Function Transformations and Comparisons

The video tutorial covers graphing the sum and difference of functions, finding the vertex of quadratic functions, analyzing historical sugar consumption data, and understanding odd and even functions. It also compares height functions of Ferris wheels with varying speeds and heights.

What is the main focus when sketching the graph of a function defined by the sum of two functions?

• Adding their x-values

• Subtracting their y-values

• Multiplying their x-values

• Adding their y-values

When adding two functions, if one function remains constant at 3, what happens to the graph of the sum?

• It remains unchanged

• It shifts up by 3

• It shifts down by 3

• It shifts left by 3

In the context of function subtraction, when does the new function H equal zero?

• When F is zero

• When F is less than G

• When F equals G

• When F is greater than G

For which x-values is the function H less than zero?

• When F is greater than G

• When F equals G

• When F is less than G

• When F is zero

How do you find the vertex of a quadratic equation using transformations?

• By translating the graph vertically

• By scaling the graph

• By shifting and reflecting the graph

• By rotating the graph

What transformation occurs when there is a minus one inside the quadratic equation?

• Shift down by one

• Shift up by one

• Shift to the right by one

• Shift to the left by one

How is the average sugar consumption per person calculated?

• By adding the population to sugar consumed

• By dividing the sugar consumed by the population

• By multiplying the population by sugar consumed

• By subtracting the population from sugar consumed

In 1900, what was the approximate sugar consumption per person?

• 110 pounds

• 75 pounds

• 40 pounds

• 20 pounds

Why is the function neither odd nor even?

• It has equal outputs for opposite inputs

• It is symmetric over the y-axis

• It is symmetric over the x-axis

• It does not land on itself when reflected

What happens when you reflect a function over both the y and x axes?

• It lands on itself

• It becomes even

• It becomes odd

• It does not land on itself