The future value of $4000 invested for 5 years at rate r, compounded annually, is given by S =4000(1=r)5. Find the rate r, as a percent, that gives a future value from $5610 to $6442, inclusive. Round to the nearest whole percent.

A) $7 \% \leq \mathrm { r } \leq 10 \%$ B) $7 \% \leq \mathrm { r } \leq 15 \%$ C) $8 \% \leq \mathrm { r } \leq 13 \%$ D) $6 \% \leq \mathrm { r } \leq 9 \%$ A) $7 \% \leq \mathrm { r } \leq 10 \%$ B) $7 \% \leq \mathrm { r } \leq 15 \%$ C) $8 \% \leq \mathrm { r } \leq 13 \%$ D) $6 \% \leq \mathrm { r } \leq 9 \%$

Exam 6: Higher-Degree Polynomial and Rational Functions

Use the given graph of the polynomial function to state whether the leading coefficient is positive or negative and whether the polynomial function is cubic or quartic. -

(Multiple Choice)

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Question 241

Provide an appropriate response. -In the following formula, y is the minimum number of hours of studying required to attain a test score of x: $y = \frac { 0.38 x } { 100.5 - x }$ How many hours of study are needed to score 87? Round to the nearest hundredth if necessary.

(Multiple Choice)

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Question 242

Use synthetic division to find the quotient and remainder. - $\left( 2 x ^ { 4 } - x ^ { 3 } - 15 x ^ { 2 } + 3 x \right) \div ( x + 3 )$

(Multiple Choice)

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Question 243

Match the function with its graph. - $f ( x ) = \frac { x - 1 } { x ^ { 2 } - 4 x - 5 }$

(Multiple Choice)

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Question 244

Determine whether the polynomial function is cubic or quartic. -

(Multiple Choice)

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Question 245

Give the equations of any vertical asymptotes for the graphs of the rational functions. - $g ( x ) = \frac { x - 9 } { ( x - 9 ) ( x + 5 ) }$

(Multiple Choice)

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Question 246

Solve the polynomial equation by factoring. - $x ^ { 3 } - 5 x ^ { 2 } + 6 x = 0$

(Multiple Choice)

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Question 247

Use analytical methods to solve the equation. - $\frac { 2 y + 3 } { y } = \frac { 3 } { 2 }$

(Multiple Choice)

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Question 248

Use the graph of the polynomial function f(x) to solve f( $f ( x ) \text { to solve } f ( x ) = 0$ - $Use the graph of the polynomial function f(x) to solve f( f ( x ) \text { to solve } f ( x ) = 0 -$

(Multiple Choice)

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Question 249

Use a graphing calculator to estimate the local maximum and local minimum values of the function to the nearest hundredth. -The polynomial $R ( x ) = - 0.021 x ^ { 5 } + 4.133 x ^ { 4 } + 300$ approximates the shark population in a particular area, where x is the number of years from 1985. Use a graphing calculator to describe the shark population from the years 1985 to 2010.

(Multiple Choice)

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Question 250

Determine whether the polynomial function is cubic or quartic. -

(Multiple Choice)

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Question 251

$h ( x ) = \frac { 28 x ^ { 2 } } { 7 x ^ { 2 } - 3 }$

(Multiple Choice)

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Question 252

One solution of a polynomial equation is given. Use synthetic division to find any remaining solutions. - $x ^ { 3 } - 75 x - 250 = 0 ; 10$

(Multiple Choice)

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Question 253

Use algebraic and/or graphical methods to solve the inequality. - $m ^ { 3 } - 25 m \geq 0$

(Multiple Choice)

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Question 254

Find all rational zeros of the polynomial function. - $f ( x ) = 3 x ^ { 4 } + 5 x ^ { 3 } - 10 x ^ { 2 } - 20 x - 8$

(Multiple Choice)

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Question 255

State the degree and leading coefficient of the polynomial function. - $f ( x ) = 5 ( x + 2 ) \left( x ^ { 4 } - 2 \right)$

(Multiple Choice)

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Question 256

Determine whether the second polynomial is a factor of the first polynomial. - $\left( 6 x ^ { 4 } + 11 x ^ { 3 } - 2 x ^ { 2 } + x + 2 \right) ; ( x + 2 )$

(Multiple Choice)

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Question 257

$f ( x ) = x ^ { 5 } + 5 x ^ { 4 } - x ^ { 3 } - 10 x ^ { 2 } + 3 x + 10$

(Multiple Choice)

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Question 258

The future value of $4000 invested for 5 years at rate r, compounded annually, is given by S =4000(1=r)⁵. Find the rate r, as a percent, that gives a future value from $5610 to $6442, inclusive. Round to the nearest whole percent.

