Question 15 CAPS Hyperbola | Asymptotes, Domain & Transformations Full Step-by-Step Solution

🔥 Prepare for your CAPS Mathematics exams with this complete step-by-step solution to Hyperbola Question 15! In this lesson, we solve a Grade 11 Functions and Graphs exam-style question involving graph interpretation, asymptotes, intercepts, domain, lines of symmetry, inequalities, and graph transformations. 📘 Given: f(x)= x+p a ​ +q and the graph shows: ✔ The asymptotes intersect at (−3;−1) ✔ The graph cuts the x-axis at (−5;0) Using only the information provided on the sketch, we determine the complete equation and answer all the questions step-by-step. 📘 In this video, we: ✅ Determine the values of p and q from the asymptotes ✅ Calculate the value of a ✅ Determine the y-intercept ✅ Determine the domain of the function ✅ Find the line of symmetry with a negative gradient ✅ Solve the inequality f(x)≥0 ✅ Analyse the transformation from f to g ✅ Apply CAPS exam-solving techniques step-by-step 📚 Questions covered: ✔ 5.1 Write down the values of p and q ✔ 5.2 Determine the value of a ✔ 5.3 Calculate the y-intercept of f ✔ 5.4 Write down the domain of f ✔ 5.5 Determine the line of symmetry with a negative gradient ✔ 5.6 Determine the values of x for which f(x)≥0 ✔ 5.7 Describe the transformation of f to g(x)= x−1 2 ​ +1 📖 Concepts covered: ✔ Hyperbola graphs ✔ Reading information from a sketch ✔ Vertical and horizontal asymptotes ✔ x-intercepts and y-intercepts ✔ Determining parameters a, p, and q ✔ Domain of a hyperbola ✔ Lines of symmetry ✔ Hyperbola inequalities ✔ Graph transformations ✔ Functions and Graphs revision ✔ CAPS exam-style problem solving 🎯 Perfect for: ✔ Grade 11 CAPS Maths students ✔ Grade 12 revision learners ✔ Functions and Graphs revision ✔ Test preparation ✔ Examination preparation ✔ CAPS Mathematics learners 📌 By the end of this lesson, you will be able to: ✅ Read key information directly from a hyperbola sketch ✅ Determine the equation of a hyperbola from a graph ✅ Find asymptotes and intercepts confidently ✅ Solve hyperbola inequalities accurately ✅ Understand graph transformations ✅ Answer CAPS exam-style hyperbola questions with confidence 📌 Don’t forget to: 👍 Like the video 🔔 Subscribe for more CAPS Maths lessons 💬 Comment your questions below #CAPSMaths #Hyperbola #Grade11Maths #FunctionsAndGraphs #Mathematics #MathsRevision #Asymptotes #GraphInterpretation #Transformations #Domain #ExamPreparation #SouthAfrica #MathsTutorial #HyperbolaQuestions #CAPSRevision #FunctionsAndGraphsRevision #Grade11CAPSMaths #HyperbolaRevision #MathsExamPrep