Suppose that the height of an object shot straight up is given by h =544t - 16t 2 . (Here h is in feet and t is in seconds.) Find the maximum height.

A) 4,724 ft B) 4,624 ft C) 1,156 ft D) 4,290 ft E) 5,189 ft A) 4,724 ft B) 4,624 ft C) 1,156 ft D) 4,290 ft E) 5,189 ft

Exam 4: Polynomial and Rational Functions Applications to Optimization

Plot the following points: (6, 2), (7, 5), (8, 8), (9, 9). In your scatter diagram, sketch a line that best seems to fit the data. Estimate the slope and the y-intercept of the line.

Free

(Multiple Choice)

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Question 1

Correct Answer:

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Sketch the graph of the function and specify all x- and y-intercepts. y =(x - 2)² + 4

Free

(Multiple Choice)

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Question 2

Correct Answer:

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Sketch the graph of the function and specify all x- and y-intercepts. y = (x - 2)(x - 1)(x + 1)

Free

(Multiple Choice)

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Question 3

Correct Answer:

Verified

Find the linear function satisfying the given conditions. $g ( 0 ) = 0$ and $g ( 2 ) = \sqrt { 3 }$

(Multiple Choice)

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Question 4

Sketch the graph of the rational function. Specify the intercepts and the asymptotes. $y = \frac { 1 } { ( x + 1 ) ^ { 2 } }$

(Multiple Choice)

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Question 5

Sketch the graph of the function and specify all x- and y-intercepts. y = - 3x⁴ + 5

(Multiple Choice)

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Question 6

A piece of wire $7 \pi y$ inches long is bent into a circle. Express the area of the circle as a function of y.

(Multiple Choice)

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Question 7

Among all rectangles having a perimeter of 24m, find the dimensions of the one with the largest area.

(Multiple Choice)

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Question 8

Suppose that the height of an object shot straight up is given by h =544t - 16t² . (Here h is in feet and t is in seconds.) Find the maximum height.

(Multiple Choice)

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(79)

Question 9

Find all fixed points of the function. $f ( x ) = - 3 x + 4$

(Multiple Choice)

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Question 10

Sketch the graph of the function and specify all x- and y-intercepts.y = x³ - 9x

(Multiple Choice)

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Question 11

Find all fixed points of the function. $f ( x ) = 13 + \sqrt { x - 1 }$

(Multiple Choice)

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(84)

Question 12

A factory owner buys a new machine for $25,000. After eight years, the machine has a salvage value of $1,000. Find a formula for the value of the machine after t years, where $0 \leq t \leq 8$

(Multiple Choice)

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Question 13

Determine the input that produces the largest or smallest output (whichever is appropriate). State whether the output is largest or smallest. s = - 24t² + 147t + 15

(Multiple Choice)

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Question 14

Sketch the graph of the function and specify all x- and y-intercepts. y = x³ (x + 1)

(Multiple Choice)

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Question 15

Find all fixed points of the function. $h ( x ) = x ^ { 2 } - 7 x - 9$

(Multiple Choice)

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Question 16

Suppose that the revenue generated by selling x units of a certain commodity is given by $R = - \frac { 1 } { 5 } x ^ { 2 } + 600 x$ . Assume that R is in dollars. What is the maximum revenue possible in this situation?

(Multiple Choice)

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Question 17

A triangle is inscribed in a semicircle of diameter 6R. Show that the smallest possible value for the area of the shaded region is $\frac { 9 ( \pi - 2 ) R ^ { 2 } } { 2 }$ . $A triangle is inscribed in a semicircle of diameter 6R. Show that the smallest possible value for the area of the shaded region is \frac { 9 ( \pi - 2 ) R ^ { 2 } } { 2 } . Hint: The area of the shaded region is a minimum when the area of the triangle is a maximum. Find the value of x that maximizes the square of the area of the triangle. This will be the same x that maximizes the area of the triangle.$ Hint: The area of the shaded region is a minimum when the area of the triangle is a maximum. Find the value of x that maximizes the square of the area of the triangle. This will be the same x that maximizes the area of the triangle.

