reflection over the y axis for g(x)=2(x/4+3)^4-5
To reflect a function over the y-axis, we replace x with -x in the function.
For the function g(x) = 2(x/4 + 3)^4 - 5, replacing x with -x, we get g(-x) = 2(-x/4 + 3)^4 - 5.
Therefore, the reflection of g(x) over the y-axis is g(-x) = 2(-x/4 + 3)^4 - 5.
To reflect a function over the y-axis, we replace x with -x in the equation.
Given the function g(x) = 2(x/4+3)^4-5, we can reflect it over the y-axis by replacing x with -x:
g(-x) = 2((-x)/4+3)^4-5
Simplifying further:
g(-x) = 2(-x/4 + 3)^4 - 5
Thus, the reflection of g(x) over the y-axis is g(-x) = 2(-x/4 + 3)^4 - 5.
To reflect a function over the y-axis, you simply replace x with -x in the original function. In this case, we need to find the reflection of the function g(x) = 2(x/4 + 3)^4 - 5.
Step 1: Replace x with -x.
g(-x) = 2((-x)/4 + 3)^4 - 5
Step 2: Simplify the expression inside the parentheses.
((-x)/4 + 3) simplifies to (-x + 12)/4.
g(-x) = 2((-x + 12)/4)^4 - 5
Step 3: Simplify the expression inside the exponent.
((-x + 12)/4)^4 can be expanded as (-x + 12)^4/4^4, using the property (a/b)^n = a^n / b^n.
g(-x) = 2(-x + 12)^4/4^4 - 5
Step 4: Simplify further if needed.
If you want, you can expand (-x + 12)^4 and then simplify the expression, but that is beyond the scope of just reflecting the function over the y-axis.
So, the reflection of the function g(x) = 2(x/4 + 3)^4 - 5 over the y-axis is g(-x) = 2((-x + 12)^4/4^4) - 5.