Exploring Parent Functions and Their Transformations

The video tutorial covers the identification and transformation of various parent functions, including linear, quadratic, cubic, exponential, square root, and absolute value functions. It explains how to determine the type of function and describes transformations such as shifts, reflections, and vertical stretches or shrinks. The tutorial includes exercises to practice these transformations, emphasizing the importance of understanding the effects of changes in function parameters.

Which of the following is a cubic function?

• f(x) = sqrt(x)

• f(x) = x^2

• f(x) = x

• f(x) = x^3

What is the parent function of an absolute value function?

• f(x) = x

• f(x) = sqrt(x)

• f(x) = |x|

• f(x) = x^2

If an absolute value function shifts left by 4 units and up by 1 unit, what is the transformation function?

• f(x) = |x + 4| + 1

• f(x) = |x - 4| - 1

• f(x) = |x - 4| + 1

• f(x) = |x + 4| - 1

What is the transformation function for a square root function that shifts right by 10 units?

• f(x) = sqrt(x) - 10

• f(x) = sqrt(x) + 10

• f(x) = sqrt(x - 10)

• f(x) = sqrt(x + 10)

Which transformation occurs when a quadratic function reflects over the x-axis and shifts right by 3 units and up by 5 units?

• f(x) = (x - 3)^2 + 5

• f(x) = -(x + 3)^2 + 5

• f(x) = (x + 3)^2 - 5

• f(x) = -(x - 3)^2 + 5

What is the transformation function for a cubic function that reflects over the x-axis and shifts down by 2 units?

• f(x) = x^3 + 2

• f(x) = -x^3 + 2

• f(x) = -x^3 - 2

• f(x) = x^3 - 2

What is the slope of a linear function that shifts down by 3 units and has a slope of 1/2?

• y = x - 3

• y = 1/2x + 3

• y = 2x - 3

• y = 1/2x - 3

What transformation occurs when a quadratic function undergoes a vertical shrink by 1/4 and shifts down by 4 units?

• f(x) = x^2 - 4

• f(x) = 1/4x^2 + 4

• f(x) = 4x^2 - 4

• f(x) = 1/4x^2 - 4

How does a function change when it shifts down by 3 units?

• It shifts down by 3 units

• It shifts right by 3 units

• It shifts left by 3 units

• It shifts up by 3 units

What transformation occurs when a function undergoes a vertical stretch by a factor of 2?

• It stretches vertically by a factor of 2

• It shrinks horizontally by a factor of 2

• It shrinks vertically by a factor of 2

• It stretches horizontally by a factor of 2