Answer:
The equations that represent the reflected function are


Step-by-step explanation:
The correct question in the attached figure
we have the function

we know that
A reflection across the y-axis interchanges positive x-values with negative x-values, swapping x and −x.
therefore

The reflection of the given function across the y-axis will be equal to
(Remember interchanges positive x-values with negative x-values)

An equivalent form will be
![f(x)=5(\frac{1}{5})^{(-1)(x)}=5[(\frac{1}{5})^{-1})]^{x}=5(5)^{x}](https://tex.z-dn.net/?f=f%28x%29%3D5%28%5Cfrac%7B1%7D%7B5%7D%29%5E%7B%28-1%29%28x%29%7D%3D5%5B%28%5Cfrac%7B1%7D%7B5%7D%29%5E%7B-1%7D%29%5D%5E%7Bx%7D%3D5%285%29%5E%7Bx%7D)
therefore
The equations that represent the reflected function are


Given that

, then

The slope of a tangent line in the polar coordinate is given by:

Thus, we have:

Part A:
For horizontal tangent lines, m = 0.
Thus, we have:

Therefore, the <span>values of θ on the polar curve r = θ, with 0 ≤ θ ≤ 2π, such that the tangent lines are horizontal are:
</span><span>θ = 0
</span>θ = <span>2.02875783811043
</span>
θ = <span>4.91318043943488
Part B:
For vertical tangent lines,

Thus, we have:

</span>Therefore, the <span>values of θ on the polar curve r = θ, with 0 ≤ θ ≤ 2π, such that the tangent lines are vertical are:
</span>θ = <span>4.91718592528713</span>
Answer:
a b
Step-by-step explanation: