Please help so confused

Question

Write the equation for logarithmic function that has the following transformations from the parent logarithmic function. The function will have a base 10. You will not have to write the 10 . It is assumed

shifted 3 units left

vertical compression by a factor of 2

reflected across the y-axis

shifted down 5 units

Answer 1

Any function is shifted and compressed in the same way. a f(b(x-h)) + k

h = horizontal shift - It says -h because it's shifted in the opposite direction. For example, if x+3, f(x) shifts left 3 and if x-3, f(x) shifts right 3.

k = vertical shift For example if f(x) + 3, then f(x) shifts up 3 and if f(x) - 3, then f(x) shifts down 3

a = vertical dilation/compression - If a = 3 then f(x) is stretched vertically by 3 times or if it's a fraction a = 1/3, then f(x) is compressed by 1/3.. If a is negative, it is flipped across the x-axis (a vertical flip)

b = horizontal compression/dilation by 1/b, the opposite direction - If b= 3 then f(x) is compressed horizontally by 1/3, and if b=1/3 then f(x) is stretched horizontally by 3. If b is negative, it is flipped across the y-axis (horizontal flip).

Following these rules, the function given in the problem is transformed: 1/2 f(-(x+3)) - 5

And because it's a log function, it looks like this. 1/2 log(-(x+3)) - 5