Construct & Describe Functions

Front

What is a function?

Back

A function is a relation that assigns exactly one output for each input. It can be represented as an equation, a graph, or a table.

Front

What is the slope of a linear function?

Back

The slope of a linear function is the rate of change of the function, calculated as the change in y divided by the change in x (rise/run).

Front

What does it mean for a function to be linear?

Back

Front

What is the y-intercept of a function?

Back

The y-intercept is the point where the graph of a function crosses the y-axis, represented by the value of y when x = 0.

Front

How do you determine if a function is increasing or decreasing?

Back

A function is increasing if the output values rise as the input values increase, and decreasing if the output values fall as the input values increase.

Front

What is a nonlinear function?

Back

A nonlinear function is a function that does not graph to a straight line. Its rate of change varies and can be represented by curves.

Front

What is the formula for calculating the rate of change between two points?

Back

Front

What is the difference between a linear increasing function and a linear decreasing function?

Back

A linear increasing function has a positive slope (rises from left to right), while a linear decreasing function has a negative slope (falls from left to right).

Front

What does it mean for a function to be increasing?

Back

A function is increasing if, for any two points in its domain, if the first point has a smaller x-value than the second, the first point will have a smaller y-value.

Front

What is a graph?

Back

A graph is a visual representation of a function, showing the relationship between the input (x-axis) and output (y-axis) values.