How do you reflect a function across the x-axis (flip it upside down)?
Responses
Change the variable
Change the variable
Subtract a number larger than 10
Subtract a number larger than 10
Use an irrational exponent
Use an irrational exponent
Multiply by a negative coefficient
To reflect a function across the x-axis, you need to multiply the function by a negative coefficient. Specifically, you multiply each y-value (output) of the function by -1. This will flip the function upside down.
For example, let's say you have the function f(x) = x^2. To reflect this function across the x-axis, you need to multiply each output value by -1. The reflection, in this case, would be f(x) = -x^2.
Similarly, if you have a more complex function, such as f(x) = 2x^3 - 4x + 1, to reflect it across the x-axis, you would again multiply the whole function by -1. The reflection would be f(x) = -2x^3 + 4x - 1.
By multiplying the function by a negative coefficient, you essentially reverse the sign of all the y-values, which results in a reflection across the x-axis.
To reflect a function across the x-axis (flip it upside down), you can follow these steps:
1. Identify the given function. Let's call it f(x).
2. Replace the variable x in the function with -x. This change will result in the function being reflected across the x-axis. The new function will be f(-x).
3. Simplify the function if necessary.
By replacing x with -x in the original function, you are essentially reflecting the graph of the function across the x-axis.
To reflect a function across the x-axis (flip it upside down), you need to multiply the function by a negative coefficient.
Here's how you can do it step by step:
1. Start with the original function, let's say it's f(x).
2. Multiply the function by -1. This will change the sign of the function, effectively flipping it upside down.
The reflected function would be -f(x), or you can also write it as f(x) multiplied by -1.
For example, let's say you have the function f(x) = x^2. To reflect it across the x-axis, you would multiply it by -1:
Reflected function = -1 * f(x) = -1 * x^2 = -x^2
Now the function -x^2 is the reflection of the original function f(x) = x^2 across the x-axis.