Answer
- The graph represents a function.
- It is a discrete function.
- Domain = (-7 ≤ x ≤ 7) OR [-7, 7]
- Range = (-3 ≤ y ≤ 6) OR [-3, 6]
Step-by-step explanation
- Determine whether it's a function or not,
A function is an expression that takes up each value of an independent variable (x) and gives a corresponding value of a dependent variable (y) without the same values of the independent variable (x) giving different values of the dependent variable (y).
We can see from the image attached that each value of x gives only one value of y not one value of x giving numerous y-values.
So, this relation is a function.
- Discrete or Continuous function,
A discrete function is a function whose possible values are limited within a particular range. The numbers vary from one another in a regular pattern. The graph of discrete function has endpoints.
A continuous function is one where the function can take on virtually any real number value. The graph of a continous extends to infinity with two arrows added to the end of the arrows to indicate that it extends till infinity.
So, we can see from the graph again that the graph of this only covers a limited area with no arrows at the end of the graphs, hence, this graph is a discrete function and not a continuous function.
- Domain of the function,
The domain of a function refers to the values of the independent variable (x), where the dependent variable [y or f(x)] or the function has a corresponding real value. The domain is simply the values of x for which the output also exists. It is the region around the x-axis that the graph of the function spans.
From this graph, we can see that the region of the x-axis that this graph covers is from x = -7 to x = 7. So,
Domain = (-7 ≤ x ≤ 7) OR [-7, 7]
- Range of the function,
The range of a function refers to the region of values where the function can exist. It refers to the values that the dependent variable [y or f(x)] can take on. It is the region around the y-axis that the graph of the function spans.
From the graph, we can see that the region of the y-axis that thsi graph covers is from y = -3 to y = 6. So,
Range = (-3 ≤ y ≤ 6) OR [-3, 6]
Hope this Helps!!!