Solve the problem -The population of a small town is given by the table. $\begin{array}{r|cccc} \text { Year } & 1980 & 1990 & 2000 & 2010 \\ \hline \mathrm{p} & 6500 & 6508 & 6532 & 6572 \end{array}$ If the population is modeled by $p ( t ) = a t ^ { 2 } + b$ where $t$ is in years and $t = 0$ corresponds to the year 19: and $t = 1$ corresponds the year 1990 , find $a$.

A) 20 B) 10 C) 16 D) 8 A) 20 B) 10 C) 16 D) 8

Exam 4: Polynomial and Rational Functions

Graph the polynomial function. Factor first if the expression is not in factored form. - f(x)=+5+7x+3 $Graph the polynomial function. Factor first if the expression is not in factored form. - \begin{array} { l } f ( x ) = x ^ { 3 } + 5 x ^ { 2 } + 7 x + 3 \\ \end{array}$

(Multiple Choice)

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Question 301

Find an equation for the rational function graph. -

(Multiple Choice)

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Question 302

Use synthetic division to decide whether the given number k is a zero of the given polynomial function. - $k = - 3 ; f ( x ) = - x ^ { 4 } + 6 x ^ { 2 } - x - 7$

(Multiple Choice)

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Question 303

Round your answer to two decimal places. -The weight of a person on or above the surface of the earth varies inversely as the square of the distance the person is from the center of the earth. If a person weighs 180 pounds on the surface of The earth and the radius of the earth is 3900 miles, what will the person weigh if he or she is 125 Miles above the earth's surface? Round your answer to the nearest hundredth of a pound.

(Multiple Choice)

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Question 304

Give the equations of any horizontal asymptotes. - $h ( x ) = \frac { 5 x ^ { 2 } } { 5 x ^ { 2 } - 8 }$

(Multiple Choice)

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Question 305

Graph the function. - $f ( x ) = \frac { 1 } { x } + 2$ $Graph the function. - f ( x ) = \frac { 1 } { x } + 2$

(Multiple Choice)

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Question 306

Graph the polynomial function. Factor first if the expression is not in factored form. - $f ( x ) = x ( x + 2 ) ( x - 2 ) ^ { 3 }$ $Graph the polynomial function. Factor first if the expression is not in factored form. - f ( x ) = x ( x + 2 ) ( x - 2 ) ^ { 3 }$

(Multiple Choice)

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Question 307

Sketch the graph of the rational function. - f(x)= $Sketch the graph of the rational function. - \begin{array} { l } f ( x ) = \frac { x ^ { 2 } + 3 x - 4 } { 2 x ^ { 2 } + 1 } \\ \end{array}$

(Multiple Choice)

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Question 308

Identify the vertex of the parabola. - $f ( x ) = - 3 x ^ { 2 }$

(Multiple Choice)

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Question 309

Find the zeros of the polynomial function and state the multiplicity of each. - $f ( x ) = 4 ( x + 2 ) ^ { 3 } ( x - 4 ) ( x - 3 + i )$

(Multiple Choice)

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Question 310

Sketch the graph of the parabola. - $y = - x ^ { 2 } + 3 x - 8$ $Sketch the graph of the parabola. - y = - x ^ { 2 } + 3 x - 8$

(Multiple Choice)

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Question 311

Use synthetic division to perform the division. - $\frac { x ^ { 4 } + 7 x ^ { 3 } + 12 x ^ { 2 } + 11 x + 5 } { x + 5 }$

(Multiple Choice)

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Question 312

Round your answer to two decimal places. -The current I in an electrical conductor varies inversely as the resistance R of the conductor. The current is 8 amperes when the resistance is 727 ohms. What is the current when the resistance is 899 Ohms? Round to the nearest tenth.

(Multiple Choice)

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Question 313

Sketch the graph of the parabola. - $y = - 3 x ^ { 2 } - 2 x - 8$ $Sketch the graph of the parabola. - y = - 3 x ^ { 2 } - 2 x - 8$

(Multiple Choice)

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Question 314

Solve the problem -The population of a small town is given by the table. Year 1980 1990 2000 2010 6500 6508 6532 6572 If the population is modeled by $p ( t ) = a t ^ { 2 } + b$ where $t$ is in years and $t = 0$ corresponds to the year 19: and $t = 1$ corresponds the year 1990 , find $a$ .

