Comparing Functions and Reflections

The video tutorial explores the concepts of reflections in linear equations by comparing functions f(x) and g(x). It explains opposite numbers and how they relate to reflections, using examples of slopes and y-intercepts. The tutorial demonstrates how to identify reflections through algebraic representations and coordinate transformations, emphasizing the concept of mirror images across axes.

What operation can you perform on a positive number to find its opposite?

• Multiply by -1

• Subtract 1

• Multiply by 2

• Add 1

How does the slope of f(x) compare to the slope of g(x)?

• They are the same

• They are opposites

• One is double the other

• They are unrelated

What is the relationship between the y-intercepts of f(x) and g(x)?

• They are the same

• They are opposites

• One is double the other

• They are unrelated

When x is the same for both functions, how do the y-coordinates of f(x) and g(x) compare?

• They are the same

• They are opposites

• One is double the other

• They are unrelated

What does the transformation x, y to x, -y represent?

• Reflection across the y-axis

• Reflection across the x-axis

• Translation

• Rotation

How can you express g(x) in terms of f(x) when reflecting across the x-axis?

• g(x) = f(-x)

• g(x) = f(x)

• g(x) = -f(x)

• g(x) = 2f(x)

What happens to the function when you multiply f(x) by -1?

• It reflects across the y-axis

• It shifts up

• It shifts down

• It reflects across the x-axis

In a reflection across the y-axis, what happens to the x-coordinates?

• They remain the same

• They become opposites

• They halve

• They double

What is the algebraic representation of g(x) if it is a reflection of f(x) across the y-axis?

• g(x) = f(x)

• g(x) = -f(x)

• g(x) = 2f(x)

• g(x) = f(-x)

If the y-intercepts of f(x) and g(x) are the same, what does this indicate about their reflection?

• They are identical

• They reflect across the x-axis

• They are not reflections

• They reflect across the y-axis