How do you reflect a function across the x-axis (flip it upside down)?
Responses
Multiply by a negative coefficient
Multiply by a negative coefficient
Change the variable
Change the variable
Subtract a number larger than 10
Subtract a number larger than 10
Use an irrational exponent
None of the provided responses accurately describe how to reflect a function across the x-axis. To reflect a function across the x-axis (flip it upside down), you need to multiply the function by -1. This can be achieved by multiplying the function's output or y-values by -1.
To reflect a function across the x-axis (flip it upside down), you can follow these steps:
1. Multiply the function by a negative coefficient: Multiply the entire function by -1. This will reverse the sign of every term in the function and flip it upside down.
For example, if you have a function f(x), reflecting it across the x-axis would be -f(x).
2. Change the variable: Replace all instances of x in the function with -x. This will cause the graph of the function to be mirrored across the y-axis.
For example, if you have a function f(x), reflecting it across the x-axis would be f(-x).
3. Subtract a number larger than 10: Subtract a number greater than 10 from the function. This will shift the graph vertically downwards and flip it upside down.
For example, if you have a function f(x), reflecting it across the x-axis would be f(x) - 20.
4. Use an irrational exponent: If you have a function with an exponent, using an irrational exponent can also reflect the function across the x-axis. However, this might lead to a more complicated function.
For example, if you have a function f(x) = x^2, reflecting it across the x-axis would be f(x) = x^(√2).
These are different ways to reflect a function across the x-axis, depending on the specific transformation you want to achieve.
To reflect a function across the x-axis and flip it upside down, you can follow these steps:
1. Start with the original function, which can be written as f(x).
2. To flip the function, you need to multiply it by a negative coefficient. This means multiplying f(x) by -1. The resulting function would be -f(x).
For example, if the original function is f(x) = x^2, after reflecting it across the x-axis, it becomes -f(x) = -(x^2). This flipped function is now the reflection of the original function across the x-axis.