(Multiple Choice)

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Question 315

Tell whether a linear model or a quadratic model is appropriate for the data. If linear, tell whether the slope should be positive or negative. If quadratic, decide whether the leading coefficient a of $x ^ { 2 }$ should be positive or negative. - $Tell whether a linear model or a quadratic model is appropriate for the data. If linear, tell whether the slope should be positive or negative. If quadratic, decide whether the leading coefficient a of x ^ { 2 } should be positive or negative. -$

(Multiple Choice)

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Question 316

Answer the question - $\text { How can the graph of } f ( x ) = \frac { 5 } { ( x + 11 ) ^ { 2 } } \text { by obtained from the graph of } y = \frac { 1 } { x ^ { 2 } }$

(Multiple Choice)

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Question 317

Find the domain and range of the function. - $f ( x ) = ( x + 5 ) ^ { 2 } - 5$

(Multiple Choice)

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Question 318

Find the equation that the given graph represents. -

(Multiple Choice)

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Question 319

Factor f(x) into linear factors given that k is a zero of f(x). - $f ( x ) = x ^ { 3 } - 3 x ^ { 2 } - 49 x + 147 ; k = 7$

(Multiple Choice)

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Question 320

Showing 301 - 320 of 508

Graph the polynomial function. Factor first if the expression is not in factored form. - f(x)=+5+7x+3 $Graph the polynomial function. Factor first if the expression is not in factored form. - \begin{array} { l } f ( x ) = x ^ { 3 } + 5 x ^ { 2 } + 7 x + 3 \\ \end{array}$

Find an equation for the rational function graph. -

Use synthetic division to decide whether the given number k is a zero of the given polynomial function. - $k = - 3 ; f ( x ) = - x ^ { 4 } + 6 x ^ { 2 } - x - 7$

Give the equations of any horizontal asymptotes. - $h ( x ) = \frac { 5 x ^ { 2 } } { 5 x ^ { 2 } - 8 }$

Graph the function. - $f ( x ) = \frac { 1 } { x } + 2$ $Graph the function. - f ( x ) = \frac { 1 } { x } + 2$

Graph the polynomial function. Factor first if the expression is not in factored form. - $f ( x ) = x ( x + 2 ) ( x - 2 ) ^ { 3 }$ $Graph the polynomial function. Factor first if the expression is not in factored form. - f ( x ) = x ( x + 2 ) ( x - 2 ) ^ { 3 }$

Sketch the graph of the rational function. - f(x)= $Sketch the graph of the rational function. - \begin{array} { l } f ( x ) = \frac { x ^ { 2 } + 3 x - 4 } { 2 x ^ { 2 } + 1 } \\ \end{array}$

Identify the vertex of the parabola. - $f ( x ) = - 3 x ^ { 2 }$

Find the zeros of the polynomial function and state the multiplicity of each. - $f ( x ) = 4 ( x + 2 ) ^ { 3 } ( x - 4 ) ( x - 3 + i )$

Sketch the graph of the parabola. - $y = - x ^ { 2 } + 3 x - 8$ $Sketch the graph of the parabola. - y = - x ^ { 2 } + 3 x - 8$

Use synthetic division to perform the division. - $\frac { x ^ { 4 } + 7 x ^ { 3 } + 12 x ^ { 2 } + 11 x + 5 } { x + 5 }$

Round your answer to two decimal places. -The current I in an electrical conductor varies inversely as the resistance R of the conductor. The current is 8 amperes when the resistance is 727 ohms. What is the current when the resistance is 899 Ohms? Round to the nearest tenth.

Sketch the graph of the parabola. - $y = - 3 x ^ { 2 } - 2 x - 8$ $Sketch the graph of the parabola. - y = - 3 x ^ { 2 } - 2 x - 8$

Solve the problem -The population of a small town is given by the table. Year 1980 1990 2000 2010 6500 6508 6532 6572 If the population is modeled by $p ( t ) = a t ^ { 2 } + b$ where $t$ is in years and $t = 0$ corresponds to the year 19: and $t = 1$ corresponds the year 1990 , find $a$ .

Answer the question - $\text { How can the graph of } f ( x ) = \frac { 5 } { ( x + 11 ) ^ { 2 } } \text { by obtained from the graph of } y = \frac { 1 } { x ^ { 2 } }$

Find the domain and range of the function. - $f ( x ) = ( x + 5 ) ^ { 2 } - 5$

Find the equation that the given graph represents. -

Factor f(x) into linear factors given that k is a zero of f(x). - $f ( x ) = x ^ { 3 } - 3 x ^ { 2 } - 49 x + 147 ; k = 7$

Review of Basic Concepts

Equations and Inequalities

Graphs and Functions

Inverse, Exponential, and Logarithmic Functions

Trigonometric Functions

The Circular Functions and Their Graphs

Trigonometric Identities and Equations

Applications of Trigonometry

Systems and Matrices

Analytic Geometry

Further Topics in Algebra

Filters

Exam 4: Polynomial and Rational Functions

Graph the polynomial function. Factor first if the expression is not in factored form. - f(x)=+5+7x+3

Find an equation for the rational function graph. -

Use synthetic division to decide whether the given number k is a zero of the given polynomial function. - k=−3;f(x)=−x4+6x2−x−7k = - 3 ; f ( x ) = - x ^ { 4 } + 6 x ^ { 2 } - x - 7k=−3;f(x)=−x4+6x2−x−7

Give the equations of any horizontal asymptotes. - h(x)=5x25x2−8h ( x ) = \frac { 5 x ^ { 2 } } { 5 x ^ { 2 } - 8 }h(x)=5x2−85x2​

