Function or Not a Function?

Front

What is a function?

Back

A function is a relation where each input (x value) has exactly one output (y value).

Front

What is the vertical line test?

Back

The vertical line test is a method to determine if a graph represents a function. If a vertical line intersects the graph at more than one point, it is not a function.

Front

What does it mean if a graph passes the vertical line test?

Back

If a graph passes the vertical line test, it means that for every x value, there is only one corresponding y value, confirming it is a function.

Front

What is an example of a function?

Back

An example of a function is the equation y = 2x + 3, where each x value has a unique y value.

Front

What is an example of a relation that is not a function?

Back

An example of a relation that is not a function is the equation x^2 + y^2 = 1, which can have multiple y values for a single x value.

Front

What is the definition of a domain in a function?

Back

The domain of a function is the set of all possible input values (x values) that the function can accept.

Front

What is the definition of a range in a function?

Back

The range of a function is the set of all possible output values (y values) that the function can produce.

Front

Can a function have the same y value for different x values?

Back

Yes, a function can have the same y value for different x values, as long as each x value has only one y value.

Front

What is a one-to-one function?

Back

A one-to-one function is a function where each x value corresponds to a unique y value and each y value corresponds to a unique x value.

Front

What is a linear function?

Back

A linear function is a function that graphs to a straight line and can be expressed in the form y = mx + b, where m is the slope and b is the y-intercept.