Question

Review for test not worth any points Could u also make a box like the one I showed

Answer 1

2. Exponential function:

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

Substituting with x = 0, we get:

`\begin{gathered} f(0)=((1)/(4))^0 \\ f(0)=1 \end{gathered}`

Then, f(x) passes through the point (0 ,1)

Substituting with x = -1, we get:

`\begin{gathered} f(-1)=((1)/(4))^(-1) \\ f(-1)=4 \end{gathered}`

Then, f(x) passes through the point (-1 ,4)

Substituting with x = -2, we get:

`\begin{gathered} f(-2)=((1)/(4))^(-2) \\ f(-2)=4^2 \\ f(-2)=16 \end{gathered}`

Then, f(x) passes through the point (-2 ,16)

Substituting with x = 1, we get:

`\begin{gathered} f(1)=((1)/(4))^1 \\ f(1)=(1)/(4) \end{gathered}`

Then, f(x) passes through the point (1, 1/4)

Substituting with x = 2, we get:

`\begin{gathered} f(2)=((1)/(4))^2 \\ f(2)=(1^2)/(4^2)^{} \\ f(2)=(1)/(16)^{} \end{gathered}`

Then, f(x) passes through the point (2, 1/16)

f(x) has the form:

`y=b^x^{}`

where b, the base, is between 0 and 1. This means that, when x tends to infinity, f(x) tends to zero, and when x tends to negative infinity, f(x) tends to

infinity.

Taking into account these characteristics and the points where f(x) passess, its graph is: