Question

The graph below is a transformation of f(x)= \frac{1}{4} ^x . Write an equation describing the transformation.As x approaches negative infinity f(x) approaches infinity. As x approaches infinity f(x) approaches 1.(-3,5) is on the graphThe coefficient on our transformed function is AnswerThe exponent on our transformed function is AnswerThe constant we are adding to our function f(x)= \frac{1}{4} ^x is Answer

Answer 1

The function is given to be:

`y=(1)/(4)^x`

The graph of the function is shown below:

The graph is shifted up and to the left.

The graph is shifted up by 1 unit. This transformation rule is given to be:

`f(x)\to f(x)+1`

Therefore, the function becomes:

`y=(1)/(4)^x+1`

The graph is shifted to the left by 2 units. The transformation rule is given to be:

`f(x)\to f(x+2)_{}`

Therefore, the function becomes:

`y=(1)/(4)^((x+2))+1`

To check if the function is correct, we can use the points (-3, 5) if it gives a true statement:

`\begin{gathered} (x,y)=(-3,5) \\ \therefore \\ 5=(1)/(4)^((-3+2))+1 \\ 5=(1)/(4)^((-1))+1 \\ 5=4+1 \\ 5=5(\text{True)} \end{gathered}`

Therefore, the function is:

`y=(1)/(4)^((x+2))+1`

The coefficient is 1.

The exponent is x + 2.

The added constant is 1.