Bartleby Sitemap - Textbook Solutions
All Textbook Solutions for Precalculus
In Problems, use the Rational Zeros Theorem to find all the real zeros of each polynomial function. Use the zeros to factor over the real numbers.
51.
In Problems, use the Rational Zeros Theorem to find all the real zeros of each polynomial function. Use the zeros to factor over the real numbers.
52.
In Problems 51-68, find the real zeros of f. Use the real zeros to factor f 59. f( x )= x 4 + x 3 -3 x 2 -x+2In Problems 51-68, find the real zeros of f. Use the real zeros to factor f 60. f( x )= x 4 - x 3 -6 x 2 +4x+8In Problems 4556, use the Rational Zeros Theorem to find all the real zeros of each polynomial function. Use the zeros to factor f over the real numbers. f(x)=4x4+5x3+9x2+10x+2In Problems 4556, use the Rational Zeros Theorem to find all the real zeros of each polynomial function. Use the zeros to factor f over the real numbers. f(x)=3x4+4x3+7x2+8x+2In Problems 75-84, find the real solutions of each equation. x 4 - x 3 +2 x 2 -4x-8=0In Problems 75-84, find the real solutions of each equation. 2 x 3 +3 x 2 +2x+3=0In Problems 75-84, find the real solutions of each equation. 3 x 3 +4 x 2 -7x+2=0In Problems 75-84, find the real solutions of each equation. 2 x 3 -3 x 2 -3x-5=0In Problems 75-84, find the real solutions of each equation. 3 x 3 - x 2 -15x+5=0In Problems 75-84, find the real solutions of each equation. 2 x 3 -11 x 2 +10x+8=0In Problems 75-84, find the real solutions of each equation. x 4 +4 x 3 +2 x 2 -x+6=0In Problems 75-84, find the real solutions of each equation. x 4 -2 x 3 +10 x 2 -18x+9=0In Problems 75-84, find the real solutions of each equation. x 3 - 2 3 x 2 + 8 3 x+1=0In Problems 75-84, find the real solutions of each equation. x 3 - 2 3 x 2 +3x-2=0In Problems 5768, solve each equation in the real number system. 2x419x3+57x264x+20=068AYUIn Problems 6978, find bounds on the real zeros of each polynomial function. f(x)=x43x24In Problems, find bounds on the real zeros of each polynomial function.
70.
In Problems 6978, find bounds on the real zeros of each polynomial function. f(x)=x4+x3x1In Problems 6978, find bounds on the real zeros of each polynomial function. f(x)=x4x3+x1In Problems 6978, find bounds on the real zeros of each polynomial function. f(x)=3x4+3x3x212x12In Problems 6978, find bounds on the real zeros of each polynomial function. f(x)=3x43x35x2+27x36In Problems, find bounds on the real zeros of each polynomial function.
75.
In Problems, find bounds on the real zeros of each polynomial function.
76.
In Problems 85-90, use the Intermediate Value Theorem to show that each function has a zero in the given interval. Approximate the zero correct to two decimal places. f( x )=8 x 4 -2 x 2 +5x-1 ; [ 0,1 ]In Problems 85-90, use the Intermediate Value Theorem to show that each function has a zero in the given interval. Approximate the zero correct to two decimal places. f( x )= x 4 +8 x 3 - x 2 +2 ; [ 1,0 ]In Problems 85-90, use the Intermediate Value Theorem to show that each function has a zero in the given interval. Approximate the zero correct to two decimal places. f( x )=2 x 3 +6 x 2 -8x+2In Problems 85-90, use the Intermediate Value Theorem to show that each function has a zero in the given interval. Approximate the zero correct to two decimal places. f( x )=3 x 3 -10x+9In Problems 85-90, use the Intermediate Value Theorem to show that each function has a zero in the given interval. Approximate the zero correct to two decimal places. f( x )= x 5 - x 4 +7 x 3 -7 x 2 -18x+18 ; [ 1.4,1.5 ]In Problems 85-90, use the Intermediate Value Theorem to show that each function has a zero in the given interval. Approximate the zero correct to two decimal places. f( x )= x 5 -3 x 4 -2 x 3 +6 x 2 +x+2 ; [ 1.7,1.8 ]In Problems, each equation has a solution in the interval indicated. Use the method of Example to approximate this solution correct to two decimal places
85.
In Problems, each equation has a solution in the interval indicated. Use the method of Example to approximate this solution correct to two decimal places
86.
In Problems 8588, each equation has a solution r in the interval indicated. Use the method of Example 10 to approximate this solution correct to two decimal places 2x3+6x28x+2=0;5r4In Problems, each equation has a solution in the interval indicated. Use the method of Example to approximate this solution correct to two decimal places
88.
