Question

I need help answering this question Also, provide domain and range of the function.

Answer 1

The y value of the functions when x is less than -1 is y = 2. The y values of the function when x is bigger than 2 is y = -1; also the filled circle is the one at y = 2. Then the rule for the function is:

Option A:

`f(x)=\begin{cases}2,\text{ if }x\le-1 \\ -1,\text{ if }x>2\end{cases}`

Domain of f(x):

The domain are all the values of x for which f(x) is defined. Since there is a leap from x = -1 to x = 2, the domain is:

Interval notation:

`\text{ The domain is }(-\infty,-1\rbrack\cup(2,\infty)`

Range of f(x):

The range are all the values of y that the function gets. We have two values, -1 and 2

`\text{ The range is }\mleft\lbrace-1,2\mright\rbrace`