Weekly Math Problem #77

Asymptotes. Oh man...I was "this" 🤏🏿 close to skipping this week's problem. Nonetheless, I pressed on. I was scrolling through a College Algebra Study Guide (from my personal archives) when I came across the question you will see below. When I read it, it thought to myself, "Do I remember how to find asymptotes?". 🤔 Then I recalled that there are some rules to remember when it comes to finding any existing asymptotes for rational functions. So, this topic is the focus of this week's WMP.

Check out WMP #11 where I did some previous work with asymptotes.

To solve this week's problem in completion, you need to recall the following math skills and information:

        ✔️     Rules for finding asymptotes 
        ✔️     How to solve linear equations

            

WMP #77 says ...

Happy solving!

Check back on Saturday, April 2nd for the solution, which will be posted below ⬇️.

Shameless 🔌 Plug: Follow me on Instagram @TheYoungeLady
Buy Me a ☕️ Coffee: TheYoungeLady ( I'm gonna need it this year. 😆 )

✏️📓 Solution Time! 📓✏️

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Let's start with the HA (horizontal asymptote). There are two ways you can find the HA. One way is to pay attention to the degrees of the numerator and denominator, then follow the rule. In our case, the degree of the numerator and denominator are the same (each is degree one ---> linear). When the degrees are the same, then the value for the equation of the line is the ratio of the leading coefficients.

Alternatively, you can evaluate the function at a very large value...say 100 or more. (The larger, the better, as long as your machine can handle it.) The result will yield the value or an an approximate value for the horizontal asymptote. Remember, the equation for a horizontal line is y = , f(x) = , etc.

As for the VA (vertical asymptote), all you need to do is set the denominator equal to zero and solve for x. Your solution is the equation of the VA.

No oblique asymptotes exist because our function doesn't fit the criteria for having any.

Here is a graph of the function:

 

** This plot was generated using Geogebra.org's calculator. **

▪️ Were you able to find the asymptotes?

▪️ Let me know what you thought about this week's problem in the comments section. 

Thank you for solving with me this week. ✏️
We're on to WMP! #78. 🤓

Cheers!

The Younge Lady

Weekly Math Problem! #11

Conic Sections. Graphing is cool. I like pictures a lot; I'm very visual. Conic sections are cool. I just thought I'd throw this problem in the mix, so I could do some more graphing.  

To solve this week's problem in completion, you need to recall the following math skills:

    ✔️  Completing the square method

    ✔️  Factoring polynomials

    ✔️  Other algebra techniques 🤷🏿

    

I present to you WMP! #11...

Happy solving! 

Check back on Friday, July 17th for the solution, which will be posted below ⬇️.

Shameless plug: Follow me on Instagram @TheYoungeLady

✏️📓 Solution Time! 📓✏️

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I previously used the completing the square method in WMP! #7 which required me to solve a quadratic equation. Here's how the completing the square method looks for the curve from this week's problem:

L👀ks like we have a...🥁drum roll please🥁...HYPERBOLA! 🎉 Now that we know we have a HYPERBOLA, we can find the center, vertices, and asymptotes. I color coordinated the important information from the standard form with the components associated with a HYPERBOLA.

Here is the graph of the HYPERBOLA with the center, vertices, and asymptotes identified:

*This graph was generated on Geogebra.org.*

😄 I had fun with this one. 😄

◾️ Have you ever studied conic sections?? 

◾️ If so, what was your experience like?? 

◾️ Comment below with your responses and let me know what you thought about this week's problem.

See you next week for...WMP! #12 📚

Cheers!

The Younge Lady