

Further explanation:

Concept used:

The domain of the function f(x) is the set of all -values for which the function f(x) exists as a real number and range is defined as all the corresponding values of f(x) for the values of in domain.

Calculation:

Part (1)

Th function is given as follows:

$f(x)=\sqrt{-x}$

In the given function a radical term is present and the argument is .

From the given function to be defined the argument should be always greater or equal to .

$\begin{aligned}-x\geq 0\\x\leq 0\end{aligned}$

From the above calculation it is concluded that the domain of given function is $(-\infty,0]$ .

Figure 1 (attached in the end) represents the graph of the function $f(x)=\sqrt{-x}$ .

From figure 1 it is observed that the curve of the function $f(x)=\sqrt{-x}$ always the above -axis so, it can be said that the value of the function is always greater or equal to .

Therefore, the range of the function $f(x)=\sqrt{-x}$ is $[0,\infty)$ .

This implies that the correct option is $\boxed{\bf option C}$ .

Part (2)

The function is $f(x)=-\sqrt{x}$ .

In the given function a radical term is present and the argument is .

From the given function to be defined the argument should be always greater or equal to .

$\boxed{x\geq 0}$

Therefore, the domain of the function $f(x)=-\sqrt{x}$ is $[0,\infty)$ .

Figure 2 (attached in the end) represents the graph of the function $f(x)=-\sqrt{x}$ .

From figure 2 it is observed that the curve of the function $f(x)=-\sqrt{x}$ always below the -axis so, it can be said that the value of function always less than or equal to .

As per the above statement it is concluded that the range of the function $f(x)=-\sqrt{x}$ is $(-\infty,0]$ .

This implies that the correct option is $\boxed{\bf option C}$ .

Learn more:

1. Learn more about functions link

2. Learn more about problem on numbers link

Answer details:

Grade: Senior school

Subject: Mathematics

Chapter: Function

Keywords: Function, domain, range, corresponding value, real number, exist, domain set, range set, radical, inequality, greater than, less than, argument, square root of -x, -square root of x.