Identifying Linear Functions and Characteristics

This video tutorial explains how to identify linear functions from both graphs and equations. It begins by defining a linear function as one whose graph is a straight line and discusses the vertical line test to determine if a graph represents a function. The tutorial then demonstrates how to identify linear functions from equations by plotting points and checking if the graph is a straight line. It also covers the general form of linear equations, y = mx + b, and the importance of exponents. Finally, the video provides practice examples and summarizes the key points.

What is the main objective of this lesson?

• To learn about quadratic functions

• To explore exponential functions

• To identify linear functions from graphs and equations

• To understand polynomial functions

How is a linear function graphically represented?

• As a parabola

• As a curve

• As a circle

• As a straight line

What is the purpose of the vertical line test?

• To calculate the y-intercept

• To find the slope of a line

• To check if a graph is a function

• To determine if a graph is a linear function

Which of the following graphs represents a linear function?

• A graph that is a straight line and passes the vertical line test

• A graph that is a curve

• A graph that is a straight line but fails the vertical line test

• A graph that is a circle

What is the first step in identifying a linear function from an equation?

• Find the y-intercept

• Solve for x

• Graph the equation

• Check if the equation is quadratic

What does it mean if a graph of an equation is not a straight line?

• The equation is exponential

• The equation is quadratic

• The equation does not represent a linear function

• The equation represents a linear function

What is the slope-intercept form of a linear equation?

• y = a^x

• y = x^2 + y^2 = r^2

• y = ax^2 + bx + c

• y = mx + b

What is the degree of a variable if it has no exponent shown?

• 3

• 1

• 0

• 2

Which of the following equations is a linear function?

• y = x^2 + 2x + 1

• y = x^3 - x

• y = 2x - 1

• y = 1/x

What is the key characteristic of a linear function's graph?

• It is a straight line

• It is a curve

• It is a circle

• It is a parabola