Functions and Their Properties

The video tutorial covers a range of mathematical concepts, including the properties of even and odd functions, transformations of quadratic graphs, and the analysis of projectile motion using quadratic equations. It also explores modeling bacteria growth with exponential functions, calculating the average rate of change, understanding the end behavior of quadratic functions, and identifying exponential functions from data points.

Which of the following is a characteristic of an even function?

• It has only odd exponents.

• It has only even exponents.

• It has both even and odd exponents.

• It has no exponents.

What happens to a function when it is reflected over the x-axis?

• It remains unchanged.

• It shifts to the right.

• It shifts to the left.

• It flips upside down.

How does a vertical stretch by a factor of 3 affect a graph?

• It stretches the graph horizontally.

• It stretches the graph vertically.

• It compresses the graph horizontally.

• It compresses the graph vertically.

What is the initial height of the disc in the quadratic function modeling its flight?

• 50 feet

• 0 feet

• 25 feet

• 75 feet

At what time does the disc hit the ground according to the quadratic model?

• 10 seconds

• 2.3 seconds

• 4.6 seconds

• 5 seconds

What is the growth rate of the bacteria population?

• 1%

• 2%

• 10%

• 5%

If the initial population of bacteria is 200, what will it be after 100 hours?

• 2000

• 1448

• 800

• 400

What is the formula used to calculate the future population of bacteria?

• A = P0 * 1.10^T

• A = P0 * 1.05^T

• A = P0 * 1.02^T

• A = P0 * 1.01^T

What is the average rate of change of f(x) over the interval [-2, 0]?

• -10

• -5

• 0

• 5

How do you calculate the average rate of change?

• By finding the difference between two points.

• By finding the sum of the points.

• By multiplying the points.

• By dividing the points.