Exam 11: Nonlinear Functions, Conic Sections, and Nonlinear Systems

Solve the system by the elimination method or a combination of the elimination and substitution methods. - $4 x^{2}-2 y^{2}=-2$ $2 x^{2}+2 y^{2}=26$

(Multiple Choice)

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Question 21

The $x$ -intercepts of the ellipse with equation $\frac{x^{2}}{4}+\frac{y^{2}}{36}=1$ are $(2,0)$ and $(-2,0)$ .

(True/False)

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Question 22

Graph the ellipse. - $\frac{(x+5)^{2}}{9}+\frac{(y-1)^{2}}{4}=1$ $Graph the ellipse. - \frac{(x+5)^{2}}{9}+\frac{(y-1)^{2}}{4}=1$

(Multiple Choice)

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Question 23

Which method should be used to solve the system? Explain your answer, including a description of the first step. - -2- =9 3+4 =4

(Essay)

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Question 24

The circle or ellipse shown in the calculator-generated graph was created using function mode with a square viewing window. What are the two functions $y_{1}$ and $y_{2}$ that were used to obtain the graph whose equation is given? - $\frac{x^{2}}{16}+\frac{y^{2}}{25}=1$ $The circle or ellipse shown in the calculator-generated graph was created using function mode with a square viewing window. What are the two functions y_{1} and y_{2} that were used to obtain the graph whose equation is given? - \frac{x^{2}}{16}+\frac{y^{2}}{25}=1$

(Multiple Choice)

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Question 25

Solve the problem. -A satellite is to be put into an elliptical orbit around a moon. The moon is a sphere with radius 589 $\mathrm{km}$ . Determine an equation for the ellipse, where $\mathrm{x}$ and $\mathrm{y}$ are measured in $\mathrm{km}$ , if the distance of the satellite from the surface of the moon varies from $864 \mathrm{~km}$ to $174 \mathrm{~km}$ . $Solve the problem. -A satellite is to be put into an elliptical orbit around a moon. The moon is a sphere with radius 589 \mathrm{km} . Determine an equation for the ellipse, where \mathrm{x} and \mathrm{y} are measured in \mathrm{km} , if the distance of the satellite from the surface of the moon varies from 864 \mathrm{~km} to 174 \mathrm{~km} .$

(Multiple Choice)

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Question 26

Find the equation of a circle satisfying the given conditions. -Center: $(10,0)$ ; radius: $\sqrt{13}$

(Multiple Choice)

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Question 27

The hyperbola shown in the calculator-generated graph was graphed in function mode with a square viewing window. What are the two functions $y_{1}$ and $y_{2}$ that were used to obtain the graph whose equation is given? - $\frac{x^{2}}{16}-y^{2}=1$ $The hyperbola shown in the calculator-generated graph was graphed in function mode with a square viewing window. What are the two functions y_{1} and y_{2} that were used to obtain the graph whose equation is given? - \frac{x^{2}}{16}-y^{2}=1$

(Multiple Choice)

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Question 28

Choose the equation that matches the graph. -

(Multiple Choice)

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Question 29

Graph the step function. -Assume it costs 25 cents to mail a letter weighing one ounce or less, and then 20 cents for each additional ounce or fraction of an ounce. Let $\mathrm{L}(\mathrm{x})$ be the cost of mailing a letter weighing $\mathrm{x}$ ounces. Graph $y=L(x)$ . Use the interval $(0,4]$ .

(Multiple Choice)

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Question 30

Graph the function. Give the domain and range. - $f(x)=|x-4|$

(Multiple Choice)

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Question 31

Graph the rational function. -f(x) = $\frac{1}{ x }$ + 3 $Graph the rational function. -f(x) = \frac{1}{ x } + 3$

(Multiple Choice)

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Question 32

The circle or ellipse shown in the calculator-generated graph was created using function mode with a square viewing window. What are the two functions $y_{1}$ and $y_{2}$ that were used to obtain the graph whose equation is given? - $(x-5)^{2}+y^{2}=25$ $The circle or ellipse shown in the calculator-generated graph was created using function mode with a square viewing window. What are the two functions y_{1} and y_{2} that were used to obtain the graph whose equation is given? - (x-5)^{2}+y^{2}=25$

(Multiple Choice)

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Question 33

Graph the circle. - $(x-6)^{2}+(y-2)^{2}=16$ $Graph the circle. - (x-6)^{2}+(y-2)^{2}=16$

(Multiple Choice)

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Question 34

Graph the system of inequalities. - x\leq0 y\leq0 +\geq9 y+x\geq-5 $Graph the system of inequalities. - \begin{array}{l}x \leq 0 \\ y \leq 0 \\ x^{2}+y^{2} \geq 9 \\ y+x \geq-5\end{array}$

(Multiple Choice)

