Exploring Transformations of Parent Functions

This video tutorial covers the transformations of various parent functions, including linear, quadratic, absolute value, square root, cube root, exponential, logarithmic, and rational functions. It explains how to apply horizontal and vertical shifts, reflections, and the importance of reference points and asymptotes. The tutorial emphasizes following the order of operations and provides examples for each type of function transformation.

What is the first step in applying transformations to functions?

• Vertical changes

• Horizontal changes

• Drawing the graph

• Identifying the reference point

What does the transformation y = x + 4 do to the linear parent function?

• Moves it down 4 units

• Moves it left 4 units

• Moves it up 4 units

• Moves it right 4 units

In the function y = (x - 2)^2 + 1, what does the (x - 2) part do?

• Moves the graph left 2 units

• Moves the graph right 2 units

• Moves the graph up 2 units

• Moves the graph down 2 units

How does the negative sign outside the absolute value bars affect the graph of an absolute value function?

• Moves it down

• Moves it up

• Reflects it across the x-axis

• Reflects it across the y-axis

What is the reference point for the square root function?

• (0, 1)

• (0, 0)

• (1, 0)

• (1, 1)

In the function y = √(x - 5) + 2, what does the +2 part do?

• Moves the graph right 2 units

• Moves the graph up 2 units

• Moves the graph down 2 units

• Moves the graph left 2 units

What is the reference point for the exponential function y = e^x?

• (0, 0)

• (1, 0)

• (0, 1)

• (1, 1)

In the function y = ln(x - 2) + 3, what does the (x - 2) part do?

• Moves the graph right 2 units

• Moves the graph left 2 units

• Moves the graph up 2 units

• Moves the graph down 2 units

What is the new asymptote for the function y = e^(x - 3) - 1?

• y = 0

• y = -1

• x = 0

• x = -1

In a rational function, where do horizontal changes occur?

• In the numerator

• Inside the fraction

• In the denominator

• Outside the fraction