Reflections in Function Graphs

This video tutorial explains how to apply reflections to functions on the x-axis, y-axis, and both axes. It begins with an introduction to reflections, followed by detailed explanations of how negative signs affect the graph of a function. The video uses examples to illustrate reflections on the y-axis and x-axis separately, and then combines these transformations. The tutorial concludes with a summary and encourages viewers to practice the concepts learned.

What changes in the equation of a function are needed to reflect it on the x-axis?

• Add a constant to the function.

• Multiply the x variable by a negative.

• Multiply the entire function by a negative.

• Subtract a constant from the function.

How can reflections be generalized from quadratic equations to all functions?

• By using only polynomial functions.

• By applying the same reflection rules to any function.

• By using only linear functions.

• By ignoring the negative sign.

What happens to the graph of G(x) if G(x) = F(-x)?

• It remains unchanged.

• It shifts vertically.

• It reflects along the y-axis.

• It reflects along the x-axis.

If F(x) = 1/x, what is the result of applying a negative sign to the x variable?

• The graph reflects along the x-axis.

• The graph remains unchanged.

• The graph shifts horizontally.

• The graph reflects along the y-axis.

What is the effect of applying a negative sign outside the function F(x)?

• The graph shifts horizontally.

• The graph reflects along the y-axis.

• The graph reflects along the x-axis.

• The graph remains unchanged.

How does a reflection affect a parabola that is shifted horizontally and vertically?

• It only reflects along the x-axis.

• It causes a vertical shift in the opposite direction.

• It only reflects along the y-axis.

• It remains unchanged.

Why does a reflection along the x-axis cause a vertical shift?

• Because the graph is initially above the x-axis.

• Because the graph is initially to the left of the y-axis.

• Because the graph is initially below the x-axis.

• Because the graph is initially to the right of the y-axis.

What happens if the negative sign is not applied to the entire function?

• The graph reflects along the y-axis.

• The graph shifts horizontally.

• The graph reflects along the vertex point.

• The graph remains unchanged.

In the final example, what transformations are applied to the function?

• Reflections on both the x-axis and y-axis.

• No transformations are applied.

• Reflection on the x-axis only.

• Reflection on the y-axis only.

What is the result of distributing a negative sign across the entire function?

• The graph shifts horizontally.

• The graph reflects along the x-axis.

• The graph reflects along the y-axis.

• The graph remains unchanged.