1. Determine the domain and range of each relation and determine if it’s a function or not.x y 2 1
1) {( 1 , 3),(– 1 , 3 ),( 2 , 0)} 2) D R 3
– 1 1 2 D R 2 1 2
Yes, it’s a function because each member in the domain is assigned to exactly one member in the range.
No, it’s not a function because 2 is assigned to both 1 and 2.

2. 8.02 Linear and Non – Linear Functions

3. Functional Notation The equation y = 5x + 1
can be rewritten in functional notation.
To do this, replace the y with f(x)
y = 5x f(x) = 5x + 1
f(x) is read as “f of x”
Any equation with f(x) is written in functional notation.

4. We can tell if a function is linear by examination.
An equation represents a linear function if all the variables are raised to the first power.
Determine if the following represent a linear function.
f(x) = x – 4
Yes
f(x) = x2
No, because x is raised to the 2nd power.
f(x) = 2x + 8
Yes
f(x) = 2
Yes
f(x) =
No, because it’s a square root.

5. Determine if the graph represent a function.
We can determine if a graph represents a function by using the vertical line test.
A line represents a function if one draws a vertical line anywhere along the graph of a line and that vertical line intersects the line at only one point.
Determine if the graph represent a function.
Yes, it’s a function because any drawn vertical line will only intersect the graph at only one point.

6. Determine if the graphs represent a function.
No, it’s not a function because the vertical line intersects the graph at two points.
Yes, it’s a function because the vertical line intersects the graph at only one point.

7. Try This: f(x) = 3x2 – x + 2 No f(x) = 5x + 2 Yes
Determine if the following represents a linear function.
f(x) = 3x2 – x + 2 No
f(x) = 5x + 2
Yes
Determine if the following represents a function.
No, the vertical line intersects the graph at two points.
Yes, the vertical line intersects the graph at only one point.