Hello, i need help with these questions from calculus, I'm quite stuck

Question

1) Find f(x)=ab^x if f(2)=1 and f(-1)=4

2) Define the new functions based on the transformations of the initial functions :

a) g(x) is obtained by shifting f(x)=3^x

four units to the left .

b) h(x) is obtained by shifting f(x)=log₃x two units down.

Answer 1

1) This is a systems of equations problem. You have to solve for a and b.

Plug in the points given (2, 1) and (-1, 4) into the function

1 = a*b²

4 = a*b^-1

Do you think you can solve for a and b?

Once you do, just plug in a and b into the function f(x) = a*b^x

To transform a function c units to the right, replace x with (x - c).

Here your transforming the function to the left so replace x with (x- -4) or (x+4)

To shift a function down just subtract the function by the amount you're shifting by.

If you want to shift a function up, you add the function by the amount you're shifting by.