Chapter 3 Midpoint Flashcard

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

How can you determine if a relation is a function?

Back

A relation is a function if every input (x-value) has exactly one output (y-value). This can be checked using the vertical line test on a graph.

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 the curve is not a function.

Front

What is an example of a function?

Back

An example of a function is f(x) = 2x + 3, where for every x-value, there is a unique y-value.

Front

What is an example of a non-function?

Back

An example of a non-function is the relation defined by the equation x^2 + y^2 = 1, as it can produce multiple y-values for a single x-value.

Front

What does it mean for a function to be one-to-one?

Back

A one-to-one function is a function where each output is related to exactly one input, meaning no two different inputs produce the same output.

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

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 f(x) = 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 f(x) = ax^2 + bx + c, where a, b, and c are constants and a ≠ 0.