Understanding Function Behavior and Graphs

The video tutorial covers lesson 3-6 on sketching graphs and comparing functions. It reviews key concepts such as positive and negative functions, intercepts, and end behavior. Two examples are provided: sketching a graph of a roller coaster's line throughout the day and a dolphin's height above water over time. The tutorial emphasizes understanding graph features like x-intercepts, y-intercepts, relative minimums and maximums, and symmetry.

What is the main focus of lesson 3-6?

• Learning about geometry

• Solving algebraic equations

• Sketching graphs and comparing functions

• Understanding calculus concepts

When is a function considered positive?

• When it is on the origin

• When it is below the x-axis

• When it is above the x-axis

• When it is on the y-axis

What does it mean when a function is increasing?

• The function is constant

• The function is moving downwards

• The function is at its maximum

• The function is moving upwards

What are x-intercepts?

• Points where the graph crosses the x-axis

• Points where the graph crosses the y-axis

• Points where the graph is at its maximum

• Points where the graph is at its minimum

What is the end behavior of a function?

• The behavior of the function at its minimum

• The behavior of the function at the start

• The behavior of the function at the end

• The behavior of the function at its maximum

In the roller coaster example, what is the y-intercept?

• 12

• 5.3

• 0

• 220

What is the relative maximum in the roller coaster example?

• 9.9 at 643

• 1.4 at 440

• Both 1.4 at 440 and 9.9 at 643

• 5.3 at 133

When is the roller coaster graph positive?

• Between -0.5 and 12

• Less than -0.5

• Between 5.3 and 9.9

• Greater than 12

What is the end behavior of the roller coaster graph?

• Y increases as X increases

• Y increases as X decreases

• Y remains constant

• Y decreases as X increases

In the dolphin example, where are the x-intercepts?

• At 2 and 6 seconds

• At 4 and 10 seconds

• At 0 and 8 seconds

• At 1 and 9 seconds