Step 1:
Write the parent function formula of an exponential function
[tex]f(x)=ab^x[/tex]
Step 2:
Pick two values from the graph
Step 3
[tex]\begin{gathered} Fromy=ab^x^{} \\ \text{when x = 0, y = 3} \\ \text{3 = a }\times b^0 \\ \text{3 = a }\times\text{ 1} \\ \text{a = 3} \\ \text{when x = 1 , y = 6} \\ 6\text{ = 3 }\times b^1 \\ b\text{ = }\frac{6}{3}\text{ = 2} \end{gathered}[/tex]
Step 4
[tex]f(x)=3(2^x)[/tex]
y-intercept = (0 , 3)
[tex]\begin{gathered} Domain\text{ = (-}\infty\text{ , }\infty) \\ \text{Range = }(0\text{ , }\infty) \end{gathered}[/tex]
Horizontal asymptote: y = 0
Step 5
End behavior
Right end behavior
[tex]\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}[/tex]
Left end behavior
[tex]\begin{gathered} \lim _{x\to-\infty}(3.2^x)\text{= 0} \\ \mathrm{as}\: x\to\: -\infty\: ,\: f\mleft(x\mright)\to\: 0 \end{gathered}[/tex]
Increasing or decreasing
[tex]\mathrm{Increasing}\colon-\infty\:
