Question
Let
This function has:
- Ay intercept at the point
-
intercepts at the point(s)
- Vertical asymptotes at
This function has:
Ask by Lang Garza. in the United States
Mar 17,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
The vertical asymptotes of the function are at
and
.
Solution

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Beyond the Answer
To find the vertical asymptotes of the function
, we need to identify where the denominator equals zero. Setting the denominator
and solving for
will yield the points of vertical asymptotes.
Using the quadratic formula,
, with
, we find the roots:
Thus, the roots are:
This means the vertical asymptotes occur at
and
.
So, summarizing:
- The vertical asymptotes are at
and .
Now, let’s add more flavor to this mathematical journey!
Have you ever pondered how ancient civilizations approached ratios and fractions? The ancient Egyptians had their unique fraction system, using only unit fractions (like
,
) to represent values. They would reject using fractions like
directly! The reasoning? Simplicity and clarity, reminiscent of how we simplify algebraic functions today!
And after diving into the world of mathematical functions, why not explore some fun applications? Rational functions like
pop up everywhere from physics (think of ratios of forces) to economics (modeling cost-revenue relationships). Understanding these functions not only hones your algebra skills but also sets you on the path to conquering real-world scenarios – where math meets money and mechanics!