Question
How do you reflect a function across the x-axis (flip it upside down)?
Responses
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
Multiply by a negative coefficient
Change the variable
Change the variable to its negative value.
To reflect a function across the x-axis (flip it upside down), you can follow these steps:
1. Subtract the y-coordinate of each point on the function from 0. This will essentially flip the positive and negative values of the function.
For example, let's say you have the function f(x) = x^2. To reflect it across the x-axis, you would subtract the y-coordinate from 0: g(x) = -f(x) = -(x^2).
2. Another way to reflect a function across the x-axis is by multiplying the function by -1. This will change the sign of each term in the function.
Continuing with the previous example of f(x) = x^2, you can multiply the function by -1 to get g(x) = -1 * f(x) = -x^2.
Both methods will achieve the same result of reflecting the function across the x-axis.
To reflect a function across the x-axis and flip it upside down, you need to multiply the function by a negative coefficient.
1. Start with your original function, for example, f(x).
2. Multiply the entire function by -1. This will change the sign of every term in the function and flip it across the x-axis.
For example, if we have the function f(x) = x^2, to reflect it across the x-axis, we multiply it by -1, resulting in -f(x) = -x^2. Now the function is flipped upside down with respect to the x-axis.
It's important to note that if the original function has any constants or coefficients, they will also be multiplied by -1. However, the terms within the function (like exponents or logarithms) remain the same.