(Multiple Choice)

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Question 18

Sketch the graph of the rational function. Specify the intercepts and the asymptotes. $y = \frac { x - 3 } { x + 3 }$

(Multiple Choice)

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Question 19

Sketch the graph of the function and specify all x- and y-intercepts. y =- ( x - 3)³ - 1

(Multiple Choice)

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Question 20

Showing 1 - 20 of 25

Plot the following points: (6, 2), (7, 5), (8, 8), (9, 9). In your scatter diagram, sketch a line that best seems to fit the data. Estimate the slope and the y-intercept of the line.

Sketch the graph of the function and specify all x- and y-intercepts. y =(x - 2)² + 4

Sketch the graph of the function and specify all x- and y-intercepts. y = (x - 2)(x - 1)(x + 1)

Find the linear function satisfying the given conditions. $g ( 0 ) = 0$ and $g ( 2 ) = \sqrt { 3 }$

Sketch the graph of the rational function. Specify the intercepts and the asymptotes. $y = \frac { 1 } { ( x + 1 ) ^ { 2 } }$

Sketch the graph of the function and specify all x- and y-intercepts. y = - 3x⁴ + 5

A piece of wire $7 \pi y$ inches long is bent into a circle. Express the area of the circle as a function of y.

Among all rectangles having a perimeter of 24m, find the dimensions of the one with the largest area.

Suppose that the height of an object shot straight up is given by h =544t - 16t² . (Here h is in feet and t is in seconds.) Find the maximum height.

Find all fixed points of the function. $f ( x ) = - 3 x + 4$

Sketch the graph of the function and specify all x- and y-intercepts.y = x³ - 9x

Find all fixed points of the function. $f ( x ) = 13 + \sqrt { x - 1 }$

A factory owner buys a new machine for $25,000. After eight years, the machine has a salvage value of $1,000. Find a formula for the value of the machine after t years, where $0 \leq t \leq 8$

Determine the input that produces the largest or smallest output (whichever is appropriate). State whether the output is largest or smallest. s = - 24t² + 147t + 15

Sketch the graph of the function and specify all x- and y-intercepts. y = x³ (x + 1)

Find all fixed points of the function. $h ( x ) = x ^ { 2 } - 7 x - 9$

Suppose that the revenue generated by selling x units of a certain commodity is given by $R = - \frac { 1 } { 5 } x ^ { 2 } + 600 x$ . Assume that R is in dollars. What is the maximum revenue possible in this situation?

Sketch the graph of the rational function. Specify the intercepts and the asymptotes. $y = \frac { x - 3 } { x + 3 }$

Sketch the graph of the function and specify all x- and y-intercepts. y =- ( x - 3)³ - 1

Fundamentals

Equations and Inequalities

Functions

Exponential and Logarithmic Functions

An Introduction to Trigonometry Via Right Triangles

The Trigonometric Functions

Graphs of the Trigonometric Functions

Analytical Trigonometry

Additional Topics in Trigonometry

Systems of Equations

The Conic Sections

Roots of Polynomial Equations

Additional Topics in Algebra

Filters

Exam 4: Polynomial and Rational Functions Applications to Optimization

Plot the following points: (6, 2), (7, 5), (8, 8), (9, 9). In your scatter diagram, sketch a line that best seems to fit the data. Estimate the slope and the y-intercept of the line.

Sketch the graph of the function and specify all x- and y-intercepts. y =(x - 2) 2 + 4

Sketch the graph of the function and specify all x- and y-intercepts. y = (x - 2)(x - 1)(x + 1)

Find the linear function satisfying the given conditions. g(0)=0g ( 0 ) = 0g(0)=0 and g(2)=3g ( 2 ) = \sqrt { 3 }g(2)=3​

Sketch the graph of the rational function. Specify the intercepts and the asymptotes. y=1(x+1)2y = \frac { 1 } { ( x + 1 ) ^ { 2 } }y=(x+1)21​

Sketch the graph of the function and specify all x- and y-intercepts. y = - 3x 4 + 5

A piece of wire 7πy7 \pi y7πy inches long is bent into a circle. Express the area of the circle as a function of y.

