T Misconceptions Transformations of Functions

The video addresses common misconceptions about function transformations, providing false statements and counterexamples. It covers how horizontal shifts and reflections affect domain, the impact of vertical shifts and reflections on range, and the misconception that horizontal stretches alter vertical asymptotes. The importance of applying transformations in the correct order is also discussed, emphasizing the need to follow the order of operations.

Which transformation can affect the domain of a function besides a horizontal shift?

• Vertical stretch

• Reflection about the X-axis

• Reflection about the Y-axis

• Vertical shift

What happens to the range of a cubic function when it undergoes vertical shifts and reflections?

• The range changes to positive numbers only

• The range remains all real numbers

• The range becomes restricted

• The range changes to negative numbers only

If a function has a vertical asymptote at x = 2, what happens to the asymptote when a horizontal stretch is applied?

• The asymptote moves to a new position

• The asymptote remains at x = 2

• The asymptote disappears

• The asymptote becomes a horizontal line

What is the effect of a horizontal stretch on the vertical asymptotes of a function?

• It shifts the asymptotes left or right

• It removes the asymptotes

• It changes the asymptotes to horizontal

• It does not affect the asymptotes

Why is it important to follow the order of operations when applying transformations to a graph?

• To ensure the graph is shifted correctly

• To avoid changing the domain

• To maintain the correct shape of the graph

• To prevent the graph from becoming undefined

What is the correct order of transformations for the function f(x) = -x^2 + 1?

• Reflect, then shift down

• Reflect, then shift up

• Shift up, then reflect

• Shift down, then reflect

What happens if you apply transformations in the wrong order?

• The graph remains unchanged

• The graph becomes a straight line

• The graph disappears

• The graph may not represent the intended function