(Multiple Choice)

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Question 259

One solution of a polynomial equation is given. Use synthetic division to find any remaining solutions. - $x ^ { 3 } - 3 x ^ { 2 } - 25 x + 75 = 0 ; - 5$

(Multiple Choice)

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Question 260

Use the given graph of the polynomial function to state whether the leading coefficient is positive or negative and whether the polynomial function is cubic or quartic. -

Provide an appropriate response. -In the following formula, y is the minimum number of hours of studying required to attain a test score of x: $y = \frac { 0.38 x } { 100.5 - x }$ How many hours of study are needed to score 87? Round to the nearest hundredth if necessary.

Use synthetic division to find the quotient and remainder. - $\left( 2 x ^ { 4 } - x ^ { 3 } - 15 x ^ { 2 } + 3 x \right) \div ( x + 3 )$

Match the function with its graph. - $f ( x ) = \frac { x - 1 } { x ^ { 2 } - 4 x - 5 }$

Determine whether the polynomial function is cubic or quartic. -

Give the equations of any vertical asymptotes for the graphs of the rational functions. - $g ( x ) = \frac { x - 9 } { ( x - 9 ) ( x + 5 ) }$

Solve the polynomial equation by factoring. - $x ^ { 3 } - 5 x ^ { 2 } + 6 x = 0$

Use analytical methods to solve the equation. - $\frac { 2 y + 3 } { y } = \frac { 3 } { 2 }$

Use the graph of the polynomial function f(x) to solve f( $f ( x ) \text { to solve } f ( x ) = 0$ - $Use the graph of the polynomial function f(x) to solve f( f ( x ) \text { to solve } f ( x ) = 0 -$

Determine whether the polynomial function is cubic or quartic. -

$h ( x ) = \frac { 28 x ^ { 2 } } { 7 x ^ { 2 } - 3 }$

One solution of a polynomial equation is given. Use synthetic division to find any remaining solutions. - $x ^ { 3 } - 75 x - 250 = 0 ; 10$

Use algebraic and/or graphical methods to solve the inequality. - $m ^ { 3 } - 25 m \geq 0$

Find all rational zeros of the polynomial function. - $f ( x ) = 3 x ^ { 4 } + 5 x ^ { 3 } - 10 x ^ { 2 } - 20 x - 8$

State the degree and leading coefficient of the polynomial function. - $f ( x ) = 5 ( x + 2 ) \left( x ^ { 4 } - 2 \right)$

Determine whether the second polynomial is a factor of the first polynomial. - $\left( 6 x ^ { 4 } + 11 x ^ { 3 } - 2 x ^ { 2 } + x + 2 \right) ; ( x + 2 )$

$f ( x ) = x ^ { 5 } + 5 x ^ { 4 } - x ^ { 3 } - 10 x ^ { 2 } + 3 x + 10$

The future value of $4000 invested for 5 years at rate r, compounded annually, is given by S =4000(1=r)⁵. Find the rate r, as a percent, that gives a future value from $5610 to $6442, inclusive. Round to the nearest whole percent.

One solution of a polynomial equation is given. Use synthetic division to find any remaining solutions. - $x ^ { 3 } - 3 x ^ { 2 } - 25 x + 75 = 0 ; - 5$

Functions, Graphs, and Models; Linear Functions

Linear Models, Equations, and Inequalities

Quadratic, Piecewise-Defined, and Power Functions

Additional Topics With Functions

Exponential and Logarithmic Functions

Systems of Equations and Matrices

Special Topics in Algebra

Filters

Exam 6: Higher-Degree Polynomial and Rational Functions

Use the given graph of the polynomial function to state whether the leading coefficient is positive or negative and whether the polynomial function is cubic or quartic. -

Use synthetic division to find the quotient and remainder. - (2x4−x3−15x2+3x)÷(x+3)\left( 2 x ^ { 4 } - x ^ { 3 } - 15 x ^ { 2 } + 3 x \right) \div ( x + 3 )(2x4−x3−15x2+3x)÷(x+3)

Match the function with its graph. - f(x)=x−1x2−4x−5f ( x ) = \frac { x - 1 } { x ^ { 2 } - 4 x - 5 }f(x)=x2−4x−5x−1​

Determine whether the polynomial function is cubic or quartic. -

Give the equations of any vertical asymptotes for the graphs of the rational functions. - g(x)=x−9(x−9)(x+5)g ( x ) = \frac { x - 9 } { ( x - 9 ) ( x + 5 ) }g(x)=(x−9)(x+5)x−9​

Solve the polynomial equation by factoring. - x3−5x2+6x=0x ^ { 3 } - 5 x ^ { 2 } + 6 x = 0x3−5x2+6x=0

Use analytical methods to solve the equation. - 2y+3y=32\frac { 2 y + 3 } { y } = \frac { 3 } { 2 }y2y+3​=23​

Use the graph of the polynomial function f(x) to solve f( f(x) to solve f(x)=0f ( x ) \text { to solve } f ( x ) = 0f(x) to solve f(x)=0 -

