Given the function
a) When we multiply the parent function by –1, we get a reflection about the x-axis. Then
And three times as tall means 3 units up
Shifted four units to the left means shifted 4 units left
Answer: the new function is: g(x) = - ln(x+4) + 3
b) When we multiply the input by –1, we get a reflection about the y-axis.
Shifted seven units up
Half as wide means 1/2 f(x)
Answer: the new function is:
c) We find the inverse of
Then by definition of inverses, g(x) = y
Next, replace all x’s with and all y’s with x
Now, solve for y
Apply properties of logarithms
Answer: