Functions Review

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 the definition of a linear equation?

Back

A linear equation is an equation that makes a straight line when it is graphed. It can be written in the form y = mx + b, where m is the slope and b is the y-intercept.

Front

What does the slope of a line represent?

Back

The slope of a line represents the rate of change of the dependent variable with respect to the independent variable.

Front

How do 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.

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 it is not a function.

Front

What is the equation for direct variation?

Back

The equation for direct variation is y = kx, where k is a non-zero constant.

Front

What is the difference between independent and dependent variables?

Back

The independent variable is the variable that is changed or controlled in an experiment, while the dependent variable is the variable that is measured or affected.

Front

What does it mean for a function to be linear?

Back

A linear function is a function whose graph is a straight line, indicating a constant rate of change.

Front

What is a rate of change?

Back

The rate of change is a measure of how much a quantity changes in relation to another quantity, often expressed as a ratio.

Front

How do you find the rate of change from a graph?

Back

To find the rate of change from a graph, calculate the change in the y-values divided by the change in the x-values (rise over run).