Graph Transformations and Exponents

The video tutorial explores the concept of cubic functions, specifically y = x^3, using a table of values to understand how positive and negative numbers affect the outcome. It explains the process of cubing negative numbers and how it results in negative values. The tutorial also covers graphing y = x^3, highlighting its unique shape. Additionally, the video examines the equation x = y^2, discussing its graph transformation and why it does not accommodate negative x-values.

What is the result of cubing the number 2?

• 8

• 10

• 4

• 6

When you cube a negative number, what is the sign of the result?

• Negative

• Zero

• Undefined

• Positive

What shape does the graph of y = x^3 resemble on one side?

• A sine wave

• A parabola

• A straight line

• A circle

What happens to the graph of y = x^3 when you look at negative x values?

• It mirrors the positive side

• It becomes a straight line

• It disappears

• It flips upside down

What is the result of cubing -1?

• 1

• -1

• 2

• 0

What happens to the graph of y = x^2 when you swap x and y?

• It becomes a circle

• It rotates 90 degrees

• It remains unchanged

• It flips upside down

What is the equation when x and y are swapped in y = x^2?

• y = x

• y = x^2

• x = y^2

• x = y

Why can't you use negative x values in the equation x = y^2?

• It results in an undefined value

• It results in a negative number

• It results in a complex number

• It results in zero

What happens when you try to square a negative number?

• You get a negative result

• You get a positive result

• You get zero

• You get an undefined result

What is the result of squaring -5?

• 25

• -25

• 0

• 5