Question

Which of the following could be an example of a function with a domain. [a,∞) and a range (-∞, b] where a>0 and b>0? ○ A. f(x)=√√√x+a-b А. O B. f₁.x) = -√√√x=a+b ○ c. f(x)=√√√(x−b) + a ○ D. f(x) = √x + a−b|

Answer 1

Explanation:

Step 1. We need to find the option for which the domain is:

$\lbrack a,\infty)$

and the range

$(-\infty,b\rbrack$

Step 2. Let's start with the domain. The domain is the set of possible x values.

when we have a square root, the value inside the square root has to be greater than or equal to 0, for options B and D:

Solving for x on each inequality:

Step 3. That means that for B, the domain is:

$\begin{gathered} \lbrack a,\infty) \\ and\text{ for B:} \\ \lbrack-a,\infty) \end{gathered}$

Only B meets the condition for the domain, since the other two options A, and C has third roots, the values inside of them can be negative and the domain is not [a, infinity).

Step 4. If we graph the function for option B, here we are using a=1 and b=2 but these could be any values since it is just for demonstration

We can see that the values possible for the y-axis (the range) go from minus infinity and stop at value b.

Therefore, option B also has the correct range.

Answer.

B

$f(x)=-\sqrt{x-a}+b$