Graph the function. - f(x)=1x+2f ( x ) = \frac { 1 } { x } + 2f(x)=x1​+2

Graph the polynomial function. Factor first if the expression is not in factored form. - f(x)=x(x+2)(x−2)3f ( x ) = x ( x + 2 ) ( x - 2 ) ^ { 3 }f(x)=x(x+2)(x−2)3

Sketch the graph of the rational function. - f(x)=

Identify the vertex of the parabola. - f(x)=−3x2f ( x ) = - 3 x ^ { 2 }f(x)=−3x2

Find the zeros of the polynomial function and state the multiplicity of each. - f(x)=4(x+2)3(x−4)(x−3+i)f ( x ) = 4 ( x + 2 ) ^ { 3 } ( x - 4 ) ( x - 3 + i )f(x)=4(x+2)3(x−4)(x−3+i)

Sketch the graph of the parabola. - y=−x2+3x−8y = - x ^ { 2 } + 3 x - 8y=−x2+3x−8

Use synthetic division to perform the division. - x4+7x3+12x2+11x+5x+5\frac { x ^ { 4 } + 7 x ^ { 3 } + 12 x ^ { 2 } + 11 x + 5 } { x + 5 }x+5x4+7x3+12x2+11x+5​

Round your answer to two decimal places. -The current I in an electrical conductor varies inversely as the resistance R of the conductor. The current is 8 amperes when the resistance is 727 ohms. What is the current when the resistance is 899 Ohms? Round to the nearest tenth.

Sketch the graph of the parabola. - y=−3x2−2x−8y = - 3 x ^ { 2 } - 2 x - 8y=−3x2−2x−8

Tell whether a linear model or a quadratic model is appropriate for the data. If linear, tell whether the slope should be positive or negative. If quadratic, decide whether the leading coefficient a of x2x ^ { 2 }x2 should be positive or negative. -

Find the domain and range of the function. - f(x)=(x+5)2−5f ( x ) = ( x + 5 ) ^ { 2 } - 5f(x)=(x+5)2−5

Find the equation that the given graph represents. -

Factor f(x) into linear factors given that k is a zero of f(x). - f(x)=x3−3x2−49x+147;k=7f ( x ) = x ^ { 3 } - 3 x ^ { 2 } - 49 x + 147 ; k = 7f(x)=x3−3x2−49x+147;k=7

Review of Basic Concepts

Equations and Inequalities

Graphs and Functions

Inverse, Exponential, and Logarithmic Functions

Trigonometric Functions

The Circular Functions and Their Graphs

Trigonometric Identities and Equations

Applications of Trigonometry

Systems and Matrices

Analytic Geometry

Further Topics in Algebra

Filters

Graph the polynomial function. Factor first if the expression is not in factored form. - f(x)=+5+7x+3 $Graph the polynomial function. Factor first if the expression is not in factored form. - \begin{array} { l } f ( x ) = x ^ { 3 } + 5 x ^ { 2 } + 7 x + 3 \\ \end{array}$

Use synthetic division to decide whether the given number k is a zero of the given polynomial function. - $k = - 3 ; f ( x ) = - x ^ { 4 } + 6 x ^ { 2 } - x - 7$

Give the equations of any horizontal asymptotes. - $h ( x ) = \frac { 5 x ^ { 2 } } { 5 x ^ { 2 } - 8 }$

Graph the function. - $f ( x ) = \frac { 1 } { x } + 2$ $Graph the function. - f ( x ) = \frac { 1 } { x } + 2$

Graph the polynomial function. Factor first if the expression is not in factored form. - $f ( x ) = x ( x + 2 ) ( x - 2 ) ^ { 3 }$ $Graph the polynomial function. Factor first if the expression is not in factored form. - f ( x ) = x ( x + 2 ) ( x - 2 ) ^ { 3 }$

Sketch the graph of the rational function. - f(x)= $Sketch the graph of the rational function. - \begin{array} { l } f ( x ) = \frac { x ^ { 2 } + 3 x - 4 } { 2 x ^ { 2 } + 1 } \\ \end{array}$

Identify the vertex of the parabola. - $f ( x ) = - 3 x ^ { 2 }$

Find the zeros of the polynomial function and state the multiplicity of each. - $f ( x ) = 4 ( x + 2 ) ^ { 3 } ( x - 4 ) ( x - 3 + i )$

Sketch the graph of the parabola. - $y = - x ^ { 2 } + 3 x - 8$ $Sketch the graph of the parabola. - y = - x ^ { 2 } + 3 x - 8$

Use synthetic division to perform the division. - $\frac { x ^ { 4 } + 7 x ^ { 3 } + 12 x ^ { 2 } + 11 x + 5 } { x + 5 }$

Sketch the graph of the parabola. - $y = - 3 x ^ { 2 } - 2 x - 8$ $Sketch the graph of the parabola. - y = - 3 x ^ { 2 } - 2 x - 8$

Find the domain and range of the function. - $f ( x ) = ( x + 5 ) ^ { 2 } - 5$

Factor f(x) into linear factors given that k is a zero of f(x). - $f ( x ) = x ^ { 3 } - 3 x ^ { 2 } - 49 x + 147 ; k = 7$