Graph Transformations and Effects

The video tutorial covers graphing transformations of different functions, including reciprocal, square root, and cubic functions. It explains how to apply vertical stretches, compressions, reflections, and translations to these functions. The tutorial emphasizes using a table method to graph from a shifted origin, providing a systematic approach to understanding transformations.

What effect does the 'a' value have in the equation y = a/(x-h) + k?

• It shifts the graph vertically.

• It shifts the graph horizontally.

• It stretches or compresses the graph vertically.

• It reflects the graph over the y-axis.

In the function y = 2/(x-1) + 3, what transformation occurs due to the '-1'?

• The graph shifts down by 1.

• The graph shifts right by 1.

• The graph shifts left by 1.

• The graph shifts up by 1.

How does the negative sign in y = -2√(x+2) - 4 affect the graph?

• It shifts the graph up.

• It stretches the graph horizontally.

• It reflects the graph over the x-axis.

• It compresses the graph vertically.

What is the starting point for graphing y = -2√(x+2) - 4?

• Right 2, down 4

• Left 2, up 4

• Left 2, down 4

• Right 2, up 4

When graphing transformations, what is the first step according to the order of operations?

• Apply vertical stretching or compression.

• Apply horizontal shifts.

• Apply reflections.

• Apply vertical shifts.

In the function y = 1/2(x+4)^3 - 2, what does the '1/2' do to the graph?

• It shifts the graph right.

• It stretches the graph vertically.

• It compresses the graph vertically.

• It shifts the graph left.

What is the effect of '+4' in the function y = 1/2(x+4)^3 - 2?

• The graph shifts left by 4.

• The graph shifts up by 4.

• The graph shifts down by 4.

• The graph shifts right by 4.

What is the final transformation applied in y = 1/2(x+4)^3 - 2?

• Shift right by 2.

• Shift left by 2.

• Shift down by 2.

• Shift up by 2.

Which of the following is a general rule for graph transformations?

• Always apply reflections first.

• Always apply horizontal shifts first.

• Always apply transformations from the inside out.

• Always apply vertical shifts first.

What is the main takeaway from the video on graph transformations?

• Transformations are only horizontal.

• Transformations are only vertical.

• Transformations can be applied to any parent function.

• Transformations only apply to linear functions.