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## Algebra 2

### Course: Algebra 2>Unit 9

Lesson 2: Reflecting functions

# Reflecting functions: examples

We can reflect the graph of any function f about the x-axis by graphing y=-f(x) and we can reflect it about the y-axis by graphing y=f(-x). We can even reflect it about both axes by graphing y=-f(-x). See how this is applied to solve various problems.

## Want to join the conversation?

• I don’t exactly understand how f(-x) and -f(x) get different results.
• f(-x) multiplies all the x in the equation by negative 1 whereas negative f would make the entire equation negative.
• This is super hard.Find g(x), where g(x) is the reflection across the x-axis of f(x)=–4(x+7)2–7. Which of these do i change?
• We know these two things:
-f(x) = Reflection across x-axis
f(-x) = Reflection across y-axis
These are essential to know.

Since -f(x) is a reflection across axis, we do as such:
-f(x) = -1(-4(x+7)²-7)
-f(x) = 4(x+7)²+7 <-- you're new equation
• Why does f(x) = the square root of x make the type of graph it does?
• When you take the inverse of a function, its graph gets reflected across the line y=x. The graph of y=√x is half of a parabola, opening sideways, since it's a reflection of y=x².
• i still mix between the reflection over y-axis and reflection over x-axis. could someone help please
(1 vote)
• Try making a visual or mental picture of these reflections. From this picture, you can make the following observations:

1) two points that are mirror images of each other about the y-axis have the same y-coordinate and x-coordinates that are opposites of each other, and

2) two points that are mirror images of each other about the x-axis have the same x-coordinate and y-coordinates that are opposites of each other.
• Hello, sorry if someone asked this already, but why is √x a curved line? Thanks.
• the simple answer is it is curved because it is not linear (it is either linear or curved). So linear functions and absolute value functions (and step functions) are not curved, but many other functions are curved including square root.
Since perfect square roots get further apart every time, the graph goes up slower and slower between perfect squares which creates this curve. (1,1)(4,2)(9,3)(16,4) slope between first two points is 1/3, slope between second and third is 1/5, slope between third and fourth is 1/7, etc. Linear equations would have same slope between any two points on the line.
• In the equation f(x)= 2^(x-1) when the function is changed to -f(-x) the equation becomes -2^(-x-1). I get the entire problem except why doesn't -1 change to +1 in the exponent? I thought -f(-x) changed the sign in every term of the equation.
• When you find f(-x), you replace every x in the original equation with -x. In your example, if we look at just the power, x-1, it becomes (-x)-1. Additionally, the negative sign in front of f(x) multiplies the equation by -1, so we get -1*(2^(-x-1), which simplifies to the correct answer. I think you might have developed a "shortcut" for solving this type of problem that sometimes works, but not always. My recommendation would be to return to horizontal reflections, f(-x), and vertical reflections, -f(x), and consider -f(-x) as applying one, then the other.
• If the function y=x−−√ is replaced by x=y√, then the new graph can be described as a reflection of y=x
• What you have is confusing and not a function or an equation, you have minus a negative square root with nothing in the root, then you change it by leaving off the minus negative, but still have a root symbol without anything inside. If you do not have a function in the first place, there is no reflecting across anything.