precalculus 12 grade

Question

Given f(x)=5^x, which function represents a reflection across the x-axis, a vertical dilation by 3, a vertical translation of 1 unit, and a horizontal translation of 2 units

g(x)=3(-5)^x-1+2

g(x)=3(-5)^x-2+1

g(x)=-3(5)^x-2+1

Answer 1

The reflection across the x-axis is indicated by placing a negative in front of the original function so that f(x)=-5^x. The next step is to multiply the function by 3, so that you now have 3(-5^x). A vertical translation adds 1 to the end of it, 3(-5^x)+1. The horizontal translation of 2 units would be accomplished by changing the x to (x-2). So the final answer is f(x)=3(-5^(x-2))+1. I hope that helps!

None of the answers listed in the original problem are correct.

Answer 2

Reflection across the x-axis means you are reflecting in the y-direction. Consequently, you add a negative to the "y" variable. That would mean the function becomes -y = 5^(x) or y = -5^(x). For vertical dilations just add the dilation value to the front of the function. So the function becomes y = -3•5^(x)

A vertical translation of 1 unit means you add "+ 1" to the end of the function so it becomes: y = -3•5^(x) + 1

A horizontal translation of 2 units means you must group the OPPOSITE or -2 with the x-variable.

So, g(x) = -3•5^{(x - 2)} + 1