How do you reflect a function across the x-axis (flip it upside down)?
Responses
Subtract a number larger than 10
Change the variable
Use an irrational exponent
Multiply by a negative coefficient
The correct answer is to multiply the function by a negative coefficient.
To reflect a function across the x-axis, you need to multiply the function by -1. This will flip the function upside down, reflecting it across the x-axis.
For example, if we have the function f(x) = 2x^2, reflecting it across the x-axis would result in -f(x) = -2x^2. This means that all the y-coordinates of the original function become negative, effectively flipping it upside down.
To reflect a function across the x-axis (flip it upside down), you can follow these steps:
1. Multiply the entire function by a negative coefficient: Multiply each term in the function by -1. This will change the sign of each term and flip the function vertically. For example, if the original function is f(x), the reflected function would be -f(x).
Alternatively, if you are given a function in the form of an equation, you can interchange the x and y variables. This is equivalent to reflecting the function across the line y = x. The equation of the reflected function would then be y = -f(x). However, this method requires having the function expressed as an equation.
Remember, reflecting a function across the x-axis essentially flips the function upside down, so the positive values of the function become negative, and the negative values become positive.
To reflect a function across the x-axis (flipping it upside down), you need to multiply the function by a negative coefficient. Here's how you can do it:
1. Start with the original function, let's call it f(x).
2. Take the original function f(x) and multiply it by -1.
For example, let's say you have the function f(x) = x^2. To reflect it across the x-axis, you multiply it by -1:
-g(x) = -1 * f(x) = -1 * x^2
The resulting function g(x) is the reflection of f(x) across the x-axis.
Note: This works because multiplying the function by -1 changes the sign of every term, essentially flipping it upside down.