Transforming Functions: Key Concepts and Techniques

The video tutorial covers the transformation of functions, focusing on graphing absolute value and quadratic functions. It demonstrates how to use a graphing calculator to plot y = |x| and y = |x| + 2, as well as y = x^2 and y = (x + 3)^2. The tutorial explains how these transformations shift the graphs and provides step-by-step instructions for using a calculator to achieve accurate results. The teacher emphasizes the importance of understanding graph transformations and encourages students to practice using graphing tools.

Why is it important to use a graphing calculator or Desmos for this lesson?

• To make the lesson more interesting

• To avoid manual calculations

• To ensure accuracy in graphing

• To save time

What is the first step in graphing y = |x| + 2 on a calculator?

• Use a different calculator

• Plot points manually

• Go to the 'math' menu and select 'absolute value'

• Enter the equation directly

Where should the +2 be placed in the equation y = |x| + 2?

• It doesn't matter

• Inside the absolute value bars

• Outside the absolute value bars

• Before the absolute value bars

What is the y-coordinate when x = -3 for the function y = |x| + 2?

• 1

• 3

• 5

• 7

How does the graph of y = |x| change when transformed to y = |x| + 2?

• It shifts 2 units to the right

• It shifts 2 units to the left

• It shifts 2 units upward

• It shifts 2 units downward

What is the new function to be graphed after y = x^2?

• y = x^2 + 3

• y = x^2 - 3

• y = (x + 3)^2

• y = (x - 3)^2

Why did the instructor choose points like -5 and 4 for the function y = (x + 3)^2?

• To make the graph look better

• To avoid large numbers

• To simplify calculations

• To fit the points on the graph

What is the y-coordinate when x = -6 for the function y = (x + 3)^2?

• 9

• 18

• 12

• 15

How does the graph of y = x^2 change when transformed to y = (x + 3)^2?

• It shifts 3 units upward

• It shifts 3 units downward

• It shifts 3 units to the left

• It shifts 3 units to the right

What should students do with their notes for the next class?

• Review them

• Share them with friends

• Discard them

• Forget about them