Reflecting Functions: Key Concepts and Applications

The video tutorial covers the concept of reflecting functions over the x-axis and y-axis using examples from Khan Academy. It begins with an introduction to reflections, followed by detailed explanations of how to reflect a function over the y-axis and x-axis. The tutorial then explores combining these reflections to transform functions and concludes with deriving the equation of a reflected function.

What is the effect on the graph of a function when you replace x with -x?

• It reflects the graph over the x-axis.

• It shifts the graph down.

• It reflects the graph over the y-axis.

• It shifts the graph up.

If f(4) = 2, what is g(-4) when g(x) = f(-x)?

• -4

• -2

• 4

• 2

What is the value of g(0) if g(x) = f(-x) and f(0) = -2?

• 0

• -2

• 2

• -1

What transformation occurs when g(x) = -f(x)?

• Reflection over the y-axis

• Shifting down

• Reflection over the x-axis

• Shifting up

If f(0) = 2, what is g(0) when g(x) = -f(x)?

• -1

• 0

• -2

• 2

What is the value of g(x) if g(x) = -f(x) and f(2) = 3?

• 2

• -2

• 3

• -3

What is the combined effect of reflecting a function over both the x-axis and y-axis?

• The graph shifts left and right.

• The graph remains unchanged.

• The graph is reflected over both axes.

• The graph shifts up and down.

If f(x) is reflected over the y-axis and then the x-axis, what is the resulting function g(x)?

• g(x) = f(x)

• g(x) = -f(-x)

• g(x) = f(-x)

• g(x) = -f(x)

What is the equation of g(x) if g(x) is a reflection of f(x) across the y-axis and f(x) = 4√(2 - x) - 8?

• g(x) = 4√(2 - x) + 8

• g(x) = 4√(2 - x) - 8

• g(x) = 4√(2 + x) - 8

• g(x) = 4√(2 + x) + 8

If f(-8) = 4, what is g(8) when g(x) = f(-x)?

• -4

• -8

• 4

• 8