Graph Transformations and Their Effects

This video lecture from Bay College covers section 3.5 on transformations in college algebra. It explains various transformations applied to library functions, focusing on f(x) = x^2. The lecture discusses horizontal shifts, compressing and stretching, reflections, and vertical shifts. It also outlines the order of operations for applying these transformations, using examples to illustrate each concept.

What is the primary library function used in this section on transformations?

• Exponential function

• Cubic function

• Quadratic function

• Linear function

What happens to the graph of a function when a horizontal shift is applied with c > 0?

• The graph shifts to the right

• The graph shifts to the left

• The graph stretches vertically

• The graph compresses horizontally

If c is a fraction between 0 and 1, what effect does it have on the function relative to the x-axis?

• It stretches the graph away from the x-axis

• It shifts the graph vertically

• It compresses the graph towards the x-axis

• It reflects the graph across the y-axis

What is the result of replacing x with -x in a function?

• The graph is compressed

• The graph is shifted up

• The graph is reflected across the y-axis

• The graph is reflected across the x-axis

How does adding a positive constant to a function affect its graph?

• It reflects the graph across the x-axis

• It shifts the graph up

• It shifts the graph down

• It compresses the graph

What is the correct order of operations for applying transformations?

• Stretching/compressing, reflections, horizontal shifts, vertical shifts

• Vertical shifts, reflections, horizontal shifts, stretching/compressing

• Horizontal shifts, stretching/compressing, reflections, vertical shifts

• Reflections, horizontal shifts, vertical shifts, stretching/compressing

In the example of applying transformations, what is the first transformation applied to the function?

• Stretching

• Horizontal shift

• Reflection through y

• Vertical shift

What is expected in the quiz regarding the graphing of transformations?

• Graph only the final transformation

• Graph each transformation step separately

• Graph only the initial function

• Graph transformations without any reference points