Understanding Intercepts of a Function

The video tutorial explains how to find the intercepts of a given function, specifically focusing on both X and Y intercepts. It begins by introducing the concept of intercepts and the method to find them. The tutorial then details the process of finding X-intercepts by setting the function equal to zero and solving the resulting absolute value equation. It also covers finding the Y-intercept by setting X to zero and solving for Y. Finally, the video demonstrates how to verify these intercepts graphically using Desmos, ensuring the calculations are correct.

What is the first step in finding the X-intercepts of a function?

• Set y equal to zero and solve for x

• Set x equal to zero and solve for y

• Graph the function

• Differentiate the function

When solving an absolute value equation, what should you do after isolating the absolute value?

• Multiply both sides by the coefficient of the absolute value

• Divide both sides by the coefficient of the absolute value

• Subtract a constant from both sides

• Add a constant to both sides

What are the possible values for the expression inside the absolute value when solving for X-intercepts?

• Only positive values

• Only negative values

• Both positive and negative values

• Zero only

How do you express the X-intercepts of a function?

• As a single number

• As a fraction

• As a decimal

• As ordered pairs

What is the Y-intercept of the function given in the problem?

• (1, 1)

• (0, -1)

• (1, 0)

• (0, 1)

What is the process to find the Y-intercept of a function?

• Graph the function

• Differentiate the function

• Set y equal to zero and solve for x

• Set x equal to zero and solve for y

Which tool was used to verify the intercepts graphically?

• Calculator

• Excel

• Mathematica

• Desmos.com

What is the significance of verifying intercepts graphically?

• To check for calculation errors

• To find the slope of the function

• To calculate the derivative

• To determine the domain of the function

What are the X-intercepts of the function as found in the problem?

• (1, 0) and (-1, 0)

• (0.5, 0) and (-2.5, 0)

• (3, 0) and (-3, 0)

• (2, 0) and (-2, 0)

Why is it important to express intercepts as ordered pairs?

• To make the function continuous

• To accurately represent points on a graph

• To find the derivative

• To simplify calculations