How do I solve the transformations for these 2 problems?

 1)

 k^x

 2k^(x + 5) - 6

 sqrt(abs(2 k^(x + 5) - 6)^2 + abs(k^x)^2)

 2)

 log x

 log(-x + 3) + 2

 sqrt(abs(log(3 - x) + 2)^2 + abs(log(x))^2)

You should learn to identify various transformations of a function:

Reflections:

vertical: -f(x), horizontal: f(-x)

Translations (shifts):

vertical: f(x) + k, horizontal: f(x + k)

Dilations:

vertical: k * f(x), horizontal f(kx)

PROBLEM 1:

Your original function is:

f(x) = k^x

Your transformed function is:

g(x) = 2 * f(x + 5) - 6

That's a horizontal dilation (compression) by a factor of 2 in width.

Then a shift of 5 units to the left.

And a shift of 6 units down.

PROBLEM 2:

Your original function is:

f(x) = log(x)

Your transformed function is:

g(x) = log(-x + 3) + 2

That's a horizontal reflection (across the y-axis).

There's a shift of 3 units to the left.

And a shift of 2 units up.