Translations of Functions and Their Effects

The video tutorial explains how to graph a quadratic function with two translations: a vertical shift down by one unit and a horizontal shift left by four units. It begins with an introduction to quadratic functions and their parent function, y = x^2. The tutorial then details how to apply the vertical and horizontal translations, calculate the new ordered pairs, and graph the translated function. Finally, it covers how to determine the domain and range of the function, with the domain being all real numbers and the range being y ≥ -1.

What is the parent function of the quadratic function discussed in the video?

• y = 2x

• y = x^2

• y = x^3

• y = x

What does the minus one outside the function indicate?

• A shift to the right by one unit

• A shift to the left by one unit

• A shift up by one unit

• A shift down by one unit

How does the minus one affect the y-values of the function?

• Subtract one from all y-values

• Add one to all y-values

• Multiply all y-values by one

• Divide all y-values by one

What is the effect of a vertical translation on a function?

• It shifts the graph up or down

• It shifts the graph left or right

• It stretches the graph vertically

• It compresses the graph horizontally

What does the plus four inside the function indicate?

• A shift to the right by four units

• A shift to the left by four units

• A shift up by four units

• A shift down by four units

How does the plus four affect the x-values of the function?

• Add four to all x-values

• Subtract four from all x-values

• Multiply all x-values by four

• Divide all x-values by four

What is the effect of a horizontal translation on a function?

• It compresses the graph horizontally

• It stretches the graph vertically

• It shifts the graph left or right

• It shifts the graph up or down

What is the new x-value for the original x-value of 0 after translation?

• -1

• -4

• 4

• 0

What is the new y-value for the original y-value of 4 after translation?

• 2

• 5

• 3

• 4

Which ordered pair is correct after applying both translations?

• (-6, 4)

• (-3, 0)

• (-5, 0)

• (-4, 1)