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Question 35

Describe the graph of the solution set of the following inequality: $\mathrm{y}<\mathrm{x}^{2}-1$

(Essay)

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Question 36

Solve the system by the substitution method. - $x^{2}+y^{2}=16$ $y=x^{2}-4$

(Multiple Choice)

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Question 37

The hyperbola shown in the calculator-generated graph was graphed in function mode with a square viewing window. What are the two functions $y_{1}$ and $y_{2}$ that were used to obtain the graph whose equation is given? - $\frac{y^{2}}{49}-\frac{x^{2}}{9}=1$ $The hyperbola shown in the calculator-generated graph was graphed in function mode with a square viewing window. What are the two functions y_{1} and y_{2} that were used to obtain the graph whose equation is given? - \frac{y^{2}}{49}-\frac{x^{2}}{9}=1$

(Multiple Choice)

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Question 38

Solve the problem. Round your answer to the nearest tenth. -The roof of a building is in the shape of the top half of the hyperbola $y^{2}-x^{2}=21$ , where $x$ and $y$ are in meters. Refer to the figure and determine the distance, $\mathrm{w}$ , between the two outside walls. $Solve the problem. Round your answer to the nearest tenth. -The roof of a building is in the shape of the top half of the hyperbola y^{2}-x^{2}=21 , where x and y are in meters. Refer to the figure and determine the distance, \mathrm{w} , between the two outside walls.$

(Multiple Choice)

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Question 39

What is the only real number not in the domain of $f(x)=\frac{1}{x-3}$ ?

(Multiple Choice)

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Question 40

Showing 21 - 40 of 233

Solve the system by the elimination method or a combination of the elimination and substitution methods. - $4 x^{2}-2 y^{2}=-2$ $2 x^{2}+2 y^{2}=26$

The $x$ -intercepts of the ellipse with equation $\frac{x^{2}}{4}+\frac{y^{2}}{36}=1$ are $(2,0)$ and $(-2,0)$ .

Graph the ellipse. - $\frac{(x+5)^{2}}{9}+\frac{(y-1)^{2}}{4}=1$ $Graph the ellipse. - \frac{(x+5)^{2}}{9}+\frac{(y-1)^{2}}{4}=1$

Which method should be used to solve the system? Explain your answer, including a description of the first step. - -2- =9 3+4 =4

Find the equation of a circle satisfying the given conditions. -Center: $(10,0)$ ; radius: $\sqrt{13}$

Choose the equation that matches the graph. -

Graph the step function. -Assume it costs 25 cents to mail a letter weighing one ounce or less, and then 20 cents for each additional ounce or fraction of an ounce. Let $\mathrm{L}(\mathrm{x})$ be the cost of mailing a letter weighing $\mathrm{x}$ ounces. Graph $y=L(x)$ . Use the interval $(0,4]$ .

Graph the function. Give the domain and range. - $f(x)=|x-4|$

Graph the rational function. -f(x) = $\frac{1}{ x }$ + 3 $Graph the rational function. -f(x) = \frac{1}{ x } + 3$

Graph the circle. - $(x-6)^{2}+(y-2)^{2}=16$ $Graph the circle. - (x-6)^{2}+(y-2)^{2}=16$

Graph the system of inequalities. - x\leq0 y\leq0 +\geq9 y+x\geq-5 $Graph the system of inequalities. - \begin{array}{l}x \leq 0 \\ y \leq 0 \\ x^{2}+y^{2} \geq 9 \\ y+x \geq-5\end{array}$

Describe the graph of the solution set of the following inequality: $\mathrm{y}<\mathrm{x}^{2}-1$

Solve the system by the substitution method. - $x^{2}+y^{2}=16$ $y=x^{2}-4$

What is the only real number not in the domain of $f(x)=\frac{1}{x-3}$ ?

Review of the Real Number System

Linear Equations, Inequalities, and Applications

Linear Equations, Graphs, and Functions

Systems of Linear Equations

Exponents, Polynomials, and Polynomial Functions

Factoring

Rational Expressions and Functions

Roots, Radicals, and Root Functions

Quadratic Equations, Inequalities, and Functions

Inverse, Exponential, and Logarithmic Functions

Further Topics in Algebra

Appendices

Filters

Exam 11: Nonlinear Functions, Conic Sections, and Nonlinear Systems

Solve the system by the elimination method or a combination of the elimination and substitution methods. - 4x2−2y2=−24 x^{2}-2 y^{2}=-24x2−2y2=−2 2x2+2y2=262 x^{2}+2 y^{2}=262x2+2y2=26

The xxx -intercepts of the ellipse with equation x24+y236=1\frac{x^{2}}{4}+\frac{y^{2}}{36}=14x2​+36y2​=1 are (2,0)(2,0)(2,0) and (−2,0)(-2,0)(−2,0) .

