Solve. -A biking club has increased its membership each year since its founding in 1984. The table provides membership data for several years. \[\begin{array} { c | c } \text { Year } & \text { \# of Members } \\ \hline 0 & 7 \\ 5 & 12 \\ 10 & 16 \\ 12 & 19 \\ 14 & 20 \end{array}\] Determine the linear, quadratic, cubic, or quartic function that best fits the data.

A) $f ( x ) = 0.003 x ^ { 4 } - 0.98 x ^ { 2 } + 7.03 x + 1.57$ B) $f ( x ) = - 0.003 x ^ { 2 } + 0.98 x + 7.03$ C) $f ( x ) = 0.94 x + 7.08$ D) $f ( x ) = 0.0002 x ^ { 3 } - 0.006 x ^ { 2 } + 0.99 x + 7.03$ A) $f ( x ) = 0.003 x ^ { 4 } - 0.98 x ^ { 2 } + 7.03 x + 1.57$ B) $f ( x ) = - 0.003 x ^ { 2 } + 0.98 x + 7.03$ C) $f ( x ) = 0.94 x + 7.08$ D) $f ( x ) = 0.0002 x ^ { 3 } - 0.006 x ^ { 2 } + 0.99 x + 7.03$

Exam 4: Polynomial and Rational Functions

Use the equation and the corresponding graph for the quadratic function to find what is requested. - $f ( x ) = ( x - 4 ) ^ { 2 } - 1$ $Use the equation and the corresponding graph for the quadratic function to find what is requested. - f ( x ) = ( x - 4 ) ^ { 2 } - 1 Find the domain and range.$ Find the domain and range.

(Multiple Choice)

4.9/5

(48)

Question 281

Sketch the graph of the parabola. - $y=(x-6)^{2}-5$ $Sketch the graph of the parabola. - y=(x-6)^{2}-5$

(Multiple Choice)

4.8/5

(37)

Question 282

Use synthetic division to perform the division. - $\frac { - 6 x ^ { 3 } - 30 x ^ { 2 } - 22 x + 8 } { x + 4 }$

(Multiple Choice)

4.8/5

(39)

Question 283

Provide an appropriate response. -Explain the behavior of the graph of f(x) as it approaches its vertical asymptote. $f ( x ) = \frac { - 3 } { x - 4 }$

(Multiple Choice)

4.8/5

(40)

Question 284

Find the correct end behavior diagram for the given polynomial function. - $P ( x ) = 7 x ^ { 3 } + 2 x ^ { 2 } - 6 x + 7$

(Multiple Choice)

4.7/5

(37)

Question 285

Round your answer to two decimal places. -The pitch P of a musical tone varies inversely as its wavelength W. One tone has a pitch of 463 vibrations per second and a wavelength of 14.4 ft. Find the wavelength of another tone that has a Pitch of 370 vibrations per second. Round to the nearest tenth.

(Multiple Choice)

4.8/5

(33)

Question 286

Use synthetic division to decide whether the given number k is a zero of the given polynomial function. - $k = - 2 + 5 i ; f ( x ) = x ^ { 2 } + 4 x + 29$

(Multiple Choice)

4.9/5

(36)

Question 287

Solve. -A biking club has increased its membership each year since its founding in 1984. The table provides membership data for several years. Year \# of Members 0 7 5 12 10 16 12 19 14 20 Determine the linear, quadratic, cubic, or quartic function that best fits the data.

(Multiple Choice)

4.8/5

(35)

Question 288

Find all rational zeros and factor f(x). - $f ( x ) = 6 x ^ { 3 } + 19 x ^ { 2 } + 8 x - 5$

(Multiple Choice)

4.8/5

(41)

Question 289

2Given the equation or other information for a parabola, find the matching description or graph. - f(x)=a+bx+c a>0;-4ac<0

(Multiple Choice)

4.8/5

(27)

Question 290

Find all rational zeros and factor f(x). - $f ( x ) = x ^ { 3 } - 5 x ^ { 2 } - 2 x + 24$

(Multiple Choice)

4.9/5

(43)

Question 291

Round your answer to two decimal places. -If $\mathrm { f }$ varies jointly as $\mathrm { q } ^ { 2 }$ and $\mathrm { h }$ , and $\mathrm { f } = 96$ when $\mathrm { q } = 4$ and $\mathrm { h } = 3$ , find $\mathrm { q }$ when $\mathrm { f } = 40$ and $\mathrm { h } = 5$

(Multiple Choice)

4.8/5

(36)

Question 292

Find the domain and range of the function. - $f ( x ) = ( x + 2 ) ^ { 2 } + 7$

(Multiple Choice)

4.8/5

(38)

Question 293

Solve the problem -Of all possible pairs of positive numbers having a sum of 82, which pair has the maximum product?