Among all rectangles having a perimeter of 24m, find the dimensions of the one with the largest area.

Suppose that the height of an object shot straight up is given by h =544t - 16t 2 . (Here h is in feet and t is in seconds.) Find the maximum height.

Find all fixed points of the function. f(x)=−3x+4f ( x ) = - 3 x + 4f(x)=−3x+4

Sketch the graph of the function and specify all x- and y-intercepts.y = x 3 - 9x

Find all fixed points of the function. f(x)=13+x−1f ( x ) = 13 + \sqrt { x - 1 }f(x)=13+x−1​

A factory owner buys a new machine for $25,000. After eight years, the machine has a salvage value of $1,000. Find a formula for the value of the machine after t years, where 0≤t≤80 \leq t \leq 80≤t≤8

Determine the input that produces the largest or smallest output (whichever is appropriate). State whether the output is largest or smallest. s = - 24t 2 + 147t + 15

Sketch the graph of the function and specify all x- and y-intercepts. y = x 3 (x + 1)

Find all fixed points of the function. h(x)=x2−7x−9h ( x ) = x ^ { 2 } - 7 x - 9h(x)=x2−7x−9

Suppose that the revenue generated by selling x units of a certain commodity is given by R=−15x2+600xR = - \frac { 1 } { 5 } x ^ { 2 } + 600 xR=−51​x2+600x . Assume that R is in dollars. What is the maximum revenue possible in this situation?

Sketch the graph of the rational function. Specify the intercepts and the asymptotes. y=x−3x+3y = \frac { x - 3 } { x + 3 }y=x+3x−3​

Sketch the graph of the function and specify all x- and y-intercepts. y =- ( x - 3) 3 - 1

Fundamentals

Equations and Inequalities

Functions

Exponential and Logarithmic Functions

An Introduction to Trigonometry Via Right Triangles

The Trigonometric Functions

Graphs of the Trigonometric Functions

Analytical Trigonometry

Additional Topics in Trigonometry

Systems of Equations

The Conic Sections

Roots of Polynomial Equations

Additional Topics in Algebra

Filters

Sketch the graph of the function and specify all x- and y-intercepts. y =(x - 2)² + 4

Find the linear function satisfying the given conditions. $g ( 0 ) = 0$ and $g ( 2 ) = \sqrt { 3 }$

Sketch the graph of the rational function. Specify the intercepts and the asymptotes. $y = \frac { 1 } { ( x + 1 ) ^ { 2 } }$

Sketch the graph of the function and specify all x- and y-intercepts. y = - 3x⁴ + 5

A piece of wire $7 \pi y$ inches long is bent into a circle. Express the area of the circle as a function of y.

Suppose that the height of an object shot straight up is given by h =544t - 16t² . (Here h is in feet and t is in seconds.) Find the maximum height.

Find all fixed points of the function. $f ( x ) = - 3 x + 4$

Sketch the graph of the function and specify all x- and y-intercepts.y = x³ - 9x

Find all fixed points of the function. $f ( x ) = 13 + \sqrt { x - 1 }$

A factory owner buys a new machine for $25,000. After eight years, the machine has a salvage value of $1,000. Find a formula for the value of the machine after t years, where $0 \leq t \leq 8$

Determine the input that produces the largest or smallest output (whichever is appropriate). State whether the output is largest or smallest. s = - 24t² + 147t + 15

Sketch the graph of the function and specify all x- and y-intercepts. y = x³ (x + 1)

Find all fixed points of the function. $h ( x ) = x ^ { 2 } - 7 x - 9$

Suppose that the revenue generated by selling x units of a certain commodity is given by $R = - \frac { 1 } { 5 } x ^ { 2 } + 600 x$ . Assume that R is in dollars. What is the maximum revenue possible in this situation?

Sketch the graph of the rational function. Specify the intercepts and the asymptotes. $y = \frac { x - 3 } { x + 3 }$

Sketch the graph of the function and specify all x- and y-intercepts. y =- ( x - 3)³ - 1