Determine whether the polynomial function is cubic or quartic. -

h(x)=28x27x2−3h ( x ) = \frac { 28 x ^ { 2 } } { 7 x ^ { 2 } - 3 }h(x)=7x2−328x2​

One solution of a polynomial equation is given. Use synthetic division to find any remaining solutions. - x3−75x−250=0;10x ^ { 3 } - 75 x - 250 = 0 ; 10x3−75x−250=0;10

Use algebraic and/or graphical methods to solve the inequality. - m3−25m≥0m ^ { 3 } - 25 m \geq 0m3−25m≥0

Find all rational zeros of the polynomial function. - f(x)=3x4+5x3−10x2−20x−8f ( x ) = 3 x ^ { 4 } + 5 x ^ { 3 } - 10 x ^ { 2 } - 20 x - 8f(x)=3x4+5x3−10x2−20x−8

State the degree and leading coefficient of the polynomial function. - f(x)=5(x+2)(x4−2)f ( x ) = 5 ( x + 2 ) \left( x ^ { 4 } - 2 \right)f(x)=5(x+2)(x4−2)

Determine whether the second polynomial is a factor of the first polynomial. - (6x4+11x3−2x2+x+2);(x+2)\left( 6 x ^ { 4 } + 11 x ^ { 3 } - 2 x ^ { 2 } + x + 2 \right) ; ( x + 2 )(6x4+11x3−2x2+x+2);(x+2)

f(x)=x5+5x4−x3−10x2+3x+10f ( x ) = x ^ { 5 } + 5 x ^ { 4 } - x ^ { 3 } - 10 x ^ { 2 } + 3 x + 10f(x)=x5+5x4−x3−10x2+3x+10

The future value of $4000 invested for 5 years at rate r, compounded annually, is given by S =4000(1=r)5. Find the rate r, as a percent, that gives a future value from $5610 to $6442, inclusive. Round to the nearest whole percent.

One solution of a polynomial equation is given. Use synthetic division to find any remaining solutions. - x3−3x2−25x+75=0;−5x ^ { 3 } - 3 x ^ { 2 } - 25 x + 75 = 0 ; - 5x3−3x2−25x+75=0;−5

Functions, Graphs, and Models; Linear Functions

Linear Models, Equations, and Inequalities

Quadratic, Piecewise-Defined, and Power Functions

Additional Topics With Functions

Exponential and Logarithmic Functions

Systems of Equations and Matrices

Special Topics in Algebra

Filters

Use synthetic division to find the quotient and remainder. - $\left( 2 x ^ { 4 } - x ^ { 3 } - 15 x ^ { 2 } + 3 x \right) \div ( x + 3 )$

Match the function with its graph. - $f ( x ) = \frac { x - 1 } { x ^ { 2 } - 4 x - 5 }$

Give the equations of any vertical asymptotes for the graphs of the rational functions. - $g ( x ) = \frac { x - 9 } { ( x - 9 ) ( x + 5 ) }$

Solve the polynomial equation by factoring. - $x ^ { 3 } - 5 x ^ { 2 } + 6 x = 0$

Use analytical methods to solve the equation. - $\frac { 2 y + 3 } { y } = \frac { 3 } { 2 }$

Use the graph of the polynomial function f(x) to solve f( $f ( x ) \text { to solve } f ( x ) = 0$ - $Use the graph of the polynomial function f(x) to solve f( f ( x ) \text { to solve } f ( x ) = 0 -$

$h ( x ) = \frac { 28 x ^ { 2 } } { 7 x ^ { 2 } - 3 }$

One solution of a polynomial equation is given. Use synthetic division to find any remaining solutions. - $x ^ { 3 } - 75 x - 250 = 0 ; 10$

Use algebraic and/or graphical methods to solve the inequality. - $m ^ { 3 } - 25 m \geq 0$

Find all rational zeros of the polynomial function. - $f ( x ) = 3 x ^ { 4 } + 5 x ^ { 3 } - 10 x ^ { 2 } - 20 x - 8$

State the degree and leading coefficient of the polynomial function. - $f ( x ) = 5 ( x + 2 ) \left( x ^ { 4 } - 2 \right)$

Determine whether the second polynomial is a factor of the first polynomial. - $\left( 6 x ^ { 4 } + 11 x ^ { 3 } - 2 x ^ { 2 } + x + 2 \right) ; ( x + 2 )$

$f ( x ) = x ^ { 5 } + 5 x ^ { 4 } - x ^ { 3 } - 10 x ^ { 2 } + 3 x + 10$

The future value of $4000 invested for 5 years at rate r, compounded annually, is given by S =4000(1=r)⁵. Find the rate r, as a percent, that gives a future value from $5610 to $6442, inclusive. Round to the nearest whole percent.

One solution of a polynomial equation is given. Use synthetic division to find any remaining solutions. - $x ^ { 3 } - 3 x ^ { 2 } - 25 x + 75 = 0 ; - 5$