Graphing Function Transformations: Part 1 Insights

This video tutorial explains how to graph functions with multiple transformations, focusing on the effects of parameters A, B, C, and D. It provides step-by-step examples of graphing functions with vertical and horizontal compressions, reflections, and shifts. The video emphasizes understanding parent functions and applying transformations without a graphing calculator. It concludes with a preview of additional examples in the next video.

What is the significance of the value of A in the function F(x) = -1/2 |x + 1| - 2?

• It indicates a horizontal compression.

• It indicates a reflection and vertical compression.

• It indicates a vertical stretch.

• It indicates a horizontal shift.

If C = +1 in the function F(x) = -1/2 |x + 1| - 2, what transformation does it represent?

• Shift down one unit

• Shift up one unit

• Shift left one unit

• Shift right one unit

How do you graph the reflection and vertical compression of the function Y = -1/2 |x|?

• Multiply the Y coordinate by -1/2 and leave the X coordinate the same.

• Add 1 to the X coordinate and subtract 2 from the Y coordinate.

• Subtract 1 from the X coordinate and add 2 to the Y coordinate.

• Multiply the X coordinate by -1/2 and leave the Y coordinate the same.

What are the new coordinates of the point (4, -2) after shifting it left one unit and down two units?

• (3, -4)

• (5, -4)

• (3, -1)

• (2, -3)

In the function F(x) = √(2(x - 2)) + 1, what does the value B = 2 represent?

• Vertical stretch

• Horizontal stretch

• Horizontal compression

• Vertical compression

What is the parent function for the second example function?

• Y = |x|

• Y = 1/x

• Y = x^2

• Y = √x

How do you perform a horizontal compression on the parent function Y = √x?

• Multiply the Y coordinate by B

• Subtract B from the Y coordinate

• Divide the X coordinate by B

• Add B to the X coordinate

What are the new coordinates of the point (2, 2) after shifting it right two units and up one unit?

• (2, 1)

• (0, 1)

• (4, 3)

• (4, 1)

What is the final transformation applied to the second example function?

• Shift left two units and down one unit

• Shift right two units and up one unit

• Shift right one unit and down two units

• Shift left one unit and up two units

What is the main idea conveyed in the video about graphing transformed functions?

• Transformed functions are always more complex than parent functions.

• You can graph transformed functions quickly and easily if you know the parent function.

• You need a graphing calculator to graph transformed functions.

• You should always graph transformed functions without any steps.