Reflections in Functions and Graphs

The video tutorial discusses reflections of functions over the x-axis and y-axis, focusing on quadratics and exponential functions. Quadratics are symmetrical across a vertical line, so reflecting them over the y-axis doesn't change their graph. However, exponential functions are not symmetrical, requiring reflections over both axes. The tutorial explains how multiplying by negative one reflects a function over the x-axis and how a negative exponent reflects it over the y-axis. The key takeaway is understanding these reflections without needing graphing technology.

What are the two main types of reflections discussed in the introduction?

• Reflection over the a-axis and b-axis

• Reflection over the m-axis and n-axis

• Reflection over the z-axis and w-axis

• Reflection over the x-axis and y-axis

How does reflecting a quadratic function over the y-axis affect its graph?

• It creates a completely different graph

• It results in a graph that is a mirror image

• It produces the same graph

• It shifts the graph upwards

What is the result of reflecting a quadratic function over its axis of symmetry?

• A new graph is formed

• The graph is stretched vertically

• The graph remains unchanged

• The graph is shifted upwards

Why are exponential functions not symmetrical about the y-axis?

• Because they are not defined for negative x-values

• Because they have a horizontal asymptote

• Because they are linear

• Because they do not have symmetry like quadratics

What happens when you multiply a function by negative one?

• It stretches the function vertically

• It shifts the function to the right

• It reflects the function over the y-axis

• It reflects the function over the x-axis

How does a reflection over the x-axis affect the end behavior of a polynomial?

• It stretches the polynomial horizontally

• It reflects the polynomial downwards

• It reflects the polynomial upwards

• It shifts the polynomial to the right

What is the significance of the order of operations in reflections?

• It ensures the correct application of negative multiplication

• It changes the function's domain

• It determines the direction of the reflection

• It affects the symmetry of the function

In the context of reflections, what does a negative exponent indicate?

• A vertical stretch

• A reflection over the y-axis

• A reflection over the x-axis

• A horizontal shift

What is the effect of a negative number raised to an even power?

• It results in a positive number

• It results in an undefined value

• It results in a negative number

• It results in zero

What is the main takeaway regarding graphing technology and reflections?

• Graphing technology is essential for understanding reflections

• You don't need graphing technology to understand reflections

• Graphing technology is only useful for quadratic functions

• Graphing technology is only useful for exponential functions