All of the four functions are exponential functions of the form:![f(x)=Pa^{x}+Q](/tpl/images/0382/8310/41d5e.png)
Where,
P changes the parent function's,
![f(x)=a^{x}](/tpl/images/0382/8310/927c7.png)
, slope (more steep or less steep)Q shifts the parent function,
![f(x)=a^{x}](/tpl/images/0382/8310/927c7.png)
, upwards if Q is positive and downwards if Q is negative.
The parent function looks like the first image attached. Note that the x-axis (y=0) is the horizontal asymptote.
Since question asked for a function with horizontal asymptote of y=3, we can shift the function 3 units above by changing Q to +3. The fourth option has an equation of an exponential that has Q value of +3. This is the correct choice.
ANSWER: ![f(x)=2(4^{x})+3](/tpl/images/0382/8310/78751.png)
![Which function has a horizontal asymptote of y = 3? f(x) = 3(2^x) f(x) = 2(4)^x–3 f(x) = 2(3^x) f(](/tpl/images/0382/8310/d8361.jpg)