Cumulative Review. Name. 13) 2x = -4 13) SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.

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1 Cumulative Review Name SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. Evaluate the algebraic expression for the given value or values of the variable(s). 1) 5(x + 5) + 8; x = -9 1) Evaluate the expression for the given values of x and y. 2) x x + y y ; x = 6 and 2) y = -2 Simplify the exponential expression. 3) (-5x 3 y)(-10x 4 y 2 ) 3) 4) -8x13 2x 2 4) 5) (-10x 7 y 3 ) 2 5) 13) 2x = -4 13) 14) 3 x - 3 = 18 14) Solve the equation by factoring. 15) 6x x + 20 = 0 15) 16) 7x 2-20x = 3 16) Solve the quadratic equation using the quadratic formula. 17) x 2 + 5x - 14 = 0 17) Solve the linear equation. 18) (-8x - 1) + 3 = -7(x - 3) 18) Solve the linear inequality. Other than, use interval notation to express the solution set and graph the solution set on a number line. 19) 3x + 2 < 26 19) Use the product rule to simplify the expression. 6) 98x 2 6) 7) 245 7) Perform the indicated operations. Write the resulting polynomial in standard form. 8) (-8x 5 + 7x 4-8x 3 + 1) + (3 x 5-5x 4 + 4x 3 + 9) Find the product. 9) (2x + 5)(x - 9) 9) 8) Solve the absolute value inequality. Other than, use interval notation to express the solution set and graph the solution set on a number line. 20) 3(x + 1) ) Graph the line whose equation is given. 21) y = 3x ) Factor the trinomial, or state that the trinomial is prime. 10) 5x x ) 11) 12x x ) Solve the absolute value equation or indicate that the equation has no solution. 12) 3 x - 3 = 18 12) 1

2 Begin by graphing the standard quadratic function f(x) = x 2. Then use transformations of this graph to graph the given function. 22) h(x) = (x - 5) ) Find the inverse of the one-to-one function. 25) f(x) = 4x ) Solve the quadratic equation using the quadratic formula. Express the solution in standard form. 26) x 2-10x + 61 = 0 26) Find the product and write the result in standard form. 27) (-5-3i)(3 + i) 27) Use the vertex and intercepts to sketch the graph of the quadratic function. 28) f(x) = x 2 + 6x ) Identify the intervals where the function is changing as requested. 23) Decreasing 23) Determine whether the given quadratic function has a minimum value or maximum value. Then find the coordinates of the minimum or maximum point. 29) f(x) = x 2-2x ) Use the graph of the given function to find any relative maxima and relative minima. 24) f(x) = x3-3x ) Use the Leading Coefficient Test to determine the end behavior of the polynomial function. 30) f(x) = 5x 4 + 5x 3 + 3x 2-2x ) 31) f(x) = -3x 3-2x 2 + 3x ) Find the zeros of the polynomial function. 32) f(x) = x 3 + 5x 2-4x ) Find the zeros for the polynomial function and give the multiplicity for each zero. State whether the graph crosses the x-axis or touches the x-axis and turns around, at each zero. 33) f(x) = x 3 + x 2-42x 33) 2

3 Determine the maximum possible number of turning points for the graph of the function. 34) f(x) = x 6 + 8x 7 34) Graph the polynomial function. 35) f(x) = x 4-4x 2 35) Solve the problem. 39) Solve the equation 3x 3-28x x - 20 = 0 given that 5 is a zero of f(x) = 3x 3-28x x ) Find a rational zero of the polynomial function and use it to find all the zeros of the function. 40) f(x) = x 3 + 2x 2-5x ) Use Descartes's Rule of Signs to determine the possible number of positive and negative real zeros for the given function. 41) f(x) = -5x 7 + x 3 - x ) Divide using synthetic division. 36) (x x + 48) (x + 8) 36) Graph the polynomial function. 37) f(x) = x 3 + 5x 2 - x ) Use synthetic division and the Remainder Theorem to find the indicated function value. 38) f(x) = x 4 + 7x 3 + 3x 2 + 9x - 6; f(-4) 38) 3

4 Answer Key Testname: CUMULATIVE REVIEW 1) -12 2) 0 3) 50x 7 y 3 4) -4x 11 5) 100x 14 y 6 6) 7 x 2 7) 7 5 8) -5x 5 + 2x 4-4x ) 2x 2-13x ) (5x + 2)(x + 6) 11) (4x + 3)(3x + 2) 12) {9, -3} 13) 14) {9, -3} 15) - 5 2, ) - 1 7, 3 17) {-7, 2} 18) {- 19} 19) (-, 8) 20) [-7, 1] 21) 4

5 Answer Key Testname: CUMULATIVE REVIEW 22) 23) (-, 3) 24) maximum: (0, 1); minimum: (2, -3) 25) f -1 (x) = x ) {5 ± 6i} 27) i 28) 29) minimum; 1, ) rises to the left and rises to the right 31) rises to the left and falls to the right 32) x = -5, x = -2, x = 2 33) 0, multiplicity 1, crosses the x-axis - 7, multiplicity 1, crosses the x-axis 6, multiplicity 1, crosses the x-axis 34) 6 5

6 Answer Key Testname: CUMULATIVE REVIEW 35) 36) x ) 38) ) 5, 4, ) {-3, -1, 2} 41) 3 or 1 positive zeros, 2 or 0 negative zeros 6