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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(x) = 2(4^x) + 3

Respuesta :

TaeKwonDoIsDead

All of the four functions are exponential functions of the form:[tex]f(x)=Pa^{x}+Q[/tex]

Where,

  • P changes the parent function's, [tex]f(x)=a^{x}[/tex], slope (more steep or less steep)
  • Q shifts the parent function, [tex]f(x)=a^{x}[/tex], 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: [tex]f(x)=2(4^{x})+3[/tex]

Ver imagen TaeKwonDoIsDead
MrRoyal

The function that has an horizontal asymptote of 3 is f(x) = 2(4^x) + 3

How to determine the function?

Looking through the options, we can see that the four functions are exponential functions.

Assume that an exponential function is represented as:

f(x) = a(b)^x + c

The horizontal asymptote of the function is at:

y = c

From the list of given options, we have the function f(x) = 2(4^x) + 3, where c = 3

Hence, the function that has an horizontal asymptote of 3 is f(x) = 2(4^x) + 3

Read more about asymptote at:

https://brainly.com/question/1851758

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