Question

generally speaking, we use x to represent
and y to represent of a function.
question 3 8 pts
which of the following best describes the difference
between a relation and a function? select all that
apply.
if it is a function, it can be graphed.
in a function, each input should only have one output.
in a function, each output should have only one input.
if it is a function, it has an equation.
a function passes the vertical line test test

Explanation:

1. Analyze each option:

• "If it is a FUNCTION, it can be GRAPHED": Relations can also be graphed (e.g., a circle is a relation but not a function), so this is incorrect.
• "In a FUNCTION, each INPUT should only have one OUTPUT": By definition, a function is a special type of relation where each input (domain element) has exactly one output (range element). This is correct.
• "In a FUNCTION, each OUTPUT should have only one INPUT": A function can have multiple inputs mapping to the same output (e.g., \(y = x^2\), \(x = 2\) and \(x=- 2\) both map to \(y = 4\)), so this is incorrect.
• "If it is a FUNCTION, it has an EQUATION": Relations can also be defined by equations (e.g., \(x^{2}+y^{2}=1\) is a relation), so this is incorrect.
• "A FUNCTION passes the Vertical Line Test": The vertical line test is a way to determine if a graph represents a function. If a graph passes the vertical line test, it means no vertical line intersects the graph more than once, which is equivalent to saying each input has one output. This is correct.

Answer:

• In a FUNCTION, each INPUT should only have one OUTPUT.
• A FUNCTION passes the Vertical Line Test.