ch 3 rev for final

Front

What is a linear function?

Back

A linear function is a function that can be graphically represented as a straight line. It has the form f(x) = mx + b, where m is the slope and b is the y-intercept.

Front

What is a nonlinear function?

Back

A nonlinear function is a function that does not form a straight line when graphed. Its graph can be curved or have varying slopes.

Front

How can you determine if a graph represents a function?

Back

A graph represents a function if every vertical line intersects the graph at most once (Vertical Line Test).

Front

What is the slope of a linear function?

Back

The slope of a linear function is the ratio of the change in y to the change in x (rise over run). It indicates the steepness of the line.

Front

What does the y-intercept represent in a linear function?

Back

The y-intercept is the point where the graph of the function crosses the y-axis, representing the value of f(x) when x = 0.

Front

Given f(x) = -4x - 10, what is the slope?

Back

The slope is -4.

Front

What is the solution to the equation f(x) = -4x - 10 when f(x) = 10?

Back

x = -5.

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) has exactly one output (y-value).

Front

What is the standard form of a linear equation?

Back

The standard form of a linear equation is Ax + By = C, where A, B, and C are integers, and A should be non-negative.

Front

What does it mean for a function to be increasing?

Back

A function is increasing if, as x increases, the value of f(x) also increases.