Transformations of Functions Explained

The video tutorial covers transformations of functions, focusing on both vertical and horizontal transformations. It explains how these transformations affect the graph's outputs and inputs, respectively. The tutorial also discusses how to apply these transformations to solve problems, emphasizing their relevance in AP and SAT contexts. The video includes practical examples and exercises to reinforce understanding.

What is the primary focus of transformations in this class compared to Algebra 2?

• Reflecting graphs over axes

• Stretching and shrinking graphs

• Transforming function values

• Shifting graphs left and right

What is a vertical translation of a function?

• Adding a number to the input

• Multiplying the output by a constant

• Multiplying the input by a constant

• Adding a number to the output

How does a vertical dilation affect a function?

• It reflects the graph over the y-axis

• It stretches or shrinks the graph vertically

• It adds a constant to the input

• It shifts the graph left or right

What does a horizontal translation of f(x + h) do to the graph?

• Shifts it down by h units

• Shifts it up by h units

• Shifts it left by h units

• Shifts it right by h units

What is the effect of a horizontal dilation by a factor of 1/b?

• Shrinks the graph horizontally by 1/b

• Stretches the graph horizontally by 1/b

• Shrinks the graph horizontally by b

• Stretches the graph horizontally by b

Which transformations affect the domain of a function?

• Only horizontal dilations

• Horizontal translations and dilations

• Vertical translations and dilations

• Only vertical translations

If a function f(x) is vertically stretched by a factor of 2 and then shifted up by 3 units, what is the new function?

• 2f(x + 3)

• f(2x) + 3

• 2f(x) + 3

• f(2x + 3)

What happens to the point (4, 2) on the function f(x) when it is horizontally translated by +1 and vertically dilated by 2?

• (5, 4)

• (3, 4)

• (5, 7)

• (3, 7)

How many solutions does the equation G(x) = 0 have if G(x) = 2f(x - 1) + 3?

• Three

• Two

• One

• None

What is the new range of a function f(x) with an original range of [-3, 3] after a vertical dilation by 2 and a vertical translation of +3?

• [0, 6]

• [-9, 3]

• [-3, 9]

• [-6, 6]