Function Transformations: Vertical Stretches and Reflections

This video tutorial by Kirk Wier from emath instruction covers Common Core Algebra 1, focusing on function transformations. The lesson includes exercises on evaluating functions, understanding domains and ranges, and exploring vertical stretches and compressions. The tutorial also covers quadratic transformations and provides a summary of key concepts. Resources such as worksheets and homework assignments are available for further practice.

What is the main topic of Unit 11 in this lesson?

• Function transformations

• Solving quadratic equations

• Factoring polynomials

• Graphing linear equations

In Exercise 1, what is the y-value of f(3)?

• 4

• 3

• 2

• -2

Why is it impossible to evaluate f(9) in Exercise 1?

• x=9 is not in the domain of the function

• All of the above

• The graph does not extend to x=9

• The function is undefined at x=9

What is the domain of the function in Exercise 1?

• [-7, 7]

• [-4, 4]

• [-9, 9]

• [-5, 5]

In Exercise 2, what is the value of G(-7) if G(x) = 2 * f(x)?

• 4

• -8

• 8

• -4

How can you interpret the function rule G(x) = 2 * f(x) in terms of the graph of f(x)?

• Each y-value is divided by 2

• Each x-value is divided by 2

• Each y-value is multiplied by 2

• Each x-value is multiplied by 2

What happens to the graph of a function when it is multiplied by a constant greater than 1?

• It shifts to the right

• It shifts to the left

• It compresses vertically

• It stretches vertically

What is the effect of multiplying a function by a negative constant?

• It shifts the graph up

• It shifts the graph down

• It reflects the graph across the x-axis

• It reflects the graph across the y-axis

In the final example, what is the range of the new function G(x) if the maximum y-value is 2?

• y = 2

• y ≥ 2

• y ≤ 2

• y ≠ 2

Which function represents a vertical compression by a factor of 1/2?

• G(x) = 2 * f(x)

• K(x) = 1/2 * f(x)

• L(x) = f(x) + 2

• H(x) = -f(x)