Inverse Functions and Polynomial Behavior

This video tutorial covers polynomial functions, focusing on transformations, inverse functions, and properties such as one-to-one, even, and odd functions. It also includes graphing techniques for cubic and quartic functions, providing a comprehensive review for students preparing for a quiz or test.

What happens to a graph when a vertical factor greater than 1 is applied?

• It compresses vertically.

• It stretches vertically.

• It reflects over the y-axis.

• It shifts horizontally.

How does a negative sign in front of a function affect its graph?

• It reflects the graph over the x-axis.

• It shifts the graph upwards.

• It stretches the graph vertically.

• It compresses the graph horizontally.

What is the first step in finding the inverse of a function?

• Multiply by the reciprocal.

• Solve for y.

• Substitute y for f(x).

• Switch the x and y variables.

If a function has x-intercepts at 3, -2, and 5, what are the y-intercepts of its inverse?

• (0, 3), (0, -2), (0, 5)

• (3, 0), (-2, 0), (5, 0)

• (0, 0), (0, 0), (0, 0)

• (3, 3), (-2, -2), (5, 5)

What is the slope of the inverse of a linear function with a slope of 3/5?

• -3/5

• 3/5

• -5/3

• 5/3

What does it mean for a function to be one-to-one?

• Each x-value maps to exactly one y-value.

• Each x-value maps to multiple y-values.

• Each y-value maps to exactly one x-value.

• Each y-value maps to multiple x-values.

How can you determine if a function is even?

• It has no symmetry.

• It is symmetric about the origin.

• It is symmetric about the y-axis.

• It is symmetric about the x-axis.

What is the behavior of a cubic function with a positive leading coefficient?

• Has no specific pattern.

• Starts high and ends low.

• Starts low and ends high.

• Starts and ends in the same direction.

How many humps does a cubic function typically have?

• One

• Three

• Two

• None

What is a double root in a polynomial function?

• A root that appears twice and causes a tangent to the x-axis.

• A root that appears once and crosses the x-axis.

• A root that appears three times.

• A root that does not affect the graph.