Int Math 3 Midterm Review Handout (Modules 5-7)

Transcription

1 Int Math 3 Midterm Review Handout (Modules 5-7) 1 Graph f(x) = x and g(x) = 1 x 4. Then describe the transformation from the graph of f(x) = x to the graph 2 of g(x) = 1 2 x 4. The transformations are a translation and a reflection. The transformations are a translation, a reflection, and a rotation. The transformations are a rotation and a translation. The transformations are a rotation and a reflection. 2 What are the real or imaginary solutions of each polynomial equation? x = 0 3, 3 ± , 3 ± 3i 3 2 3, 3 no solution 1

2 I: 3 Short nswer: (Put all work and answers in the box below). How would you shift the graph of y = x 2 to produce the graph of y = 3(x 2) 2 9? 4 Factor x 3 + 2x 2 4x 8. (x + 2)(x 2)(x + 2) (x 2)(x 2 + 4) (x + 2)(x 2 + 4) (x 2)(x 2)(x + 2) 5 Find the product (x 4y) 3. x y 3 x 3 64y 3 x x 2 y + 48xy y 3 x 3 12x 2 y + 48xy 2 64y 3 6 rectangular garden has a length of 5z + 11 feet and a width of 6z feet. Which expression represents the area of the garden in square feet? 35z z 30z z z 30z Find the product 7c (4c 3 d 4 + 4c d 2 ). 3c 4 d 4 3c 2 d 2 28c 4 d 4 28c 2 d 2 28c 3 28c 1 7c 5 d 5 7c 3 d 3 2

3 I: 8 Graph y = 5(x + 3) and describe the end behavior. The end behavior is down and up. The end behavior is up and down. The end behavior is down and up. 9 Write a function that transforms f(x) = 2x in the following way vertical stretch by a factor of 4 and shift 3 units left. The end behavior is up and down. 10 What are the zeros of the function? What are their multiplicities? f(x) = 4x 3 + 8x 2 32x g(x) = 8x g(x) = 8(x + 3) g(x) = 8(x 3) g(x) = 8(x + 3) the numbers 4, 2, and 0 are zeros of the numbers 4, 2, and 0 are zeros of multiplicity 2 the numbers 4, 2, and 0 are zeros of multiplicity 2 the numbers 4, 2, and 0 are zeros of 3

4 I: 11 Short nswer: (Put work and answers in the box below). Is x 4 a factor of 2x 3 + 7x 2 + 2x + 8? How do you know? 12 Factor the expression 81x x 4 y 3. 3x 4 (27x y 3 ) 3x 4 (3x + 4y)(9x xy + 16y 2 ) 3x 4 (3x + 4y) 3 3x 4 (3x + 4y)(9x 2 12xy + 16y 2 ) 13 Let f(x) = 2x 3 + 4x 2 7x + 4. Write a function g that reflects f(x) across the y-axis. g(x) = 2x 3 4x 2 + 7x + 4 g(x) = 2x 3 4x 2 + 7x 4 g(x) = 2x 3 + 4x 2 + 7x + 4 g(x) = 2x 3 + 4x 2 + 7x 4 14 Solve to find the inverse of f(x) = 6x lassify 4x 4 9x 3 5x by number of terms. g(x) = 1 6 x + 7 g(x) = 6x + 7 g(x) = 1 6 x 7 6 polynomial of 4 terms polynomial of 5 terms binomial trinomial g(x) = 1 6 x

5 I: 16 What are the zeros of the function? Graph the function. y = x(x + 5)(x 2) 5, 2, 5 0, 5, 2 0, 5, 2 5, 2 17 Factor the polynomial 30x x 2 + 4x completely. (6x 2 + 2x) ( 5x + 2) 2x ( 3x + 2) ( 5x + 1) 2x ( 3x + 1) ( 5x + 2) 2( 3x + 1) ( 5x + 2) 18 dd. ( 8c 5 d + 3cd) + (3c 5 d 2cd 2) + (6cd + 9) 7c 5 d + 7cd 12 5c 5 d + 7cd + 7 7c 5 d + 9cd + 7 5c 5 d + 11cd + 7 5