In Problems 8992, each polynomial function has exactly one positive real zero. Use the method of Example 10 to approximate the zero correct to two decimal places. f(x)=x3+x2+x4In Problems, each polynomial function has exactly one positive real zero. Use the method of Example to approximate the zero correct to two decimal places.
90.
In Problems, each polynomial function has exactly one positive real zero. Use the method of Example to approximate the zero correct to two decimal places.
91.
In Problems 8992, each polynomial function has exactly one positive real zero. Use the method of Example 10 to approximate the zero correct to two decimal places. f(x)=3x32x220In Problems 91-98, analyze each polynomial function using Steps 1 through 8 on page 193 in Section 4.1. f( x )= x 3 +2 x 2 5x6 [Hint: See Problem 51.]In Problems 91-98, analyze each polynomial function using Steps 1 through 8 on page 193 in Section 4.1. f( x )= x 3 +8 x 2 +11x20 [Hint: See Problem 52.]Mixed Practice In Problems 93104, grapheach polynomial function. f(x)=2x3x2+2x1Mixed Practice In Problems 93104, grapheach polynomial function. f(x)=2x3+x2+2x+1Mixed Practice In Problems, graph each polynomial function.
97.
Mixed Practice In Problems 93104, grapheach polynomial function. f(x)=x43x24Mixed Practice In Problems 93104, grapheach polynomial function. f(x)=4x4+7x22Mixed Practice In Problems 93104, grapheach polynomial function. f(x)=4x4+15x24In Problems 91-98, analyze each polynomial function using Steps 1 through 8 on page 193 in Section 4.1. f( x )= x 4 + x 3 3 x 2 x+2 [Hint: See Problem 59.]In Problems 91-98, analyze each polynomial function using Steps 1 through 8 on page 193 in Section 4.1. f( x )= x 4 x 3 6 x 2 +4x+8 [Hint: See Problem 60.]In Problems 91-98, analyze each polynomial function using Steps 1 through 8 on page 193 in Section 4.1. f( x )=4 x 5 8 x 4 x+2 [Hint: See Problem 67.]In Problems 91-98, analyze each polynomial function using Steps 1 through 8 on page 193 in Section 4.1. f( x )=4 x 5 +12 x 4 x3 [Hint: See Problem 68.]103AYU104AYU105AYU106AYU107AYU108AYU109AYU110AYU111AYU112AYU113AYU114AYU115AYU116AYU117AYU118AYU119AYU1AYU2AYU3. Every polynomial function of odd degree with real coefficients has at least _____ real zero(s).4. If 3+4i is a zero of a polynomial function of degree 5 with real coefficients, then so is ________.5. True or False A polynomial function of degree n with real coefficients has exactly n complex zeros. At most n of them are real zeros.6. True or False A polynomial function of degree 4 with real coefficients could have 3 , 2+i , 2i , and 3+5i as its zeros.In Problems 7-16, information is given about a polynomial function f( x ) whose coefficients are real numbers. Find the remaining zeros of f . 7. Degree 3; zeros: 3, 4iIn Problems 7-16, information is given about a polynomial function f( x ) whose coefficients are real numbers. Find the remaining zeros of f . 8. Degree 3; zeros: 4, 3+iIn Problems, information is given about a polynomial function whose coefficients are real numbers. Find the remaining zeros of.
Degree; zeros: , .
In Problems 7-16, information is given about a polynomial function f( x ) whose coefficients are real numbers. Find the remaining zeros of f . 10. Degree 4; zeros: 1, 2, 2+iIn Problems, information is given about a polynomial function whose coefficients are real numbers. Find the remaining zeros of.
Degree; zeros:.
In Problems 7-16, information is given about a polynomial function f( x ) whose coefficients are real numbers. Find the remaining zeros of f . 12. Degree 5; zeros: 0, 1, 2, iIn Problems 918, information is given about a polynomial function f whose coefficients are real numbers. Find the remaining zeros of f. Degree 4; zeros: i,7,7.In Problems 7-16, information is given about a polynomial function f( x ) whose coefficients are real numbers. Find the remaining zeros of f . 14. Degree 4; zeros: 2i , iIn Problems, information is given about a polynomial function whose coefficients are real numbers. Find the remaining zeros of.
Degree; zeros:
In Problems 7-16, information is given about a polynomial function f( x ) whose coefficients are real numbers. Find the remaining zeros of f . 16. Degree 6; zeros: i , 32i , 2+iIn Problems 1924, find a polynomial function f with real coefficients having the given degree and zeros. Answers will vary depending on the choice of leading coefficient. Degree 4; zeros: 3+2i;4, multiplicity 2In Problems 1924, find a polynomial function f with real coefficients having the given degree and zeros. Answers will vary depending on the choice of leading coefficient. Degree 4; zeros: i,1+2iIn Problems 1924, find a polynomial function f with real coefficients having the given degree and zeros. Answers will vary depending on the choice of leading coefficient. Degree 5; zeros: 2;i;1+iIn Problems, find a polynomial function with real coefficients having the given degree and zeros. Answers will vary depending on the choice of leading coefficient.
