$\"\"$

The relation is $\"\"$ . \ \

\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \
\
x
\ \
y = x + 3.5
\ \
y
\ \
(x, y)
\
\
4
\ \
Y = 4 + 3.5 = 7.5
\ \
7.5
\ \
(4, 7.5)
\
\
5
\ \
Y = 5 + 3.5 = 8.5
\ \
8.5
\ \
(5, 8.5)
\
\
7
\ \
Y = 7 + 3.5 = 10.5
\ \
10.5
\ \
(7, 10.5)
\
\
8
\ \
Y = 8 + 3.5 = 11.5
\ \
11.5
\ \
(8, 11.5)
\
\
12
\ \
Y = 12 + 3.5 = 15.5
\ \
12.5
\ \
(12, 15.5)
\
\

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 y = x +3.5 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 y = x + 3.5 represents a function.

\ x \	\ *y = x +* 3.5 \	\ y \	\ *(x, y)* \
\ 4 \	\ Y = 4 + 3.5 = 7.5 \	\ 7.5 \	\ (4, 7.5) \
\ 5 \	\ Y = 5 + 3.5 = 8.5 \	\ 8.5 \	\ (5, 8.5) \
\ 7 \	\ Y = 7 + 3.5 = 10.5 \	\ 10.5 \	\ (7, 10.5) \
\ 8 \	\ Y = 8 + 3.5 = 11.5 \	\ 11.5 \	\ (8, 11.5) \
\ 12 \	\ Y = 12 + 3.5 = 15.5 \	\ 12.5 \	\ (12, 15.5) \