Transformations and Characteristics of Functions

The video tutorial covers parent functions and their transformations. It begins with an introduction to four basic parent functions: constant, linear, absolute value, and quadratic functions. The tutorial then explains transformations, focusing on translations and reflections. Vertical and horizontal translations are discussed in detail, showing how functions can be shifted up, down, left, or right. The video concludes with reflections, explaining how functions can be flipped over the x-axis and y-axis.

Which of the following is a characteristic of constant functions?

• They are V-shaped.

• Their output is always the same regardless of the input.

• They are represented by vertical lines.

• They have a constant slope.

What is the parent function of linear functions?

• f(x) = |x|

• f(x) = x

• f(x) = 1

• f(x) = x^2

How do transformations affect parent functions?

• They change the function's type.

• They modify the function's range.

• They alter the function's position and orientation.

• They change the function's domain.

What happens to a function when it undergoes a vertical translation?

• It flips over the y-axis.

• It flips over the x-axis.

• It shifts left or right.

• It shifts up or down.

If g(x) = f(x) + k, what does the value of k represent?

• A vertical shift upwards.

• A horizontal shift to the right.

• A horizontal shift to the left.

• A vertical shift downwards.

In horizontal translations, what does f(x - h) indicate?

• A shift h units to the right.

• A shift h units to the left.

• A shift h units downwards.

• A shift h units upwards.

What is a key difference between vertical and horizontal translations?

• Horizontal translations are opposite in direction to their sign.

• Horizontal translations are intuitive in direction.

• Vertical translations are opposite in direction to their sign.

• Vertical translations change the function's shape.

What does reflecting a function over the x-axis do?

• It shifts the function upwards.

• It flips the function vertically.

• It flips the function horizontally.

• It shifts the function downwards.

How is a function affected when it is reflected over the y-axis?

• The function is flipped vertically.

• The function is shifted to the left.

• The function is flipped horizontally.

• The function is shifted to the right.

Which of the following transformations involves changing the orientation of a function?

• Stretching

• Reflection

• Horizontal translation

• Vertical translation