Algebra 2 Semester 1 Final A PDF

Name______________________________________________________________________ Date _________________ Period______ Algebra 2 Semester 1 Final A 1. Which ordered pair could represent a y-intercept on...

Name______________________________________________________________________ Date _________________ Period______ Algebra 2 Semester 1 Final A 1. Which ordered pair could represent a y-intercept on a graph? a. (6, 0) b. (0, 4) c. (-1, 3) d. (2, 0) 2. The set of x-coordinates of the ordered pairs of a relation is called? a. range b. relation c. domain d. correlation 3. The set of y-coordinates of the ordered pairs of a relation is called? a. range b. relation c. domain d. correlation 4. What is the range of the relation below? {(-4, 1), (-2, 0), (8, -1) a. {-1, 1} b. {-1, 0, 1} c. {-4, -2, 8} d. {-4, -2, -1, 0, 1, 8} 5. What is the domain of the relation below? a. {-1, 0, 1, 3} b. {-2, 0, 1, 3} c. {-2, -1, 0, 1, 2, 3} d. {0, 1, 2, 3}  6. What is the domain of the relation below? a. (−∞, 5) b. [−∞, 5] c. (−∞, 5] d. (−∞, ∞) 7. Which statement is true? a. Only Graph A is a function. b. Only Graph B is a function. c. Both graphs are functions. d. Neither graph is a function. 8. Given the function below, which of the following values will result in f(x) = 10? a. 𝑓(−2) b. 𝑓(−4) c. 𝑓(4) d. 𝑓(13) 9. For 𝑓(𝑥) = −3𝑥 + 6, find 𝑓(2) a. 0 b. -12 c. 9 d. 12 10. Use the vertical-line test to determine which graph represents a function. a. y c. y 8 8 4 4 –8 –4 O 4 8 x –8 –4 O 4 8 x –4 –4 –8 –8 b. y d. y 8 8 4 4 –8 –4 4 8 x –8 –4 O 4 8 x –4 –4 –8 –8 11. If a function, is shifted to the left four unit(s), what function represents the transformation? a. c. b. d. 12. What transformations change the graph of f(x) to the graph of g(x)? ; a. The graph of is the graph of translated to the left 5 units and down 9 units. b. The graph of is the graph of translated to the up 5 units and right 9 units. c. The graph of is the graph of translated to the down 5 units and left 9 units. d. The graph of is the graph of translated to the right 5 units and up 9 units. 13. What is the graph of 𝑦 = 𝑥 2 − 3 translated up 2 units? y 8 4 –8 –4 4 8 x –4 –8 a. y b. y 8 8 4 4 –8 –4 4 8 x –8 –4 4 8 x –4 –4 –8 –8 y y c. d. 8 8 4 4 –8 –4 4 8 x –8 –4 4 8 x –4 –4 –8 –8 14. Identify the vertex and the axis of symmetry of the graph of the function. a. vertex: (2, –4); axis of symmetry: b. vertex: (–2, –4); axis of symmetry: c. vertex: (2, 4); axis of symmetry: d. vertex: (–2, 4); axis of symmetry: 15. Use the vertex form to write the equation of the parabola. y 8 6 4 2 –8 –6 –4 –2 O 2 4 6 8 x –2 –4 –6 –8 a. c. b. d. 16. What is the expression in factored form? a. c. b. d. 17. What is the expression in factored form? a. c. b. d. 18. What are the solutions of the quadratic function? a. 4, 7 c. –4, –7 b. 4, –7 d. –4, 7 19. What are the solutions of the quadratic function? a. –3, 6 c. –3, –6 b. 3, –6 d. 3, 6 20. Which equation shows 𝑥 2 + 8𝑥 + 9 = 0 after the method of completing the square has been applied? a. (𝑥 + 2)2 = −5 b. (𝑥 + 4)2 = 7 b. (𝑥 + 8)2 2 = 55 d. 