Transformations of Functions and Graphs

This video tutorial covers graphing functions with multiple transformations, providing two examples. The first example involves a quadratic function, demonstrating vertical stretching, horizontal shifting, and vertical shifting. The second example focuses on a rational function, illustrating similar transformations. The video emphasizes understanding parent functions and applying transformations systematically to graph the final function.

What is the parent function for the first example discussed in the video?

• y = sqrt(x)

• y = x^2

• y = 1/x

• y = x^3

In the function f(x) = 2(x + 4)^2 - 3, what does the '2' indicate?

• Vertical compression

• Horizontal shift

• Vertical stretch

• Horizontal stretch

How does the '+4' in the function f(x) = 2(x + 4)^2 - 3 affect the graph?

• Shifts the graph up 4 units

• Shifts the graph left 4 units

• Shifts the graph down 4 units

• Shifts the graph right 4 units

What is the effect of '-3' in the function f(x) = 2(x + 4)^2 - 3?

• Shifts the graph up 3 units

• Shifts the graph right 3 units

• Shifts the graph down 3 units

• Shifts the graph left 3 units

After applying all transformations to f(x) = 2(x + 4)^2 - 3, what is the new position of the point (2, 4)?

• (-2, 5)

• (-6, 5)

• (-2, 8)

• (-6, 8)

What is the parent function for the second example discussed in the video?

• y = 1/x

• y = sqrt(x)

• y = x^2

• y = x^3

In the function 2(1/x) - 3 + 1, what does the '2' indicate?

• Horizontal stretch

• Vertical stretch

• Vertical compression

• Horizontal compression

How does the '-3' in the function 2(1/x) - 3 + 1 affect the graph?

• Shifts the graph down 3 units

• Shifts the graph up 3 units

• Shifts the graph left 3 units

• Shifts the graph right 3 units

What is the effect of '+1' in the function 2(1/x) - 3 + 1?

• Shifts the graph up 1 unit

• Shifts the graph down 1 unit

• Shifts the graph left 1 unit

• Shifts the graph right 1 unit

After applying all transformations to 2(1/x) - 3 + 1, what is the new position of the point (1, 1)?

• (2, 1)

• (5, 2)

• (3.5, 5)

• (4, 3)