MATH College Algebra Review for Test 2

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1 MATH 4 - College Algebra Review for Test Sections. and.. For f (x) = x + 4x + 5, give (a) the x-intercept(s), (b) the -intercept, (c) both coordinates of the vertex, and (d) the equation of the axis of smmetr. (e) Graph f (x).. For f (x) = (x ) 8, give (a) the x-intercept(s), (b) the -intercept, (c) both coordinates of the vertex, and (d) the equation of the axis of smmetr. (e) Graph f (x).. The graph of the quadratic function f (x) is shown at the right. Determine the function's formula in the form f (x) = a(x h) + k. (,8) x 4. The graph of the quadratic function f (x) is shown at the right. Determine the function's formula in the form f ( x) = ax + bx + c x (, 8) 5. A baseball is hit so that its height s in feet after t seconds is given b s(t) = 5t + 40t + 5. (a) Find the maximum height of the baseball. (b) When does the baseball hit the ground? 6. Determine the zeros of the following quadratic functions and simplif our answers: (a) f ( x) = 4 x x + (b) f ( x) = x 6x + 7. Solve x 8x 4 = 0 b completing the square. Simplif our answer.

2 8. Determine the domain of f (x) = MATH 4 - College Algebra - Review for Test (Thomason) - p. of 8 x x. Give our answer in set-builder notation. x 0 9. For x 5x + = 0, (a) calculate the discriminant and (b) give the number of real solutions. Section. 0. For each of the following give our answer in a + bi form. (a) Add: ( + i) + ( 5 4i) (b) Subtract: ( 5 + 4i) ( i) (c) Multipl: ( i)( 4 + i) (d) Divide: 4 + i 5 i. Solve x = 6x 4 and simplif our answer. (Simplif radicals, reduce fractions, and express an imaginar numbers in terms of i.). How man real zeros does each of the following functions have? Section.4. The graph of f (x) = x x + is shown at the right. Solve f (x) 0 and give our answer in interval notation. (,4) (0,) (,0) (,0) 4. For the function f ( x) whose graph is show in Problem, for what values of x is f ( x) (a) increasing and (b) decreasing? Give our answers in interval notation.

3 MATH 4 - College Algebra - Review for Test (Thomason) - p. of 8 5. Solve the inequalit and write the solution set in interval notation: 7x 9x > 0 6. Solve the following inequalit and give our answer in interval notation: x + x Section.5 7. The graph of = f (x) is shown on the coordinate sstem at the right. Sketch the graphs of (a) = f (x + ), (b) = f ( x ) +, ( ), and (c) = f x (d) = f ( x). x 8. Let f (x) = x. Write a formula for a function g whose graph is similar to f (x) but is shifted right units and up 4 units. Section The graph of f (x) is shown on the coordinate sstem at the right. Determine the (a) local minima, (b) local maxima, (c) absolute minimum, (d) absolute maximum, (e) intervals in which f (x) is increasing, and (f) intervals in which f (x) is decreasing, if an. Give our answers to parts (e) and (f) in interval notation Determine whether each of the following is an even function, an odd function, or neither. Show or explain how ou determined our answer. (a) f (x) = x (b) f (x) = (x ) (c) f (x) = x + x. The table at the right is a complete representation of f. Is f an even function, an odd function, or neither? Show or explain how ou determined. x f(x)

4 Section 4.. Use the graph of the polnomial function f (x) shown at the right to answer the following. MATH 4 - College Algebra - Review for Test (Thomason) - p. 4 of 8 (a) How man turning points does the graph have? (b) Estimate the x-intercepts, assuming the are integers. x (c) Is the leading coefficient of f (x) positive or is it negative? (d) What is the minimum degree of f (x)?. For f ( x) = x + 5x +4x 5, (a) give the degree, (b) give the leading coefficient, (c) state the end behavior as x, and (d) state the end behavior as x. 4. For f ( x) = x 4 + x 8, (a) give the degree, (b) give the leading coefficient, (c) state the end behavior as x, and (d) state the end behavior as x. 5. Sketch a graph of a polnomial that satisfies the following conditions: Degree with two real zeros and a negative leading coefficient 6. Sketch a graph of a polnomial that satisfies the following conditions: Degree 4 with three real zeros and a negative leading coefficient 4 for x < 7. Let f ( x) = x for x x for x >. (a) Determine f ( ). (b) Determine f (). (c) Graph f ( x). (d) Give an values of x at which f ( x) is not continuous. Section Divide x 4x 0x b x Divide 6x x + 4 x 7 b x. 0. Is x + a factor of f (x) = x + 5x + x 6? Tell how ou determined our answer.. What is the remainder when x x + 4x 5 is divided b x?

