Identifying linear functions

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 a linear function?

Back

A linear function is a function that can be graphically represented in the Cartesian plane as a straight line. It has the form y = 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. Examples include quadratic functions, exponential functions, and any function that involves variables raised to a power other than one.

Front

Identify the linear function: y = 2x + 3 or y = x^2 - 4?

Back

y = 2x + 3 is a linear function.

Front

What does the slope of a linear function represent?

Back

The slope of a linear function represents the rate of change of the function; it indicates how much y changes for a unit change in x.

Front

What is the y-intercept in the equation y = mx + b?

Back

The y-intercept is the value of y when x is 0. It is represented by b in the equation y = mx + b.

Front

Which of the following is a linear equation: y = 3x + 2 or y = 4x^2 - 1?

Back

y = 3x + 2 is a linear equation.

Front

What is the general form of a linear equation?

Back

The general form of a linear equation is Ax + By = C, where A, B, and C are constants.

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 any vertical line intersects the curve at more than one point, then the curve is not a function.