Overview transformations, vertical shifts - Online Tutor - Free Math Videos

The video tutorial introduces the concept of transformations in functions, starting with a review of various function types such as constant, linear, quadratic, cubic, absolute value, and root functions. It then focuses on transformations, particularly vertical transformations, explaining how they affect the graph of a function by shifting it up or down. Examples are provided using the square root function to illustrate these shifts.

Which of the following is an example of a linear function?

• F(x) = x^2

• F(x) = x

• F(x) = |x|

• F(x) = sqrt(x)

What is the primary focus of transformations in functions?

• Changing the type of function

• Altering the graph's shape

• Changing the function's domain

• Shifting the graph's position

How is a vertical transformation represented mathematically?

• T(x) = F(x) + C

• F(x) = x + C

• T(x) = F(x) * C

• F(x) = x - C

What happens to the graph of a function when a positive constant is added?

• It shifts downwards

• It shifts upwards

• It shifts to the right

• It shifts to the left

If F(x) = sqrt(x) - 3, how is the graph of F(x) transformed?

• Shifted right 3 units

• Shifted left 3 units

• Shifted down 3 units

• Shifted up 3 units

In the example F(x) = -3 + sqrt(x), what is the transformation applied?

• Shifted left 3 units

• Shifted right 3 units

• Shifted down 3 units

• Shifted up 3 units

What is the starting point of the original square root function graph?

• (0, 1)

• (1, 0)

• (0, 0)

• (1, 1)