(Multiple Choice)

4.7/5

(34)

Question 294

Sketch the graph of the rational function. - $f ( x ) = \frac { x ( x - 4 ) } { ( x - 2 ) ^ { 2 } }$ $Sketch the graph of the rational function. - f ( x ) = \frac { x ( x - 4 ) } { ( x - 2 ) ^ { 2 } }$

(Multiple Choice)

4.9/5

(36)

Question 295

Sketch the graph of the rational function. - f(x)= $Sketch the graph of the rational function. - \begin{array} { l } f ( x ) = \frac { ( x + 4 ) ( x + 5 ) } { ( x + 3 ) ^ { 2 } } \\ \end{array}$

(Multiple Choice)

4.8/5

(32)

Question 296

Use the remainder theorem and synthetic division to find f(k). - $k = 3 : f ( x ) = - x ^ { 3 } + 2 x ^ { 2 } + 2$

(Multiple Choice)

4.9/5

(42)

Question 297

Use synthetic division to perform the division. - $\frac { 3 x ^ { 4 } - 2 x ^ { 3 } - 10 x ^ { 2 } + 15 } { x - 2 }$

(Multiple Choice)

4.8/5

(44)

Question 298

Find the equation that the given graph represents. -

(Multiple Choice)

4.9/5

(32)

Question 299

Solve the problem -A $15 \mathrm {~cm}$ by $18 \mathrm {~cm}$ rectangular garden is to have a gravel path of uniform width bordering it. How wide is the path if the total area covered by the garden and path is $418 \mathrm {~cm} ^ { 2 }$ ?

(Multiple Choice)

4.8/5

(39)

Question 300

Showing 281 - 300 of 508

Sketch the graph of the parabola. - $y=(x-6)^{2}-5$ $Sketch the graph of the parabola. - y=(x-6)^{2}-5$

Use synthetic division to perform the division. - $\frac { - 6 x ^ { 3 } - 30 x ^ { 2 } - 22 x + 8 } { x + 4 }$

Provide an appropriate response. -Explain the behavior of the graph of f(x) as it approaches its vertical asymptote. $f ( x ) = \frac { - 3 } { x - 4 }$

Find the correct end behavior diagram for the given polynomial function. - $P ( x ) = 7 x ^ { 3 } + 2 x ^ { 2 } - 6 x + 7$

Round your answer to two decimal places. -The pitch P of a musical tone varies inversely as its wavelength W. One tone has a pitch of 463 vibrations per second and a wavelength of 14.4 ft. Find the wavelength of another tone that has a Pitch of 370 vibrations per second. Round to the nearest tenth.

Use synthetic division to decide whether the given number k is a zero of the given polynomial function. - $k = - 2 + 5 i ; f ( x ) = x ^ { 2 } + 4 x + 29$

Solve. -A biking club has increased its membership each year since its founding in 1984. The table provides membership data for several years. Year \# of Members 0 7 5 12 10 16 12 19 14 20 Determine the linear, quadratic, cubic, or quartic function that best fits the data.

Find all rational zeros and factor f(x). - $f ( x ) = 6 x ^ { 3 } + 19 x ^ { 2 } + 8 x - 5$

2Given the equation or other information for a parabola, find the matching description or graph. - f(x)=a+bx+c a>0;-4ac<0

Find all rational zeros and factor f(x). - $f ( x ) = x ^ { 3 } - 5 x ^ { 2 } - 2 x + 24$

Round your answer to two decimal places. -If $\mathrm { f }$ varies jointly as $\mathrm { q } ^ { 2 }$ and $\mathrm { h }$ , and $\mathrm { f } = 96$ when $\mathrm { q } = 4$ and $\mathrm { h } = 3$ , find $\mathrm { q }$ when $\mathrm { f } = 40$ and $\mathrm { h } = 5$

Find the domain and range of the function. - $f ( x ) = ( x + 2 ) ^ { 2 } + 7$

Solve the problem -Of all possible pairs of positive numbers having a sum of 82, which pair has the maximum product?

