Identifying Linear Functions & Function Notation

Front

What is a linear function?

Back

A linear function is a function that graphs to a straight line. It can be expressed in the form f(x) = mx + b, where m is the slope and b is the y-intercept.

Front

What is function notation?

Back

Function notation is a way to represent functions in mathematics. It uses symbols like f(x) to denote the output of a function f for a given input x.

Front

How can you identify a linear function from a set of points?

Back

A linear function can be identified if the points form a straight line when plotted on a graph.

Front

What does the slope of a linear function represent?

Back

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

Front

What is the y-intercept in a linear function?

Back

The y-intercept is the point where the graph of the function crosses the y-axis, represented by the value of b in the function f(x) = mx + b.

Front

If f(x) = 2x + 3, what is f(0)?

Back

f(0) = 2(0) + 3 = 3.

Front

What is the difference between linear and nonlinear functions?

Back

Linear functions graph to straight lines, while nonlinear functions graph to curves or other shapes.

Front

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

Back

A table represents a linear function if the differences between consecutive y-values are constant for equal differences in x-values.

Front

What is the formula for finding the slope between two points (x1, y1) and (x2, y2)?

Back

The slope (m) is calculated as m = (y2 - y1) / (x2 - x1).

Front

If f(x) = -x + 5, what is the slope of the function?

Back

The slope of the function f(x) = -x + 5 is -1.