What is the new equation?

Question

B(X)= 2(3)^x+4 +1 is the orignial.

write a new equation of C(X) if b(x) is reflected vertically, transformed 3 units to the right and 2 units down 

Answer 1

B(x) = 2(3)^x+4 + 1 is how I read the original function

 

reflected across the x-axis

B₁(x) = -2(3)^x+4 - 1

 

Translated three to the right

B₂(x) = -2(3)^x+4-3 - 1 = -2(3)^x+1 - 1

 

Translated two units down

B₃(x) = -2(3)^x+1 - 3

 

Answer 2

Arisha, in order for b(x) to be reflected vertically, then the y-values have to switch signs, right? If we came up with b(x) = 3, then c(x) must equal -3. We do this by making 2 into -2.

 

To move left or right, we do the opposite of what is related to x, so x + 4 would become x + 4 - 3, or x + 1

 

To move up or down, we add or subtract outside of anything having to do with x. + 1 in b(x) becomes x + 1 - 2 = x - 1.

 

Sooooooo, c(x) = -2(3)^{x + 1} - 1

 

Hope this helps!