Sketch the graph of the rational function. - $f ( x ) = \frac { x ( x - 4 ) } { ( x - 2 ) ^ { 2 } }$ $Sketch the graph of the rational function. - f ( x ) = \frac { x ( x - 4 ) } { ( x - 2 ) ^ { 2 } }$

Sketch the graph of the rational function. - f(x)= $Sketch the graph of the rational function. - \begin{array} { l } f ( x ) = \frac { ( x + 4 ) ( x + 5 ) } { ( x + 3 ) ^ { 2 } } \\ \end{array}$

Use the remainder theorem and synthetic division to find f(k). - $k = 3 : f ( x ) = - x ^ { 3 } + 2 x ^ { 2 } + 2$

Use synthetic division to perform the division. - $\frac { 3 x ^ { 4 } - 2 x ^ { 3 } - 10 x ^ { 2 } + 15 } { x - 2 }$

Find the equation that the given graph represents. -

Solve the problem -A $15 \mathrm {~cm}$ by $18 \mathrm {~cm}$ rectangular garden is to have a gravel path of uniform width bordering it. How wide is the path if the total area covered by the garden and path is $418 \mathrm {~cm} ^ { 2 }$ ?

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

Use the equation and the corresponding graph for the quadratic function to find what is requested. - f(x)=(x−4)2−1f ( x ) = ( x - 4 ) ^ { 2 } - 1f(x)=(x−4)2−1 Find the domain and range.

Sketch the graph of the parabola. - y=(x−6)2−5y=(x-6)^{2}-5y=(x−6)2−5

Use synthetic division to perform the division. - −6x3−30x2−22x+8x+4\frac { - 6 x ^ { 3 } - 30 x ^ { 2 } - 22 x + 8 } { x + 4 }x+4−6x3−30x2−22x+8​

Provide an appropriate response. -Explain the behavior of the graph of f(x) as it approaches its vertical asymptote. f(x)=−3x−4f ( x ) = \frac { - 3 } { x - 4 }f(x)=x−4−3​

Find the correct end behavior diagram for the given polynomial function. - P(x)=7x3+2x2−6x+7P ( x ) = 7 x ^ { 3 } + 2 x ^ { 2 } - 6 x + 7P(x)=7x3+2x2−6x+7

Round your answer to two decimal places. -The pitch P of a musical tone varies inversely as its wavelength W. One tone has a pitch of 463 vibrations per second and a wavelength of 14.4 ft. Find the wavelength of another tone that has a Pitch of 370 vibrations per second. Round to the nearest tenth.

Use synthetic division to decide whether the given number k is a zero of the given polynomial function. - k=−2+5i;f(x)=x2+4x+29k = - 2 + 5 i ; f ( x ) = x ^ { 2 } + 4 x + 29k=−2+5i;f(x)=x2+4x+29

Solve. -A biking club has increased its membership each year since its founding in 1984. The table provides membership data for several years. Year \# of Members 0 7 5 12 10 16 12 19 14 20 Determine the linear, quadratic, cubic, or quartic function that best fits the data.

Find all rational zeros and factor f(x). - f(x)=6x3+19x2+8x−5f ( x ) = 6 x ^ { 3 } + 19 x ^ { 2 } + 8 x - 5f(x)=6x3+19x2+8x−5

2Given the equation or other information for a parabola, find the matching description or graph. - f(x)=a+bx+c a>0;-4ac<0

Find all rational zeros and factor f(x). - f(x)=x3−5x2−2x+24f ( x ) = x ^ { 3 } - 5 x ^ { 2 } - 2 x + 24f(x)=x3−5x2−2x+24

Round your answer to two decimal places. -If f\mathrm { f }f varies jointly as q2\mathrm { q } ^ { 2 }q2 and h\mathrm { h }h , and f=96\mathrm { f } = 96f=96 when q=4\mathrm { q } = 4q=4 and h=3\mathrm { h } = 3h=3 , find q\mathrm { q }q when f=40\mathrm { f } = 40f=40 and h=5\mathrm { h } = 5h=5

Find the domain and range of the function. - f(x)=(x+2)2+7f ( x ) = ( x + 2 ) ^ { 2 } + 7f(x)=(x+2)2+7

Solve the problem -Of all possible pairs of positive numbers having a sum of 82, which pair has the maximum product?

