The relation is . \ \

\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \

\ x \	\ y = 2.5x \	\ y \	\ (x, y) \
\ 0 \	\ Y = 2.5(0) = 0 \	\ 0 \	\ (0, 0) \
\ 1 \	\ Y = 2.5(1) = 2.5 \	\ 2.5 \	\ (1, 2.5) \
\ 2 \	\ Y = 2.5(2) = 5 \	\ 5 \	\ (2, 5) \
\ 3 \	\ Y = 2.5(3) = 0 \	\ 7.5 \	\ (3, 7.5) \
\ 4 \	\ Y = 2.5(4) = 0 \	\ 7 \	\ (4, 10) \

\

Express the relation as ordered pairs. 

Create a coordinate system and plot the ordered pairs.

Draw a line through the points.

Since x can be any real number, there are an infinite number of ordered pairs that can be graphed. All of them lie on the line shown

Every real number is the x-coordinate of some point on the line.

So, the domain (x-coordinates on the line) is set of all real numbers.

Every real number is the y-coordinate of some point on the line.

So, the range (y-coordinates on the line) is also set of all real numbers.

The relation is Continuous.

Draw the vertical lines through the points. Observe that there is no vertical line contains more than one of the points.

This graph passes the vertical line test.  For each x-value, there is exactly one y-value, so the equation represents a function.

The domain (x-coordinates on the line) is set of all real numbers.

The range (y-coordinates on the line) is also set of all real numbers.

The relation is Continuous.

The equation represents a function.