How to make a frame fade into view with math.min and math.max?

I rephrased my question.

--This is a working script.

fade = script.Parent
fadeGoal = 0
fadeRate = 0.05

function updateFade()
    local current = fade.BackgroundTransparency
    if current < fadeGoal then
        fade.BackgroundTransparency = math.min(fadeGoal,current+fadeRate)
    elseif current > fadeGoal then
        fade.BackgroundTransparency = math.max(fadeGoal,current-fadeRate)
    else
        fade.BackgroundTransparency = fadeGoal
    end
end

Now here's my own script by which doesn't work and need help with,

lif hit.Parent:FindFirstChild("Humanoid") ~= nil then

        if game.Players:FindFirstChild(hit.Parent.Name) ~= nil then
        local player = game.Players:FindFirstChild(hit.Parent.Name)

            if player:FindFirstChild("PlayerGui"):FindFirstChild("ScreenGui") == nil then
            sg = Instance.new("ScreenGui")
            sg.Parent = player:FindFirstChild("PlayerGui")
            end

        if player.PlayerGui.ScreenGui:FindFirstChild("MessageBox") == nil then
local ChangeRate = 0.01
local ChangeGoal = 0

        local f = Instance.new("Frame")
        f.Name = "WhiteFrame"
        f.Position = UDim2.new(0, 0, 0, 0)
        f.Size = UDim2.new(1,0, 1,0)                                
        f.Parent = player.PlayerGui:FindFirstChild("ScreenGui")
        f.BackgroundTransparency = 1
        f.BackgroundColor3 = Color3.fromRGB(255,255,255)







wait(1)
f.BackgroundTransparency = math.max(0,f.BackgroundTransparency-0.01)
 end


------------------------------------------
wait(10)

        f:Destroy()
                end
        end
    end


script.Parent.Touched:connect(onTouch)