Sketch the graph of the rational function. - f(x)=x(x−4)(x−2)2f ( x ) = \frac { x ( x - 4 ) } { ( x - 2 ) ^ { 2 } }f(x)=(x−2)2x(x−4)​

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

Use the remainder theorem and synthetic division to find f(k). - k=3:f(x)=−x3+2x2+2k = 3 : f ( x ) = - x ^ { 3 } + 2 x ^ { 2 } + 2k=3:f(x)=−x3+2x2+2

Use synthetic division to perform the division. - 3x4−2x3−10x2+15x−2\frac { 3 x ^ { 4 } - 2 x ^ { 3 } - 10 x ^ { 2 } + 15 } { x - 2 }x−23x4−2x3−10x2+15​

Find the equation that the given graph represents. -

Solve the problem -A 15 cm15 \mathrm {~cm}15 cm by 18 cm18 \mathrm {~cm}18 cm rectangular garden is to have a gravel path of uniform width bordering it. How wide is the path if the total area covered by the garden and path is 418 cm2418 \mathrm {~cm} ^ { 2 }418 cm2 ?

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

Sketch the graph of the parabola. - $y=(x-6)^{2}-5$ $Sketch the graph of the parabola. - y=(x-6)^{2}-5$

Use synthetic division to perform the division. - $\frac { - 6 x ^ { 3 } - 30 x ^ { 2 } - 22 x + 8 } { x + 4 }$

Provide an appropriate response. -Explain the behavior of the graph of f(x) as it approaches its vertical asymptote. $f ( x ) = \frac { - 3 } { x - 4 }$

Find the correct end behavior diagram for the given polynomial function. - $P ( x ) = 7 x ^ { 3 } + 2 x ^ { 2 } - 6 x + 7$

Use synthetic division to decide whether the given number k is a zero of the given polynomial function. - $k = - 2 + 5 i ; f ( x ) = x ^ { 2 } + 4 x + 29$

Find all rational zeros and factor f(x). - $f ( x ) = 6 x ^ { 3 } + 19 x ^ { 2 } + 8 x - 5$

Find all rational zeros and factor f(x). - $f ( x ) = x ^ { 3 } - 5 x ^ { 2 } - 2 x + 24$

Round your answer to two decimal places. -If $\mathrm { f }$ varies jointly as $\mathrm { q } ^ { 2 }$ and $\mathrm { h }$ , and $\mathrm { f } = 96$ when $\mathrm { q } = 4$ and $\mathrm { h } = 3$ , find $\mathrm { q }$ when $\mathrm { f } = 40$ and $\mathrm { h } = 5$

Find the domain and range of the function. - $f ( x ) = ( x + 2 ) ^ { 2 } + 7$

Sketch the graph of the rational function. - $f ( x ) = \frac { x ( x - 4 ) } { ( x - 2 ) ^ { 2 } }$ $Sketch the graph of the rational function. - f ( x ) = \frac { x ( x - 4 ) } { ( x - 2 ) ^ { 2 } }$

Sketch the graph of the rational function. - f(x)= $Sketch the graph of the rational function. - \begin{array} { l } f ( x ) = \frac { ( x + 4 ) ( x + 5 ) } { ( x + 3 ) ^ { 2 } } \\ \end{array}$

Use the remainder theorem and synthetic division to find f(k). - $k = 3 : f ( x ) = - x ^ { 3 } + 2 x ^ { 2 } + 2$

Use synthetic division to perform the division. - $\frac { 3 x ^ { 4 } - 2 x ^ { 3 } - 10 x ^ { 2 } + 15 } { x - 2 }$

Solve the problem -A $15 \mathrm {~cm}$ by $18 \mathrm {~cm}$ rectangular garden is to have a gravel path of uniform width bordering it. How wide is the path if the total area covered by the garden and path is $418 \mathrm {~cm} ^ { 2 }$ ?