How do you reflect a function across the x-axis (flip it upside down)?

Question

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

Answer 1

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.