Answer:
Option B:
Function A has a vertical asymptote at x = 1
Function B has a vertical asymptote at x = -3
Step-by-step explanation:
A function f(x) has a vertical asymptote if:
![\lim_{x \to\\k^+}f(x) = \±\infty\\\\ \lim_{x \to\\k^-}f(x) = \±\infty](https://tex.z-dn.net/?f=%5Clim_%7Bx%20%5Cto%5C%5Ck%5E%2B%7Df%28x%29%20%3D%20%5C%C2%B1%5Cinfty%5C%5C%5C%5C%20%5Clim_%7Bx%20%5Cto%5C%5Ck%5E-%7Df%28x%29%20%3D%20%5C%C2%B1%5Cinfty)
This means that if there is a value k for which f(x) has infinity or a -infinity then x = k is a vertical asymptote of f(x). Therefore, the closer x to k approaches, the closer the function becomes to infinity.
We can calculate the asymptote for function A.
![\lim_{x \to \\1^+}(\frac{1}{x-1})\\\\ \lim_{x \to \\1^+}(\frac{1}{1^-1})\\\\ \lim_{x \to \\1^+}(\frac{1}{0}) = \infty\\\\and\\ \lim_{x \to \\1^-}(\frac{1}{x-1})\\\\\lim_{x \to \\1^-}(\frac{1}{0}) = -\infty](https://tex.z-dn.net/?f=%5Clim_%7Bx%20%5Cto%20%5C%5C1%5E%2B%7D%28%5Cfrac%7B1%7D%7Bx-1%7D%29%5C%5C%5C%5C%20%5Clim_%7Bx%20%5Cto%20%5C%5C1%5E%2B%7D%28%5Cfrac%7B1%7D%7B1%5E-1%7D%29%5C%5C%5C%5C%20%5Clim_%7Bx%20%5Cto%20%5C%5C1%5E%2B%7D%28%5Cfrac%7B1%7D%7B0%7D%29%20%3D%20%5Cinfty%5C%5C%5C%5Cand%5C%5C%20%5Clim_%7Bx%20%5Cto%20%5C%5C1%5E-%7D%28%5Cfrac%7B1%7D%7Bx-1%7D%29%5C%5C%5C%5C%5Clim_%7Bx%20%5Cto%20%5C%5C1%5E-%7D%28%5Cfrac%7B1%7D%7B0%7D%29%20%3D%20-%5Cinfty)
Then, function A has a vertical asymptote at x = 1.
The asymptote of function B can be easily observed in the graph. Note that the function b is not defined for x = -3 and when x is closest to -3, f(x) approaches infinity.
Therefore x = -3 is asintota of function B.
Therefore the correct answer is option B.
Answer:
1/11
Step-by-step explanation:
First you have to times 1/3 and 1/2 and then you get 1/6. Then you add 1/3 and 1/2 and that's 1/5. then you add them both.
i’m pretty sure
Slope 2
Slope intercept form y=2x+5
y-int is 5
Slope 4
Slope intercept form y=4x+22
y-int 22
i hope this helps a little buh i’m sorry in advance
Answer:
{f|0 ≤ f(x)}; x² - 4x + 5
Step-by-step explanation:
To find the Quadratic Equation, plug the <em>vertex</em> into the Vertex Equation FIRST, <em>y = </em><em>a</em><em>(</em><em>x</em><em> </em><em>-</em><em> </em><em>h</em><em>)</em><em>²</em><em> </em><em>+</em><em> </em><em>k</em>, where (<em>h</em><em>,</em><em> </em><em>k</em>) → (<em>2,</em><em> </em><em>1</em>)<em> </em>is the vertex, plus, -h gives you the OPPOSITE terms of what they really are, and k gives you the EXACT terms of what they really are: (x - 2)² + 1. Doing this will give you the Quadratic Equation of <em>x² - 4x + 5</em>. You understand now?
I am joyous to assist you anytime.