Question

Identify the characteristics of the following exponential function write none when appropriate

Answer 1

Step 1:

Write the parent function formula of an exponential function

`f(x)=ab^x`

Step 2:

Pick two values from the graph

Step 3

`\begin{gathered} Fromy=ab^x^{} \\ \text{when x = 0, y = 3} \\ \text{3 = a }* b^0 \\ \text{3 = a }*\text{ 1} \\ \text{a = 3} \\ \text{when x = 1 , y = 6} \\ 6\text{ = 3 }* b^1 \\ b\text{ = }(6)/(3)\text{ = 2} \end{gathered}`

Step 4

`f(x)=3(2^x)`

y-intercept = (0 , 3)

`\begin{gathered} Domain\text{ = (-}\infty\text{ , }\infty) \\ \text{Range = }(0\text{ , }\infty) \end{gathered}`

Horizontal asymptote: y = 0

Step 5

End behavior

Right end behavior

`\begin{gathered} \lim _(x\to\infty)\text{ }(3.2^x)\text{ = }\infty \\ \mathrm{as}\: x\to\: +\infty\: ,\: f\mleft(x\mright)\to\: +\infty\: \end{gathered}`

Left end behavior

`\begin{gathered} \lim _(x\to-\infty)(3.2^x)\text{= 0} \\ \mathrm{as}\: x\to\: -\infty\: ,\: f\mleft(x\mright)\to\: 0 \end{gathered}`

Increasing or decreasing

[tex]\mathrm{Increasing}\colon-\infty\: