Question

can someone help me answer these? im really confused and have a quiz on it tomorrow.. thank you so much!!

Answer 1

Domain:
`x > -5` or
`(-5,\infty)`

Range:
`y\geq -3` or
`[-3,\infty)`

Explanation:

The domain is essentially the set of x-values in a given graph. In this graph. we see that the lowest x-value is an unfilled dot when x=-5. The unfilled dot means that the function
`f(x)` doesn't include -5. We then see that the x-value goes to positive infinity. This means that
`x` must be greater than -5. It is not greater or equal to -5 because the dot is not filled.

Therefore, we have that
`x > -5`. To convert to interval notation we can take the lower value (-5) and put it on the left side and put the higher value (
`\infty`) and put it on the right side. Since the graph doesn't include -5, we can put parentheses around both values to get
`(-5,\infty)`.

Note: We always put parentheses around both
`\infty` and
`-\infty`.

The range is basically the same as the domain but with the y-value. We can see that the lowest y-value is y=-3. This includes -3 since the line fills the point in. Then we see that the highest y-value is once again positive infinity. This means that
`y\geq-3`.

Now when we convert to interval notation, we have -3 and
`\infty`. This time since y=-3 is included in the function, we put a hard bracket around -3. Thus, we get
`[-3,\infty)`.

Hope this helps!