Find the vertical asymptote(s) of f of x equals quantity 4 x squared plus 3x plus 6 end quantity over quantity x squared minus 3
1 answer:
The vertical asympototes of f(x) are at x = -6 and x = 6
Step-by-step explanation:
To find the vertical asymptote(s) of a rational function,
- Equate the denominator by 0
- Solve it for x
- If x = a, then the vertical asymptote is at x = a
∵
- Equate the denominator x² - 36 by 0
∵ x² - 36 = 0
- Add 36 to both sides
∴ x² = 36
- Take √ for both sides
∴ x = ± 6
∴ There are vertical asymptotes at x = -6 and x = 6
The vertical asympototes of f(x) are at x = -6 and x = 6
Learn more:
You can learn more about the asymptotes in brainly.com/question/6459599
#LearnwithBrainly
You might be interested in
We will conclude that:
- The domain of the exponential function is equal to the range of the logarithmic function.
- The domain of the logarithmic function is equal to the range of the exponential function.
<h3>Comparing the domains and ranges.</h3>
Let's study the two functions.
The exponential function is given by:
f(x) = A*e^x
You can input any value of x in that function, so the domain is the set of all real numbers. And the value of x can't change the sign of the function, so, for example, if A is positive, the range will be:
y > 0.
For the logarithmic function we have:
g(x) = A*ln(x).
As you may know, only positive values can be used as arguments for the logarithmic function, while we know that:
So the range of the logarithmic function is the set of all real numbers.
<h3>So what we can conclude?</h3>- The domain of the exponential function is equal to the range of the logarithmic function.
- The domain of the logarithmic function is equal to the range of the exponential function.
If you want to learn more about domains and ranges, you can read: