The equation is .
Make a table:
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The ordered pairs are .
Graph:
\Graph of the equation is .
Plot the points.
Observe the graph:
\Every real number is the -coordinate of some point on the line.
So, the domain (-coordinates on the line) is set of all real numbers.
Every real number is the -coordinate of some point on the line.
So, the range (-coordinates on the line) is also set of all real numbers.
Vertical line test:
\Draw the vertical lines through the points.
\Observe the graph:
\There is no vertical line that contains more than one point.
\The equation passes the vertical line test.
\The equation represents a function.
\Find the function is one-to-one, onto and continuous or discrete.
\Each -value is paired by exactly one
-value and each
-value is paired by exactly one
-value.
Hence, the equation is one-to-one and onto function.
\As the graph is a solid line without breaks, the function is Continuous.
\The domain (-coordinates on the line) is set of all real numbers.
The range (-coordinates on the line) is also set of all real numbers.
The equation represents a function.
The equation is one-to-one and onto function.
\The function is Continuous.