Calculus I · Functions, limits, continuity, and asymptotic behavior
Classify the discontinuities and asymptotes of a rational function
Problem
For $g(x)=\displaystyle\frac{2x^2-5x-3}{x^2-x-2}$, identify the domain, every discontinuity, every vertical asymptote, any removable discontinuity (including its missing $y$-value), and the horizontal asymptote. Justify the classification with limits rather than only a cancelled formula.
Hint
Name the mathematical object that changes or is sought, and record the domain before doing algebra or calculus.
Check your work
Work the problem yourself first. Then open it in Training to check your answer and read the full worked solution.
Create a free account to check your answer and see the solution. Create a free account.
More Calculus I practice problems
- A farmer has 240 m of fencing and will enclose a rectangular pasture along a straight…Antiderivatives, definite integrals, and the Fundamental Theorem of Calculus
- Rationalize a trigonometric radical differenceFunctions, limits, continuity, and asymptotic behavior
- Differentiate an implicit curve at a specified pointDerivatives, rules, and implicit differentiation
- Differentiate a power with two changing partsDerivatives, rules, and implicit differentiation
- Relate an expanding radius to an area rateDerivative applications, optimization, and related rates
- Force two critical points from three rootsDerivative applications, optimization, and related rates
- Differentiate an accumulation function with a variable upper boundAntiderivatives, definite integrals, and the Fundamental Theorem of Calculus
- Use washers to form a volume of revolutionApplications of integration
- Diagnose a false convergence claim from the term limitIntroduction to sequences and series