Degree; zeros:
In Problems, find a polynomial function with real coefficients having the given degree and zeros. Answers will vary depending on the choice of leading coefficient.
Degree; zeros:, multiplicity
In Problems, find a polynomial function with real coefficients having the given degree and zeros. Answers will vary depending on the choice of leading coefficient.
Degree; zeros:, multiplicity
In Problems, use the given zero to find the remaining zeros of each polynomial function.
; zero:
In Problems 23-30, use the given zero to find the remaining zeros of each function. g( x )= x 3 +3 x 2 +25x+75 ; zero: 5iIn Problems 2532, use the given zero to find the remaining zeros of each polynomial function. f(x)=4x4+7x3+62x2+112x32;zero: 4iIn Problems 23-30, use the given zero to find the remaining zeros of each function. h( x )=3 x 4 +5 x 3 +25 x 2 +45x18 ; zero: 3iIn Problems 2532, use the given zero to find the remaining zeros of each polynomial function. h(x)=x47x3+23x215x522;zero: 25iIn Problems 23-30, use the given zero to find the remaining zeros of each function. f( x )= x 4 7 x 3 +14 x 2 38x60 ; zero: 1+3iIn Problems 2532, use the given zero to find the remaining zeros of each polynomial function. h(x)=3x5+2x49x36x284x56;zero: 2iIn Problems 23-30, use the given zero to find the remaining zeros of each function. g( x )=2 x 5 3 x 4 5 x 3 15 x 2 207x+108 ; zero: 3iIn Problems 31-40, find the complex zeros of each polynomial function. Write f in factored form. f( x )= x 3 1In Problems 31-40, find the complex zeros of each polynomial function. Write f in factored form. f( x )= x 4 1In Problems 31-40, find the complex zeros of each polynomial function. Write f in factored form. f( x )= x 3 8 x 2 +25x26In Problems 31-40, find the complex zeros of each polynomial function. Write f in factored form. f( x )= x 3 +13 x 2 +57x+85In Problems 31-40, find the complex zeros of each polynomial function. Write f in factored form. f( x )= x 4 +5 x 2 +4In Problems 31-40, find the complex zeros of each polynomial function. Write f in factored form. f( x )= x 4 +13 x 2 +36In Problems 31-40, find the complex zeros of each polynomial function. Write f in factored form. f( x )= x 4 +2 x 3 +22 x 2 +50x75In Problems 31-40, find the complex zeros of each polynomial function. Write f in factored form. f( x )= x 4 +3 x 3 19 x 2 +27x252In Problems 31-40, find the complex zeros of each polynomial function. Write f in factored form. f( x )=3 x 4 x 3 9 x 2 +159x52In Problems 31-40, find the complex zeros of each polynomial function. Write f in factored form. f( x )=2 x 4 + x 3 35 x 2 113x+6541AYU42AYU43AYU44AYU1RE2RE3RE4RE5RE6RE7RE8RE9RE10RE11RE12RE13RE14RE15RE16RE17RE18RE19RE20RE21RE22RE23RE24RE25RE26RE27RE28RE29RE30RE31RE32RE33RE34RE35RE36RE37RE38RE39RE40RE41RE42RE43RE44RE45RE46RE47RE48RE49RE50RE51RE52RE53RE54RE55RE56RE57RE58RE59RE60RE61RE62RE63RE64RE65RE66RE67RE68RE69RE70RE71RE72RE73RE74RE75RE76RE77RE78RE79RE80RE81RE82RE83RE84RE85RE86RE87RE88RE89RE90RE91RE92RE93RE94RE95RE96RE97RE98RE99RE100RE101RE1CT2CTFind the inverse of f(x)=23x5 and check your answer. State the domain and the range of f and f1.4CT5CT6CT7CTIn Problems, evaluate each expression, without using a calculator.
9CTIn Problems, evaluate each expression, without using a calculator.
11CT12CT13CT14CT15CT16CT17CT18CT19CT20CT21CTA 50mg sample of radioactive substance decays to 34mg after 30 days. How long will it take, for there to be 2mg remaining?23CT1CRFor the function f(x)=2x23x+1, find: f(3) (b) f(x) (c) f(x+h)Determine which points are on the graph of x2+y2=1. (12,12) (b) (12,32)4CR5CR(a) Graph the quadratic function f(x)=x2+2x3 by determining whether its graph is concave up or concave down and by finding its vertex, axis of symmetry, y-intercept, and xintercept(s), if any. (b) Solve f(x)0.Determine the quadratic function whose graph is given in the figure,Graph using transformations.
