Exploring Adding and Subtracting Rational Expressions

The video tutorial covers graphing inverse functions, starting with triangle ABC and its inverse. It explains how to graph linear functions and their inverses, demonstrating the reflection across the line y = x. The tutorial also covers quadratic functions, showing how to graph them and find their inverses, emphasizing the importance of transformations and restrictions.

What happens to the coordinates of points when finding the inverse of a relation?

• The x and y coordinates remain unchanged.

• The x and y coordinates are multiplied by -1.

• The x and y coordinates are switched.

• The x and y coordinates are squared.

What is the graphical relationship between a function and its inverse?

• They are mirror images across the line y = x.

• They are identical graphs.

• They are mirror images across the y-axis.

• They intersect at the origin.

How do you verify the inverse relationship on a graph?

• By drawing a line through y = x and reflecting.

• By drawing a vertical line.

• By drawing a horizontal line.

• By drawing a line through x = y and translating.

What is the inverse function of f(x) = 2x + 8?

• f^-1(x) = x/2 + 4

• f^-1(x) = 2/x + 8

• f^-1(x) = x/2 - 4

• f^-1(x) = 2x - 8

What is the slope of the line y = 2x + 8?

• -2

• 2

• 1/2

• 8

What is the y-intercept of the inverse function of f(x) = 2x + 8?

• 4

• 8

• -4

• -8

For the function f(x) = x^2 - 4, restricted to x >= 0, what is the domain of its inverse?

• x <= 0

• x >= -4

• x >= 0

• x <= 4

What transformation is applied to the graph of the square root function when adding 4 inside the square root?

• Shift down by 4 units

• Shift left by 4 units

• Shift up by 4 units

• Shift right by 4 units

For the function f(x) = x^2 - 4 (x >= 0), what is the y-coordinate of the vertex of its graph?

• -4

• 0

• -8

• 4

What is the correct expression for the inverse of f(x) = x^2 - 4 (x >= 0)?

• f^-1(x) = sqrt(x) - 4

• f^-1(x) = sqrt(x + 4)

• f^-1(x) = sqrt(x) + 4

• f^-1(x) = (x + 4)^2