Graph the ellipse. - (x+5)29+(y−1)24=1\frac{(x+5)^{2}}{9}+\frac{(y-1)^{2}}{4}=19(x+5)2​+4(y−1)2​=1

Which method should be used to solve the system? Explain your answer, including a description of the first step. - -2- =9 3+4 =4

Find the equation of a circle satisfying the given conditions. -Center: (10,0)(10,0)(10,0) ; radius: 13\sqrt{13}13​

The hyperbola shown in the calculator-generated graph was graphed in function mode with a square viewing window. What are the two functions y1y_{1}y1​ and y2y_{2}y2​ that were used to obtain the graph whose equation is given? - x216−y2=1\frac{x^{2}}{16}-y^{2}=116x2​−y2=1

Choose the equation that matches the graph. -

Graph the function. Give the domain and range. - f(x)=∣x−4∣f(x)=|x-4|f(x)=∣x−4∣

Graph the rational function. -f(x) = 1x\frac{1}{ x }x1​ + 3

The circle or ellipse shown in the calculator-generated graph was created using function mode with a square viewing window. What are the two functions y1y_{1}y1​ and y2y_{2}y2​ that were used to obtain the graph whose equation is given? - (x−5)2+y2=25(x-5)^{2}+y^{2}=25(x−5)2+y2=25

Graph the circle. - (x−6)2+(y−2)2=16(x-6)^{2}+(y-2)^{2}=16(x−6)2+(y−2)2=16

Graph the system of inequalities. - x\leq0 y\leq0 +\geq9 y+x\geq-5

Describe the graph of the solution set of the following inequality: y<x2−1\mathrm{y}<\mathrm{x}^{2}-1y<x2−1

Solve the system by the substitution method. - x2+y2=16x^{2}+y^{2}=16x2+y2=16 y=x2−4y=x^{2}-4y=x2−4

The hyperbola shown in the calculator-generated graph was graphed in function mode with a square viewing window. What are the two functions y1y_{1}y1​ and y2y_{2}y2​ that were used to obtain the graph whose equation is given? - y249−x29=1\frac{y^{2}}{49}-\frac{x^{2}}{9}=149y2​−9x2​=1

Solve the problem. Round your answer to the nearest tenth. -The roof of a building is in the shape of the top half of the hyperbola y2−x2=21y^{2}-x^{2}=21y2−x2=21 , where xxx and yyy are in meters. Refer to the figure and determine the distance, w\mathrm{w}w , between the two outside walls.

What is the only real number not in the domain of f(x)=1x−3f(x)=\frac{1}{x-3}f(x)=x−31​ ?

Review of the Real Number System

Linear Equations, Inequalities, and Applications

Linear Equations, Graphs, and Functions

Systems of Linear Equations

Exponents, Polynomials, and Polynomial Functions

Factoring

Rational Expressions and Functions

Roots, Radicals, and Root Functions

Quadratic Equations, Inequalities, and Functions

Inverse, Exponential, and Logarithmic Functions

Further Topics in Algebra

Appendices

Filters

Solve the system by the elimination method or a combination of the elimination and substitution methods. - $4 x^{2}-2 y^{2}=-2$ $2 x^{2}+2 y^{2}=26$

The $x$ -intercepts of the ellipse with equation $\frac{x^{2}}{4}+\frac{y^{2}}{36}=1$ are $(2,0)$ and $(-2,0)$ .

Graph the ellipse. - $\frac{(x+5)^{2}}{9}+\frac{(y-1)^{2}}{4}=1$ $Graph the ellipse. - \frac{(x+5)^{2}}{9}+\frac{(y-1)^{2}}{4}=1$

Find the equation of a circle satisfying the given conditions. -Center: $(10,0)$ ; radius: $\sqrt{13}$

Graph the function. Give the domain and range. - $f(x)=|x-4|$

Graph the rational function. -f(x) = $\frac{1}{ x }$ + 3 $Graph the rational function. -f(x) = \frac{1}{ x } + 3$

Graph the circle. - $(x-6)^{2}+(y-2)^{2}=16$ $Graph the circle. - (x-6)^{2}+(y-2)^{2}=16$

Graph the system of inequalities. - x\leq0 y\leq0 +\geq9 y+x\geq-5 $Graph the system of inequalities. - \begin{array}{l}x \leq 0 \\ y \leq 0 \\ x^{2}+y^{2} \geq 9 \\ y+x \geq-5\end{array}$

Describe the graph of the solution set of the following inequality: $\mathrm{y}<\mathrm{x}^{2}-1$

Solve the system by the substitution method. - $x^{2}+y^{2}=16$ $y=x^{2}-4$

What is the only real number not in the domain of $f(x)=\frac{1}{x-3}$ ?