5 Section 4.4 MATH 4 - College Algebra - Review for Test (Thomason) - p. 5 of 8. The graph of a rd, 4 th, or 5 th degree polnomial f (x) with integer zeros is shown at the right. Determine the factored form of f (x).. Solve exactl for x: 7x 5x x +5 = 0. Simplif our answers including removing perfect squares from under square roots and reducing fractions, when possible. 4. Solve exactl for x: x = 4x. Simplif our answers including removing perfect squares from under square roots and reducing fractions, when possible. Write an complex solutions in standard form. 5. Solve exactl for x: x 6 =0x. Simplif our answers including removing perfect squares from under square roots and reducing fractions, when possible. Write an complex solutions in standard form. 6. Find the zeros of f (x) = 7x + 5x +x 4 given that 7 is a zero. Section The graph of a 5 th degree polnomial f (x) is shown at the right. (a) How man different real zeros does f (x) have? (b) How man different imaginar zeros does f (x) have? x 8. Find the completel factored form of a polnomial f (x) with real coefficients that satisfies the following conditions: Degree ; a = ; zeros include and i

6 MATH 4 - College Algebra - Review for Test (Thomason) - p. 6 of 8 9. Find the completel factored form of a polnomial f (x) with real coefficients that satisfies the following conditions: Degree 4; a n = ; zeros include 0,, and i 40. (a) Find all the zeros of f ( x) = x x + 9x 7. (b) Write f (x) in completel factored form. 4. (a) Find all the zeros of f ( x) = 4x + x. (b) Write f (x) in completel factored form. 4. (a) Find all the zeros of f ( x) = x 4 6x +x. (b) Write f (x) in completel factored form. Section 4.7 (Polnomial Inequalities ) 4. Solve for x and give our solution in interval notation: x +5x < x 44. Solve for x and give our solution in interval notation: (x + 4)(x )(x 5) 0 Answers. (a) (,0), (5,0) (b) (0,5) (c) (,9) (d) x =. (a) (,0), (5,0) (b) (0,0) (c) (, 8) (d) x =

7 MATH 4 - College Algebra - Review for Test (Thomason) - p. 7 of 8. f ( x) = ( x +) f ( x) = x 4x 6 5. (a) ft (b) sec 6. (a) ± 5 (b) ± ± 5 8. { x x,5} 9. (a) (b) 0. (a) i (b) 8 + 6i (c) 0 +i (d) i 7 (a) x 7 (b) x. ± i. (a) (b) 0 (c). (, ] [, ) 4. (a) (, ] (b) [, ) 5. (,0) 9 7, 6. [ 4,] 7 (c) x 7 (d) x 8. g( x) = f (x ) + 4 = x (a) 0, 4 (b) (c) -4 (d) none (e) [, ], [, ) (f) (, ], [,] 0. (a) Even, because the graph is an open up parabola that is smmetric about the -axis. (b) Neither, because f ( x) = ( x ) = x + 6x + 9 but f ( x) = ( x ) = x 6x + 9 so f ( x) f ( x) and f ( x) f (x). (c) Neither, because f ( x) = ( x) + ( x) = x x but f ( x) = x + x so f ( x) f ( x) and f ( x) f (x).. Even, because f ( x) = f ( x) for all values of x in the domain of f.. (a) (b),, (c) positive (d) 4th

8 MATH 4 - College Algebra - Review for Test (Thomason) - p. 8 of 8. (a) rd (b) (c) f ( x) (d) f ( x) 4. (a) 4th (b) (c) f ( x) (d) f ( x) 5. Answers ma var. 6. Answers ma var. 7. (a) 4 (b) 9 8. x 7x + 6 x + 9. x + x + x (c) 0. Yes, because the remainder given b f () or division is 0.. (d). f ( x) = ( x +) (x )(x 4). ±, ± i 5., , ± 7 i 7. (a) (b) 8. f ( x) = (x )[x ( i)][x (+ i)] 9. f ( x) = x( x )(x i)( x + i) 40. (a), ±i (b) f ( x) = ( x )(x i)( x + i) 4. (a) 0, ±i (b) f ( x) = 4x( x i )(x + i ) ( ) ( ) 4. (a) 0, ± i (b) f ( x) = x x i x + i 4. (,0) (5, ) 44. [ 4,] {5}

MATH College Algebra Review for Test 2

MATH College Algebra Review for Test 2 MATH 34 - College Algebra Review for Test 2 Sections 3. and 3.2. For f (x) = x 2 + 4x + 5, give (a) the x-intercept(s), (b) the -intercept, (c) both coordinates of the vertex, and (d) the equation of the