6 I: 19 The area of a rectangle is equal to x x + 96 square units. If the length of the rectangle is equal to x + 12 units, what expression represents its width? x + 8 x 84 x + 84 x 8 20 Graph y = 2x x 3. How many turning points are there? There are no turning points. There are two turning points. 21 Multiply. There are no turning points. There are two turning points. (g + 8)(g 8) g g 2 64g g 2 16g 64 g g

7 I: 22 Use a table to graph the quadratic function f(x) = 3x 2 + 3x How would you translate the graph of y = x 2 to produce the graph of y = x 2 6? translate the graph of y = x 2 up 6 units translate the graph of y = x 2 left 6 units translate the graph of y = x 2 right 6 units translate the graph of y = x 2 down 6 units 24 ivide: (5x 2 7x + 5) ( x 4) 5x x 4 5x x 4 5x x 4 20x x 4 7

8 I: 25 Short nswer: (Put all work and answers in the box below). Write row 5 of Pascal's triangle. Use your answer to write (a b) 5 in expanded form. 26 onsider the leading term of each polynomial function. What is the end behavior of the graph? 3x 4 9x 3 7x The leading term is 3x 4. Since n is even and a is negative, the end behavior is up and down. The leading term is 3x 4. Since n is even and a is negative, the end behavior is up and up. The leading term is 3x 4. Since n is even and a is negative, the end behavior is down and up. The leading term is 3x 4. Since n is even and a is negative, the end behavior is down and down. 27 Factor 5x 2 13x + 6. ( x 2) ( 5x 3) ( x 2) ( 5x + 3) ( x 3) ( 5x 2) ( x 2) ( x 3) 28 Multiply. (2w + 2z ) 2 4w 2 + 8w z + 4z 2 4w 2 + 4z 2 4w 2 + 4w z + 4z 2 4w 2 + 4z 2 8

9 I: 29 What are the zeros of the function? What are their multiplicities? f(x) = x 4 + 2x 3 8x 2 the number 0 is a zero of multiplicity 2; the numbers 2 and 4 are zeros of the number 0 is a zero of multiplicity 2; the numbers 2 and 4 are zeros of the numbers 0 and 2 are zeros of multiplicity 2; the number 4 is a zero of the numbers 2 and 4 are zeros of multiplicity 2; the number 0 is a zero of 30 onsider the leading term of each polynomial function. What is the end behavior of the graph? 3x 7 + x The leading term is 3x 7. Since n is odd and a is positive, the end behavior is up and down. The leading term is 3x 7. Since n is odd and a is positive, the end behavior is down and down. The leading term is 3x 7. Since n is odd and a is positive, the end behavior is down and up. The leading term is 3x 7. Since n is odd and a is positive, the end behavior is up and up. 31 Short nswer: (Put all work and answers in the box below). Write row 4 of Pascal's triangle. Use your answer to write (3x + 2y) 4 in expanded form. 32 What is a cubic polynomial function in standard form with zeros 2, 4, and 3? f(x) = x 3 9x x 24 f(x) = x 3 + 9x x 24 f(x) = x 3 + 9x 2 26x 24 f(x) = x 3 + 9x x + 8 9

10 I: 33 Find the inverse of f(x) = x f 1 (x) = 2x 3 f 1 (x) = 3x 2 f 1 (x) = x 2 3 f 1 (x) = 2(x 3) 34 Expand (6p + q) p p 3 q + 36p 2 q 2 + 6pq 3 + q 4 6p 4 + q p p 3 q + 216p 2 q pq 3 + q p 4 + q 4 35 Factor x x (x + 25)(x + 100) (x + 2)(x + 50) (x + 5)(x + 20) (x + 1)(x + 100) 36 Graph the linear equation 9x + 3y = 27 by finding the x- and y-intercepts. 10

11 I: 37 Which of the following is a factor of 2x 3 + 6x 2 11x 12? x 4 x + 2 x + 4 x 2 38 Use the inomial Theorem to expand the binomial (2x 5y) 4. 16x 4 625y 4 16x 4 160x 3 y + 600x 2 y xy y 4 16x y 4 16x x 3 y + 600x 2 y xy y 4 39 What are the real or imaginary solutions of the polynomial equation? x 4 34x = 0 3, 5, 0 3, 5 3, 3, 5, 5 no solution 40 Factor the trinomial p 2 p 12. (p 4)(p + 3) (p 1)(p 12) (p + 1)(p 12) (p 3)(p 4) 11