Question

he graph below is a transformation of f(x)=2^x . Write an equation describing the transformation.exponential with f(x) approaching 1 as x grows to negative infinity. As x gets infinity larger f(x) gets infinity smallerThe coefficient on our transformed function is AnswerThe exponent on our transformed function is AnswerThe constant we are adding to our function f(x)=2^x is Answer

Answer 1

The coefficient on our transformed function is -4

The exponent on our transformed function is x

The constant we are adding to our function f(x)=2^x is +1

How to find the equation

To find the equation we investigate the transformed image

Firstly, we notice there was a reflection over the x-axis. This introduces a negative sign

Secondly there was one unit upward translation. This will lead to addition of one.

Lefts find the coeficient of the function (a). Assuming the function is represented by the equation

• g(x) = a(b)ˣ

From the parent function (f(x) = 2ˣ) we have that b = 2. Using the graph we translate down 1 unit (we will add the 1 later). Then we can see the graph passed through (0, -4). Hence we have that

g(x) = a(b)ˣ

-4 = a(1) (2 exponent 0 = 1)

a = -4

plugging in a and b results to g(x) = -4(2)ˣ then we add the 1 (earlier removed), to get the final equation as

• g(x) = -4(2)ˣ + 1

Answer 2

Original function:

`f(x)=2^x`

The transformed function has a reflection over the x-axis and a shift downward, as in our function, the y-intercept (when we set the x to 0 in the equation) is at (0,1).

Then, to make a reflection about the x-axis we have to add a minus sign:

`f(x)=-2^x`

Finally, to get the y-intercept at (0, -3), we have to subtract two to our function:

`f(x)=-2^x-2`

Proving that it is correct:

`f(0)=-2^0-2=-1-2=-3`

Answer:

`f(x)=-2^x-2`

• Coefficient: -2

,

• Exponent: ,x

,

• Constant: -2