Linear / Nonlinear / Functions REVIEW #2

Front

What is a function in mathematics?

Back

A function is a relation that assigns exactly one output for each input.

Front

How can you determine if a relation is a function using a mapping diagram?

Back

A relation is not a function if any input is associated with more than one output in the mapping diagram.

Front

What is the difference between linear and nonlinear functions?

Back

Linear functions create straight-line graphs, while nonlinear functions create curves or other shapes.

Front

What role do exponents play in determining the type of graph an equation will create?

Back

Exponents indicate whether the equation is linear (exponent of 1) or nonlinear (exponent greater than 1 or less than 1).

Front

What is an example of a linear equation?

Back

An example of a linear equation is y = 2x + 3.

Front

What is an example of a nonlinear equation?

Back

An example of a nonlinear equation is y = x^2 + 2.

Front

What does it mean for a line to have an undefined slope?

Back

A line with an undefined slope is vertical and does not pass the vertical line test for functions.

Front

What is the vertical line test?

Back

The vertical line test states that if a vertical line intersects a graph at more than one point, the graph does not represent a function.

Front

What are the characteristics of a linear graph?

Back

Linear graphs have a constant rate of change and can be represented by a linear equation.

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, indicating the steepness of the line.