Interpreting & Sketching 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 does it mean for a function to be linear?

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. Its rate of change varies, and it can be represented by equations that include exponents, roots, or other non-linear terms.

Front

How do you determine if a table of values represents a linear function?

Back

To determine if a table of values represents a linear function, check if the differences between consecutive outputs (y-values) are constant for equal intervals of inputs (x-values).

Front

What is the slope of a line?

Back

The slope of a line is a measure of its steepness, calculated as the change in the y-value divided by the change in the x-value (rise/run).

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

What does it mean for a function to be increasing?

Back

A function is increasing on an interval if, as the input values increase, the output values also increase.

Front

What does it mean for a function to be constant?

Back

A function is constant if its output value does not change regardless of the input value; it is represented by a horizontal line on a graph.

Front

What is a graph of a decreasing function?

Back

A graph of a decreasing function slopes downward from left to right, indicating that as the input values increase, the output values decrease.

Front

What is the domain of a function?

Back

The domain of a function is the complete set of possible values of the independent variable (input) for which the function is defined.