Question

Write the equation for the logarithmic function that has the following transformation from the parent logarithmic function. The function will have a base of 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


please help

Answer 1

Start with
y = log x
shifted 3 units left ----> y = log(x+3)
vertical compression by a factor of 2 -----> y = 2log(x+3)
reflection in the y-axis ----> y = 2log(-x+3)
shifted down 5 units : y = 2log(-x+3) - 5

I graphed each of the above using "Desmos" to confirm that each is correct
I assumed that each transformation stated was to follow the previous result