𝑥 2 = −(8𝑥 + 9) 21. What does the imaginary number 𝑖 represent? a. -1 b. √1 c. √−1 d. −√−1 22. Use the Quadratic Formula to solve the function. a. 2 , 10 c. −5, 11 b. 1 , 5 d. −5 , −1 23. Classify –2x4 – x3 + 8x2 + 12 by degree. a. quartic c. quadratic b. cubic d. quintic 24. Classify 8x4 + 7x3 + 5x2 + 8 by number of terms. a. trinomial c. Binomial b. polynomial of 5 terms d. polynomial of 4 terms 25. Divide by x + 4. a. , R 240 c. b. , R –232 d. 26. Is a factor of ? If it is, write as a product of two factors. a. yes: c. yes: b. is not a factor of d. yes: 27. Divide using synthetic division. by ( ) a. c. , R 20 b. , R –20 d. 28. Which statement describes the domain and range of 𝑓(𝑥) = 1/𝑥? a. Domain: (−∞, 0) ∪ (0, ∞) Range: (−∞, 0) ∪ (0, ∞) b. Domain: (−∞, ∞) Range: (−∞, ∞) c. Domain: (−∞, ∞) Range: (0, ∞) d. Domain: (0, ∞) Range: (−∞, ∞) 29. Which of the following functions has a slant asymptote? 2𝑥+1 𝑥 2 −2𝑥−3 𝑥 2 −1 1 a. 𝑓(𝑥) = b. ℎ(𝑥) = c. 𝑔(𝑥) = d. 𝑙(𝑥) = −3 + 𝑥+1 𝑥+3 𝑥−1 𝑥+1 30. If 𝑓(𝑥) = 3𝑥 2 − 3𝑥 + 3 and 𝑔(𝑥) = 2𝑥 + 5, then 𝑓(𝑥) ∙ 𝑔(𝑥) = a. 5𝑥 3 − 9𝑥 2 − 11𝑥 + 15 b. 6𝑥 3 + 9𝑥 2 − 9𝑥 + 15 c. 3𝑥 2 − 𝑥 + 8 d. 3𝑥 2 − 5𝑥 − 2 31. Which of the following is the quotient of (2𝑥 3 − 5𝑥 2 − 4𝑥 − 25) ÷ (𝑥 − 4)? 7 a. 𝑥 3 + 3𝑥 + 𝑥−4 b. 2𝑥 2 + 3𝑥 + 8 7 6 c. 2𝑥 2 + 3𝑥 + 8 + 𝑥−4 d. 2𝑥 2 − 𝑥 + 10 + 𝑥−4 32. Decide whether the function is a polynomial function. If so, write it in standard form and state its degree, type, and leading coefficient. a. polynomial function; ; 1 (linear), leading coefficient: –6 b. polynomial function; ; 2 (quadratic), leading coefficient: –6 c. polynomial function; ; 2 (quadratic), leading coefficient: –5 d. not a polynomial function 33. Which of the following could the function of graph is shown? a. 𝑓(𝑥) = |𝑥| b. 𝑓(𝑥) = 𝑥 3 c. 𝑓(𝑥) = 𝑥 2 d. 𝑓(𝑥) = log 𝑥 34. Write a polynomial function f of least degree that has a leading coefficient of 1 and the given zeros: a. c. b. d. 35. Graph. State the domain and range. y y a. c. 20 20 16 16 12 12 8 8 4 4 –8 –4 4 8 12 16 20 24 x –8 –4 4 8 12 16 20 24 x –4 –4 –8 –8 The domain is all real numbers except –9, The domain is all real numbers except 9, and the and the range is all real numbers except 6. range is all real numbers except –6. y y b. d. 20 20 16 16 12 12 8 8 4 4 –8 –4 4 8 12 16 20 24 x –8 –4 4 8 12 16 20 24 x –4 –4 –8 –8 The domain is all real numbers except 9, The domain is all real numbers except –9, and and the range is all real numbers except 6. the range is all real numbers except –6. 36. Simplify. 𝑥−2 𝑥−2 𝑥+2 𝑥+2 a. , 𝑥 ≠ −4 b. ,𝑥 ≠ 4 c. ,𝑥 ≠ 4 d. , 𝑥 ≠ −4 𝑥−4 𝑥−4 𝑥+4 𝑥+4 37. Simplify a. c. , , b. d. , , 38. Find the quotient: a. − 4 c. − 4 , , 5 5 b. − 5 d. − 5 , , 4 4 39. Find the sum or difference. a. c. b. d. 40. Solve the equation: a. c. b. d. 41. Solve the equation: a. x = 6 c. 3 x= 2,x=6 b. 3 d. 3 x= 2 x = 2 , x = –3 42. Which is the graph of the polynomial function 𝑝(𝑥) = (𝑥 − 1) (𝑥 + 1)(𝑥 − 4) ? a. b. c. d. 43. The graph of the polynomial function 𝑝(𝑥) is shown. What are the zeros of 𝑝(𝑥)? (Assume that the zeros of 𝑝(𝑥)are integers and that the graph of 𝑝(𝑥)does not cross the x-axis at places other than those shown.) a. 𝑥 = −3 𝑎𝑛𝑑 𝑥 = 2 b. 𝑥 = −3, 𝑥 = 0, 𝑎𝑛𝑑 𝑥 = 2 c. 𝑥=0 d. 𝑥 = −2, 𝑥 = 0, 𝑎𝑛𝑑 𝑥 = 3