Exploring Cubic and Cube Root Functions

The video tutorial covers inverse functions, focusing on cube root and cubic functions. It reviews previous topics like linear, quadratic, and square root functions, and explains the vertical and horizontal line tests to determine if a function is one-to-one. The tutorial explores the relationship between cube root and cubic functions, demonstrating how translations affect their inverses. Examples and exercises are provided to reinforce understanding, and graphing tools are used to analyze function properties. The lesson concludes with a summary and homework assignment.

What is the inverse of a horizontal line?

• A vertical line

• A curved line

• A diagonal line

• A horizontal line

Which type of function always has an inverse that is also a function?

• Square root functions

• Quadratic functions

• Cubic functions

• Linear functions

What happens to the inverse of a parabola if the domain is not restricted?

• It remains a function

• It becomes a sideways parabola

• It becomes a horizontal line

• It becomes a vertical line

What is the inverse of the function f(x) = x^3?

• f(x) = 1/x

• f(x) = cube root of x

• f(x) = x^3

• f(x) = x^2

If the cube root function is shifted up by 4 units, how is its inverse shifted?

• Up by 4 units

• Down by 4 units

• Right by 4 units

• Left by 4 units

What is the inverse of the function f(x) = cube root of (x - 6) + 1?

• f(x) = (x - 1)^3 + 6

• f(x) = (x + 1)^3 - 6

• f(x) = (x - 1)^3 - 6

• f(x) = (x + 1)^3 + 6

What is the result of switching x and y in the function f(x) = cube root of (x + 3)?

• x = (y + 3)^3

• x = cube root of (y + 3)

• y = (x + 3)^3

• y = cube root of (x + 3)

What does it mean if a function passes both the vertical and horizontal line tests?

• It is a quadratic function

• It is a one-to-one function

• It is a linear function

• It is a cubic function

What is the domain and range of cube root and cubic functions?

• All positive numbers

• All negative numbers

• All integers

• All real numbers

What is the homework assignment given at the end of the lesson?

• Numbers 1-5

• Numbers 6-8

• Numbers 14-18

• Numbers 9-13