Question

3 if x < -1

h(x) = {x+1ifx>1



I have to graph each function and identify the domain and range. If anyone could explain this to me in simple terms that would be greatly appreciated!!

Answer 1

The domain and the range of the function are (-∝, -1) U (1, ∝) and (2, ∝), respectively

How to determine the domain and the range of the function

From the question, we have the following parameters that can be used in our computation:

`h(x) = \left\{ \begin{array}{lr} 3, & \text{if } x < -1\\ x + 1, & \text{if } x > 1\end{array}`

To plot the above function, we plot each subfunction in the respective domains

i.e. we plot h(x) = 3 in the domain x < -1 and h(x) = x + 1 in the domain x > 1

The graph of the function is attached

By definition:

• The domain is the possible x values
• The range is the possible y values

From the graph, we have

x values: Start from negative infinity, stops at x = -1 (exclusive), continues indefinitely from x = 1 (exclusive)

So, the domain is (-∝, -1) U (1, ∝)

Also, have

y values: Start from y = 2 (exclusive) and continues indefinitely

So, the range is (2, ∝)