Let g(x) be the reflection of f(x)=x^2+5 What is the function rule for g(x)?
I know the first part would be-x^2 but not sure if the 2nd part is a plus or minus.
If you want to reflect the whole graph across the x-axis, that would be
-(x^2+5) = -x^2-5
Make a visit to wolframalpha.com and type in your functions. It will show the graph. Make a change a refresh, and you can see the new graph.
You can do more than one at a time by separating the equations with commas:
http://www.wolframalpha.com/input/?i=plot+y%3Dx%5E2%2B5,+y%3D+-x%5E2%2B5,+y%3D-(x%5E2%2B5)
To find the function rule for g(x), the reflection of f(x)=x^2+5, you are correct that the first part will be -x^2.
Now, let's consider the sign of the second part. When reflecting a graph across the x-axis, the sign of the y-coordinate flips. Since f(x)=x^2+5, the second part (5) is positive.
Therefore, the function rule for g(x) is g(x) = -x^2 - 5.
To find the function rule for the reflection of f(x) = x^2 + 5, which is denoted as g(x), we first need to understand what happens when we reflect a function over the x-axis.
When a function is reflected over the x-axis, the y-values (or function values) change signs, while the x-values remain the same. This means that if a point (x, y) lies on the original function f(x), the reflected point on the new function g(x) will have the same x-value but a y-value with the opposite sign.
Given that f(x) = x^2 + 5, let's consider a point on the graph, for example, (2, f(2)). The y-value of this point would be f(2) = 2^2 + 5 = 9. When reflecting, the y-value changes sign from positive to negative. Therefore, the reflected point on g(x) would be (2, -9).
Now, let's apply this reflection process to the entire function f(x) = x^2 + 5.
First, we start with the original function f(x) = x^2 + 5.
Then, we change the sign of the function values to reflect it over the x-axis, which gives us g(x) = -x^2 - 5.
Therefore, the function rule for g(x), the reflection of f(x) = x^2 + 5, is g(x) = -x^2 - 5.