Given that and , find and state its domain. What is ?
10CRFor the unction :
Graph using transformations. State the domain, range, and horizontal asymptote of the graph of . Determine the end behaviour of the graph.
Determine the inverse of . State the domain, range, and vertical asymptote of the graph of .
On the same coordinate axes as , graph.
12CR13CR14CRThe following data represent the percent of all drivers by age who have been stopped by the policy for any reason within the past year. The median age represents the midpoint of the upper and lower limit for the age range. AgeRangeMedianAge,xPercentageStopped, y161917.518.2202924.516.8303934.511.3404944.59.4505954.57.76069.53.8 Using a graphing utility, draw a scatter plot of the data treating median age, x, as the independent variable. Determine a model that best describes the relation between median age and percent stopped. You may choose from among linear, quadratic, cubic, exponential, logarithmic, and logistic models. Provide a justification for the model that you selected in part (b).Find f( 3 ) if f( x )=4 x 2 +5x . (pp. 60-62)Find f(3x) if f(x)=42 x 2 . (pp. 60-62)Find the domain of the function f(x)= x 2 1 x 2 25 . (pp. 64-66)4AYU5AYU6AYUIn Problems 9 and 10, evaluate each expression using the values given in the table. a. ( fg )( 1 ) b. ( fg )( 1 ) c. ( gf )( 1 ) d. ( gf )( 0 ) e. ( gg )( 2 ) f. ( ff )( 1 )In Problems 9 and 10, evaluate each expression using the values given in the table. a. ( fg )( 1 ) b. ( fg )( 2 ) c. ( gf )( 2 ) d. ( gf )( 3 ) e. ( gg )( 1 ) f. ( ff )( 3 )In Problems 11 and 12, evaluate each expression using the graphs of y=f(x) and y=g(x) shown in the figure. a. ( gf )( 1 ) b. ( gf )( 0 ) c. ( fg )( 1 ) d. ( fg )( 4 )In Problems 11 and 12, evaluate each expression using the graphs of y=f(x) and y=g(x) shown in the figure. a. ( gf )( 1 ) b. ( gf )( 5 ) c. ( fg )( 0 ) d. ( fg )( 2 )In Problems 13-22, for the given functions f and g , find: a. ( fg )( 4 ) b. ( gf )( 2 ) c. ( ff )( 1 ) d. ( gg )( 0 ) f( x )=2x ; g( x )=3 x 2 +1In Problems 13-22, for the given functions f and g , find: a. ( fg )( 4 ) b. ( gf )( 2 ) c. ( ff )( 1 ) d. ( gg )( 0 ) f( x )=3x+2 ; g( x )=2 x 2 1In problems for the given functions and find:
In Problems 13-22, for the given functions f and g , find: a. ( fg )( 4 ) b. ( gf )( 2 ) c. ( ff )( 1 ) d. ( gg )( 0 ) f( x )=2 x 2 ; g( x )=13 x 2In problems for the given functions and find:
In Problems 13-22, for the given functions f and g , find: a. ( fg )( 4 ) b. ( gf )( 2 ) c. ( ff )( 1 ) d. ( gg )( 0 ) f(x)= x+1 ; g(x)=3xIn problems 1322, for the given functions f and g, find: (fg)(4) (gf)(2) (ff)(1) (gg)(0) f(x)=|x|; g(x)=1x2+9In Problems 13-22, for the given functions f and g , find: a. ( fg )( 4 ) b. ( gf )( 2 ) c. ( ff )( 1 ) d. ( gg )( 0 ) f(x)=| x2 | ; g(x)= 3 x 2 +2In Problems 13-22, for the given functions f and g , find: a. ( fg )( 4 ) b. ( gf )( 2 ) c. ( ff )( 1 ) d. ( gg )( 0 ) f(x)= 3 x+1 ; g(x)= x 3In Problems 13-22, for the given functions f and g , find: a. ( fg )( 4 ) b. ( gf )( 2 ) c. ( ff )( 1 ) d. ( gg )( 0 ) f(x)= x 3/2 ; g(x)= 2 x+121AYU22AYU23AYU24AYU25AYU26AYU27AYU28AYU29AYU30AYU31AYU32AYU33AYU34AYU35AYU36AYU37AYU38AYU39AYU40AYU41AYU42AYU43AYU44AYUIn Problems 39-46, show that (fg)( x )=(gf)( x )=x . f( x )=2x ; g(x)= 1 2 xIn Problems 39-46, show that (fg)( x )=(gf)( x )=x . f( x )=4x ; g(x)= 1 4 xIn Problems 39-46, show that (fg)( x )=(gf)( x )=x . f( x )= x 3 ; g(x)= x 3In Problems 39-46, show that (fg)( x )=(gf)( x )=x . f( x )=x+5 ; g( x )=x5