Year 11 Specialist (Unit 1 & 2)
Graphing techniques
Graphing rational functions using calculus
ACCOUNT REQUIRED
Unlock all 5 questions & worked solutions
You're viewing a free preview. Create an account to access the complete question set, step-by-step solutions, and progress tracking.
All Questions
Access the full question set for every topic.
Worked Solutions
Step-by-step explanations for every answer.
Track Progress
Mark questions right or wrong and monitor your growth.
It's Free
No credit card required - sign up in under a minute.
Questions
Question 1
75373
Sketch the graph of \(y=x-4+\dfrac{4}{x}\).
Show all intercepts, asymptotes and turning points.
| \begin{align} y&=x-4+\dfrac{4}{x}\\ x \ne 0 \to x &= 0 \text{ is an asymptote}\\ \text{If } x &\ne 0 \text{ then }y \ne x-4\\ \therefore \,y&=x-4 \text{ is an asymptote}\\ \\ y&=x-4+4x^{-1}\\ y'&=1-4x^{-2}\\ y'&=0\\ \frac{4}{x^2}&=1\\ x&= \pm 2\\ (2,0),\, (-2,-8) &\text{ are turning points}\\ \\ (2,0),\ & x\text{-intercept} \end{align} |
|
📚 Want More Questions?
There are 4 more questions available. Create your free account to access the complete question set with detailed solutions.