Front

What is the composition of functions?

Back

The composition of functions, denoted as \( (g \circ f)(x) \), is the application of one function to the results of another. It is defined as \( g(f(x)) \).

Front

How do you find the domain of a function?

Back

The domain of a function is the set of all possible input values (x-values) for which the function is defined. To find the domain, identify any restrictions such as division by zero or square roots of negative numbers.

Front

What is the range of a function?

Back

The range of a function is the set of all possible output values (y-values) that the function can produce based on its domain.

Front

What does an augmented matrix represent?

Back

An augmented matrix represents a system of linear equations, where each row corresponds to an equation and the last column represents the constants from the equations.

Front

How do you solve a system of linear equations using an augmented matrix?

Back

You can solve a system of linear equations using row operations to reduce the augmented matrix to row-echelon form or reduced row-echelon form, then interpret the results to find the values of the variables.

Front

What is the significance of the vertical line test?

Back

The vertical line test is a method to determine if a curve is a function. If any vertical line intersects the curve more than once, the curve is not a function.

Front

What is a linear function?

Back

A linear function is a function that can be expressed in the form \( f(x) = mx + b \), where \( m \) is the slope and \( b \) is the y-intercept.

Front

What is the slope of a line?

Back

The slope of a line measures its steepness and is calculated as the change in y divided by the change in x (rise over run). It is often represented as \( m \).

Front

What is the y-intercept of a function?

Back

The y-intercept of a function is the point where the graph of the function intersects the y-axis, represented as \( (0, b) \) in the equation \( f(x) = mx + b \).

Front

What is the difference between a function and a relation?

Back

A function is a specific type of relation where each input (x-value) is associated with exactly one output (y-value). A relation can have multiple outputs for a single input.