Practice Sheet (02) : Functions & Graphs Part A : Domain & Range (10 questions) 1. Find the domain of π ( π₯ ) = 5 π₯ β 1 π₯ ! β 16 2. Find the domain: π ( π₯ ) = β 3 π₯ β 9 3. Find the domain of the logarithmic function: β ( π₯ ) = ln ( 2 β π₯ ) 4. Determine the domain and range of the constant function π ( π₯ ) = 7 5. Determine the domain of π ( π₯ ) = β π₯ + 2 π₯ β 3 6. State all real numbers for which the expression is defined: 7 25 β π₯ ! 7. Domain of the rational - absolute function: π ( π₯ ) = β£ π₯ + 1 β£ π₯ ! β 1 8. Domain of π ( π₯ ) = 7 2 π₯ ! β 5 π₯ β 3 9. Range of π ( π₯ ) = 3 π₯ ! + 2 10. Range of the piecewise function: π ( π₯ ) = < 2 π₯ + 1 π₯ < 0 π₯ ! π₯ β₯ 0 Part B : Function Values & Algebra (8 questions) 11. Evaluate π ( 3 ) , π ( β 5 ) , and π ( π₯ + β ) for π ( π₯ ) = π₯ ! β 4 π₯ + 1 12. Simplify: π ( π₯ + β ) β π ( π₯ ) , π ( π₯ ) = 1 π₯ 13. Find π ( π ! ) and π ( 2 π + β ) for π ( π₯ ) = β π₯ + 5 14. Compute: π ( π₯ + β ) β π ( π₯ ) , π ( π₯ ) = 3 π₯ β 7 15. Evaluate: π ( 2 π‘ + 1 ) , π ( π§ ! β 3 π§ ) , π ( π₯ + β ) , π ( π₯ ) = 4 π₯ ! 16. If π ( π₯ ) = π₯ " β 3 π₯ , find π ( β 2 ) , π ( 0 ) , and π ( 2 + β ) 17. If π ( π₯ ) = β£ 3 π₯ β 1 β£ find π ( β 1 ) , π E # " F , and π ( π₯ + β ) 18. Evaluate β ( π₯ + β ) β β ( π₯ ) , β ( π₯ ) = β π₯ Part C : Difference Quotient (6 questions) 19. Compute π ( π₯ + β ) β π ( π₯ ) β , π ( π₯ ) = π₯ ! + 2 π₯ 20. Compute DQ for π ( π₯ ) = 5 π₯ β 8 21. Compute π ( π₯ + β ) β π ( π₯ ) β , π ( π₯ ) = 1 π₯ β 4 22. Compute the difference quotient of π ( π₯ ) = β π₯ + 3 23. Compute DQ for π ( π₯ ) = π₯ " 24. Compute π ( π₯ + β ) β π ( π₯ ) β , π ( π₯ ) = π₯ π₯ + 1 Part D : Intercepts & Graph Skills (6 questions) 25. Find x - and y - intercepts of π¦ = β 3 π₯ + 9 26. Find all intercepts of π¦ = 2 π₯ β 6 π₯ + 4 27. Determine intercepts of π₯ = 5 28. Sketch the graph of π¦ = β£ π₯ β 3 β£ and label the vertex. 29. Find intercepts and sketch π¦ = 2 β π₯ 30. Graph the piecewise function and find intercepts: π ( π₯ ) = < β 2 π₯ + 1 π₯ < 1 π₯ ! β 4 π₯ β₯ 1 Part E : One - to - One & Composition (8 questions) 31. Determine whether π ( π₯ ) = π₯ " + 1 is one - to - one. 32. Is π ( π₯ ) = π₯ ! β 2 one - to - one? Why or why not? 33. Find the composition: π ( π₯ ) = 3 π₯ β 2 , π ( π₯ ) = π₯ ! Compute: β’ π ( π ( π₯ ) ) β’ π ( π ( π₯ ) ) 34. If π ( π₯ ) = β π₯ , π ( π₯ ) = 2 π₯ + 5 find π ( π ( π₯ ) ) and π ( π ( π₯ ) ) 35. Find ( π + π ) ( π₯ ) , ( π β π ) ( π₯ ) , ( ππ ) ( π₯ ) , and $ % ( π₯ ) for: π ( π₯ ) = π₯ β 1 , π ( π₯ ) = π₯ + 3 36. Determine whether β ( π₯ ) = π₯ π₯ ! + 1 is one - to - one. 37. Find the composition: π ( π₯ ) = π₯ ! + 4 , π ( π₯ ) = 1 π₯ Compute π ( π ( π₯ ) ) and π ( π ( π₯ ) ) 38. If π ( π₯ ) = β£ π₯ β£ , π ( π₯ ) = π₯ β 3 find π ( π ( π₯ ) ) Part F : Piecewise Functions (6 questions) 39. Evaluate the function at the given points: π ( π₯ ) = < 2 π₯ β 1 π₯ < 0 π₯ ! + 3 π₯ β₯ 0 Compute: β’ π ( β 2 ) β’ π ( 0 ) β’ π ( 3 ) 40. Graph the piecewise function: π ( π₯ ) = I β π₯ π₯ β€ β 1 2 π₯ + 1 β 1 < π₯ < 2 4 π₯ β₯ 2 41. Determine whether the function is continuous at π₯ = 1 : π ( π₯ ) = I π₯ + 2 π₯ < 1 3 π₯ = 1 2 π₯ β 1 π₯ > 1 42. For β ( π₯ ) = L π₯ ! π₯ < 2 π₯ + 5 π₯ β₯ 2 Find: β’ β ( 1 ) β’ β ( 2 ) β’ β ( 5 ) 43. Sketch π ( π₯ ) = I 0 π₯ < 0 π₯ 0 β€ π₯ β€ 4 4 π₯ > 4 44. Graph and find intercepts of: π ( π₯ ) = L π₯ " π₯ < 1 2 π₯ β 3 π₯ β₯ 1