Semester 1 Final Review Short Answer

Semester 1 Final Review - Short Answer Name____________________________________________Period:____________ Find the product. SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. 7) (2p - 1)(4p2 + 2p + 1) Evaluate the expression for x = -2, y = 3, and a = -4. y + 3x 3 1) y - 4a 19 8p3 - 1 Factor by grouping. 8) x3 - 2x2 + 9x - 18 (x2 + 9)(x - 2) Simplify. 2) -3(6k - 5) + 2(2k - 5) - 9 + 5k Write the expression in lowest terms and determine the numbers that must be excluded from the domain. z 2 + 9z + 18 9) z 2 + 4z - 12 -9k - 4 Evaluate the function. 3) Find f(-1) when f(x) = x2 + 5x + 3 z+3 z-2 -1 Find the product or quotient. 2p - 2 4p - 4 ÷ 10) p 6p2 For the given functions f and g , find the indicated composition. g(x) = 2x - 1 4) f(x) = 4x + 8, (f g)(x) 8x + 4 3p Solve the formula for the indicated variable. 11) A = P(1 + nr), for r For the pair of functions, find the indicated sum, difference, product, or quotient. 5) f(x) = 7x - 9, g(x) = 2x - 7 Find (f - g)(x). r= A-P Pn Solve the equation. 12) |4x - 2| = 7 5x - 2 9 5 ,4 4 Find the zeros of the polynomial function and state the multiplicity of each. 6) f(x) = -5x2 (x - 7)(x + 1)3 Solve the equation by the square root property. 13) (x - 10)2 = 81 -1 (multiplicity 3), 0 (multiplicity 2), 7 (multiplicity 1) { 1, 19 } 1 Solve the equation by the zero-factor property. 14) 21x2 + 64x + 35 = 0 - Solve the equation. 21) x = 3x + 18 {6} 7 5 ,3 7 Solve the inequality. Write the solution set in interval notation. 22) |5x - 9| + 2 < 4 Solve and graph the inequality. Give answer in interval notation. 15) -18 < 5x + 2 2 7 11 , 5 5 (-4, 0] Evaluate the function. 23) Find f(k - 1) when f(x) = 2x2 - 2x - 3 Decide whether the relation defines a function. 16) y = x3 2k2 - 6k + 1 Function Find the vertical asymptote(s) of the graph of the given function. x2 + 3x 24) f(x) = x2 - 6x - 27 Find the correct end behavior diagram for the given polynomial function (Limit Notation). 17) P(x) = - 8x3 + 2x2 + 7x - 4 x=9 Give the equations of any horizontal asymptotes. 8x2 25) h(x) = 4x 2 - 6 Find the quotient. Write the answer in standard form. 2 - 7i 18) 8 + 2i y=2 1 15 i 34 17 Write an equation for the line described. Give your answer in slope-intercept form. 26) through (-7, -9) and (0, -3) Give the equations of any vertical asymptotes. x-3 19) f(x) = x2 - 1 y= x = 1, x = -1 6 x-3 7 Find the slope and the y-intercept of the line. 5 27) y - x + 3 = 0 2 Solve the equation using the quadratic formula. 20) 6x2 + 6x + 1 = 0 -3 ± 3 6 slope: 2 5 ; y-intercept (0, -3) 2 Find the requested value. 28) f(-1) for f(x) = 4x, x - 7, Describe how the graph of the equation relates to the graph of y = x 2 . if x -1 if x > -1 31) f(x) = (x - 8)2 + 6 -4 a translation 8 units to the right and 6 units up Give the domain and range of the relation. 29) Determine the equation of the line described. Put answer in the slope-intercept form, if possible. 5 17 32) Through (-8, 1), perpendicular to y = - x + 6 3 y= 53 6 x+ 5 5 MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Solve the problem. 33) Select the equation that describes the graph shown. domain: (- , ); range: (- , 3] Identify the intervals where the function is changing as requested. 30) Increasing and Decreasing A) y = (x - 2)2 + 2 C) y = (x + 2)2 - 2 B) y = (x + 2)2 + 2 D) y = x 2 - 2 SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. Identify the vertex of the parabola. 34) y = x2 - 6x + 14 (0 , 3) and (-1, 0) (3, 5) 3 Use synthetic division to perform the division. x 3 - x2 + 4 35) x+2 x2 - 3x + 6 + Perform the indicated operations. x 4 40) 2 2 x - 16 x + 5x + 4 x2 - 3x + 16 (x - 4)(x + 4)(x + 1) -8 x+2 Solve the equation. 41) -6x + 1 - 3(x + 1) = 7x - 5 Find a rational zero of the polynomial function and use it to find all the zeros of the function. 36) f(x) = x3 + 3x2 - 4x - 12 3 16 {-3, -2, 2} Write the number as the product of a real number and i. 42) -275 Find the x-intercepts of the polynomial function. State whether the graph crosses the x-axis, or touches the x-axis and turns around, at each intercept. 37) f(x) = 6x2 - x3 5i 11 0, touches the x-axis and turns around; 6, crosses the x-axis Write the number in standard form a + bi. -2 - -20 43) 2 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. 38) f(x) = 2(x + 5)(x - 3)2 -1 - i 5 Determine the slope, if it exists, of the graph of the given linear equation. 44) x = 7 -5, multiplicity 1, crosses x-axis; 3, multiplicity 2, touches x-axis and turns around not defined Find an equation for the rational function graph. 39) Describe how the graph of the equation relates to the graph of y = x 2 . 45) f(x) = 1 2 x -5 3 vertical shrinking by a factor of units down f(x) = x+2 x(x + 4) 4 1 and a translation 5 3