Function or Not a Function

Front

What is a function?

Back

A function is a relation between a set of inputs and a set of possible outputs where each input is related to exactly one output.

Front

What is the vertical line test?

Back

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

Front

What does it mean for a relation to be not a function?

Back

A relation is not a function if at least one input is related to more than one output.

Front

Example of a function: y = 2x + 3. Is this a function?

Back

Yes, this is a function because for every value of x, there is exactly one value of y.

Front

Example of a relation that is not a function: y^2 = x. Is this a function?

Back

No, this is not a function because for some values of x, there are two corresponding values of y.

Front

What is 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 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 output for different inputs?

Back

Yes, a function can have the same output for different inputs, as long as each input has only one output.

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.

Front

What is a quadratic function?

Back

A quadratic function is a function that can be expressed in the form y = ax^2 + bx + c, where a, b, and c are constants and a ≠ 0.