Is It a Function? Yes Function Type: Both Discrete or Continuous? Continuous
Practice makes perfect
After graphing the given equation, we can find the domain and range. Then we can determine whether the equation is a function, is one-to-one, onto, both, or neither, and whether it is discrete or continuous.
Graph
To draw the graph of the given equation, we will use a table of values. Substituting some arbitrary values of x into the given equation will give us the corresponding y-values.
x
2x-3
y=2x-3
0
2( 0)-3
-3
1
2( 1)-3
- 1
2
2( 2)-3
1
3
2( 3)-3
3
Now let's plot these ( x, y) coordinate pairs and connect them with a line.
Is it a Function?
We can see that the graph we plotted passes the Vertical Line Test. Therefore, we know that the equation is a function.
One-to-one, Onto, Both, or Neither?
In order to determine if a function is one-to-one, onto, both, or neither, let's review what each of these types of relationship means.
One-to-one: Each element of the domain is paired with exactly one unique element of the range. In other words, this type of function would pass a horizontal line test.
Onto: Every element in the range must be paired with at least one element of the domain.
Both: Each element of the domain is paired with exactly one element of the range and each element in the range is paired with exactly one element in the domain.
Observing our graph, we see that every x-value is paired with exactly one unique y-value. Similarly, every y-value corresponds to an x-value. As such, the function is both one-to-one and onto.
Discrete or Continuous?
Because the graph is a solid line without breaks, the function is continuous.
