1. How many white tiles will be in Design 5 of the pattern? Explain your reasoning.

Transcription

1 Algebra 2 Semester 1 Review Answer the question for each pattern. 1. How many white tiles will be in Design 5 of the pattern Explain your reasoning. 2. What is another way to represent the expression 3. Which is a function equivalent to 4. What is another way to represent the expression 5. Simplify the polynomial expression. 6. Analyze the table of values for the functions f(x) and g(x) Which statement describes the function It has no x-intercepts. It has one x-intercept at. It has x-intercepts at and. It has x-intercepts at,, and. 7. The equation for f(x) is given. The equation for the transformed function g(x) in terms of f(x) is also given. Describe the transformation(s) performed on f(x) that produced g(x). stretched vertically by a factor of 4; shifted 3 units to the left stretched vertically by a factor of 4; shifted 3 units to the right shrunk vertically by a factor of 4; shifted 3 units to the left shrunk vertically by a factor of 4; shifted 3 units to the right 8. Which graph represents the function x f(x) g(x)

2 10. Consider the graph shown. Which function could this graph represent An odd-degree function with two relative An even-degree function with two relative An odd-degree function with three relative An even-degree function with three relative 9. Which function represents the graph 11. Determine the next number in each sequence. 3, 5, 9, 17, Does y represent the equation of the function graphed

3 12. x h(x) j(x) k(x) = h(x) + j(x) Circle the function that matches each graph. Explain your reasoning. Use the given information to determine the most efficient form you could use to write the quadratic function. Write standard form, factored form, or vertex form. 16. vertex (3, 7) and point (1, 10) 17. roots, (13, 0) and point 18. Convert to standard form. Determine whether the expressions are equivalent. 14. and 15. Draw the function j(x) with outputs such that Then complete the table of values to verify that 19. Convert to vertex form. 20. Explain the transformation(s) of g(x) compared to the graph of f(x) 21. Explain the effects of -3 on the graph of f(x).

4 31. Calculate each power of i. 22. a) b) Simplify each expression. 23. Simplify each expression, if possible write its conjugate. 26. Calculate each quotient Factor each function over the set of real or imaginary numbers. Then, identify the type of zeros. Determine the product of three linear factors. Verify graphically that the expressions are equivalent. Sketch a set of functions whose product builds a cubic function with the given characteristics. Explain your reasoning. 32. zeros: 33. Use synthetic division to find f(-1) given f(x) = 34. Is a factor of Determine each quotient using synthetic division. Write the dividend as the product of the divisor and the quotient plus the remainder. 30. Use the Binomial Theorem and substitution to expand each binomial. 35. Determine the value using the Remainder Theorem. Circle the function(s) that could model each graph. Describe your reasoning for either eliminating or choosing each function. 36. Determine if Use the Factor Theorem to determine whether the given expression is a factor of each polynomial. Explain your reasoning. 37. Is a factor of

5 Use the Factor Theorem to determine whether g(x) is the factored form of f(x). Explain your reasoning. 38. Is the factored form of Use the Factor Theorem to determine the unknown coefficient so that the given linear expression is a factor of the function. 39. Determine a if is a factor of Factor each expression completely Use the Rational Root Theorem to determine the possible rational roots for each polynomial equation. Then, solve completely. Possible rational roots: Solve completely: Possible rational roots: Solve completely: Factor each expression by factoring out the greatest common factor. Perform each calculation and simplify Factor each binomial using the sum or difference of perfect cubes formul 53. Perform each calculation and simplify Determine the possible rational roots of each polynomial using the Rational Root Theorem. 49.

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