Exploring Rational Expressions in Algebra 2

The video tutorial covers several mathematical concepts. It begins with an explanation of how adding or subtracting numbers affects the shifting of functions. It then moves on to calculating the average rate of change in daylight hours, using a specific formula. The tutorial also discusses the properties of even and odd functions, focusing on their symmetry. It explains how to find the inverse of a function and concludes with a section on parabolas, detailing how to find the vertex and equation using the focus and directrix.

What happens to the graph of a function if you add a number to the end of it?

• It shifts up.

• It shifts to the left.

• It shifts down.

• It shifts to the right.

If you subtract a number within the function, which direction does the graph move?

• Down

• Up

• To the right

• To the left

How do you calculate the average rate of change?

• Subtract the final value from the initial value and divide by the number of intervals.

• Multiply the initial value by the final value and divide by the number of intervals.

• Add the initial value to the final value and divide by 2.

• Subtract the initial value from the final value and divide by the number of intervals.

What does a positive average rate of change indicate in the context of hours of daylight?

• The number of hours of daylight is decreasing.

• The number of hours of daylight is constant.

• The number of hours of daylight is increasing.

• The number of hours of daylight is fluctuating.

What is an even function?

• A function that is symmetric to the Y-axis.

• A function that is not symmetric.

• A function that is symmetric to the origin.

• A function that is symmetric to the X-axis.

Which transformation will keep an even function even?

• Shifting it to the left

• Shifting it down

• Shifting it to the right

• Shifting it up

What is the first step in finding the original function from its inverse?

• Subtract 2 from both sides of the equation.

• Multiply both sides by the reciprocal.

• Switch the X and Y variables.

• Add 2 to both sides of the equation.

What is the reciprocal of -3/4?

• 3/4

• -4/3

• -3/4

• 4/3

Where is the vertex of a parabola located if the focus is at (4, -3) and the directrix is y = 1?

• (4, -4)

• (4, -3)

• (4, -2)

• (4, -1)

What is the equation of a parabola with a focus at (4, -3) and a directrix at y = 1?

• y = -1/8 (x - 4)^2 - 1

• y = -1/8 (x - 4)^2 + 1

• y = 1/8 (x - 4)^2 - 1

• y = 1/8 (x - 4)^2 + 1