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

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

(Multiple Choice)

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Question 101

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

(Multiple Choice)

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Question 102

Graph the inequality. - $4 y^{2}-16 x^{2} \geq 64$ $Graph the inequality. - 4 y^{2}-16 x^{2} \geq 64$

(Multiple Choice)

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Question 103

Which method should be used to solve the system? Explain your answer, including a description of the first step. - $-5 x^{2}-10 y^{2}=1$ $-6 x^{2}+3 y^{2}=49$

(Essay)

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Question 104

Solve the system by the elimination method or a combination of the elimination and substitution methods. - $x^{2}-x y+y^{2}=3$ $2 x^{2}+x y+2 y^{2}=12$

(Multiple Choice)

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Question 105

Which method should be used to solve the system? Explain your answer, including a description of the first step. - $-3 x^{2}-3 y^{2}=49$ $x-5 y=1$

(Essay)

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Question 106

Graph the system of inequalities. - x+2y\leq2 x+y\geq0 $Graph the system of inequalities. - \begin{array}{c}x+2 y \leq 2 \\ x+y \geq 0\end{array}$

(Multiple Choice)

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Question 107

Which system of inequalities matches the given calculator-generated graph? -

(Multiple Choice)

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Question 108

Graph the hyperbola. - $\frac{y^{2}}{36}-\frac{x^{2}}{25}=1$ $Graph the hyperbola. - \frac{y^{2}}{36}-\frac{x^{2}}{25}=1$

(Multiple Choice)

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Question 109

Graph the system of inequalities. - $3x - 2y \leq -6$ $x - 1 < 0$ $Graph the system of inequalities. - 3x - 2y \leq -6 x - 1 < 0$

(Multiple Choice)

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Question 110

Graph the circle. - $x^{2}+(y-3)^{2}=16$ $Graph the circle. - x^{2}+(y-3)^{2}=16$

(Multiple Choice)

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Question 111

Identify the graph of the equation as a parabola, hyperbola, ellipse, or circle. - $5 y^{2}-2 x=2$

(Multiple Choice)

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Question 112

The $y$ -intercepts of the ellipse with equation $\frac{x^{2}}{36}+\frac{y^{2}}{64}=1$ are $(0,6)$ and $(0,-6)$ .

(True/False)

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Question 113

Suppose that a nonlinear system is composed of equations whose graphs are those described, and the number of points of intersection of the two graphs is as given. Make a sketch satisfying these conditions. -A parabola and a hyperbola; four points

(Essay)

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Question 114

Graph the system of inequalities. - y\geq- y\leqx+1 y\geq-5 x\geq-4 $Graph the system of inequalities. - \begin{array}{l}y \geq-x^{2} \\ y \leq x+1 \\ y \geq-5 \\ x \geq-4\end{array}$

(Multiple Choice)

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Question 115

Choose the graph that matches the given function. - $f(x)=\sqrt{x}-2$

(Multiple Choice)

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Question 116

Graph the function. -f(x)=|-1-x|

(Multiple Choice)

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Question 117

Choose the inequality that matches the graph. -

(Multiple Choice)

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Question 118

Graph the nonlinear inequality with restrictions. - $9 x^{2}+16 y^{2} \geq 144, \quad x \geq 0, y \leq 0$ $Graph the nonlinear inequality with restrictions. - 9 x^{2}+16 y^{2} \geq 144, \quad x \geq 0, y \leq 0$

(Multiple Choice)

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Question 119

Choose the inequality that matches the graph. -

(Multiple Choice)

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Question 120

Showing 101 - 120 of 233

Graph the inequality. - $4 y^{2}-16 x^{2} \geq 64$ $Graph the inequality. - 4 y^{2}-16 x^{2} \geq 64$

Which method should be used to solve the system? Explain your answer, including a description of the first step. - $-5 x^{2}-10 y^{2}=1$ $-6 x^{2}+3 y^{2}=49$

Solve the system by the elimination method or a combination of the elimination and substitution methods. - $x^{2}-x y+y^{2}=3$ $2 x^{2}+x y+2 y^{2}=12$

Which method should be used to solve the system? Explain your answer, including a description of the first step. - $-3 x^{2}-3 y^{2}=49$ $x-5 y=1$

Graph the system of inequalities. - x+2y\leq2 x+y\geq0 $Graph the system of inequalities. - \begin{array}{c}x+2 y \leq 2 \\ x+y \geq 0\end{array}$

Which system of inequalities matches the given calculator-generated graph? -

Graph the hyperbola. - $\frac{y^{2}}{36}-\frac{x^{2}}{25}=1$ $Graph the hyperbola. - \frac{y^{2}}{36}-\frac{x^{2}}{25}=1$

Graph the system of inequalities. - $3x - 2y \leq -6$ $x - 1 < 0$ $Graph the system of inequalities. - 3x - 2y \leq -6 x - 1 < 0$

Graph the circle. - $x^{2}+(y-3)^{2}=16$ $Graph the circle. - x^{2}+(y-3)^{2}=16$

Identify the graph of the equation as a parabola, hyperbola, ellipse, or circle. - $5 y^{2}-2 x=2$

The $y$ -intercepts of the ellipse with equation $\frac{x^{2}}{36}+\frac{y^{2}}{64}=1$ are $(0,6)$ and $(0,-6)$ .

Suppose that a nonlinear system is composed of equations whose graphs are those described, and the number of points of intersection of the two graphs is as given. Make a sketch satisfying these conditions. -A parabola and a hyperbola; four points

Graph the system of inequalities. - y\geq- y\leqx+1 y\geq-5 x\geq-4 $Graph the system of inequalities. - \begin{array}{l}y \geq-x^{2} \\ y \leq x+1 \\ y \geq-5 \\ x \geq-4\end{array}$

Choose the graph that matches the given function. - $f(x)=\sqrt{x}-2$

Graph the function. -f(x)=|-1-x|

Choose the inequality that matches the graph. -

Graph the nonlinear inequality with restrictions. - $9 x^{2}+16 y^{2} \geq 144, \quad x \geq 0, y \leq 0$ $Graph the nonlinear inequality with restrictions. - 9 x^{2}+16 y^{2} \geq 144, \quad x \geq 0, y \leq 0$

Choose the inequality that matches the graph. -

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

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? - y225−x2=1\frac{y^{2}}{25}-x^{2}=125y2​−x2=1

Graph the inequality. - 4y2−16x2≥644 y^{2}-16 x^{2} \geq 644y2−16x2≥64

Which method should be used to solve the system? Explain your answer, including a description of the first step. - −5x2−10y2=1-5 x^{2}-10 y^{2}=1−5x2−10y2=1 −6x2+3y2=49-6 x^{2}+3 y^{2}=49−6x2+3y2=49

Solve the system by the elimination method or a combination of the elimination and substitution methods. - x2−xy+y2=3x^{2}-x y+y^{2}=3x2−xy+y2=3 2x2+xy+2y2=122 x^{2}+x y+2 y^{2}=122x2+xy+2y2=12

Which method should be used to solve the system? Explain your answer, including a description of the first step. - −3x2−3y2=49-3 x^{2}-3 y^{2}=49−3x2−3y2=49 x−5y=1x-5 y=1x−5y=1

Graph the system of inequalities. - x+2y\leq2 x+y\geq0

Which system of inequalities matches the given calculator-generated graph? -

Graph the hyperbola. - y236−x225=1\frac{y^{2}}{36}-\frac{x^{2}}{25}=136y2​−25x2​=1

Graph the system of inequalities. - 3x−2y≤−63x - 2y \leq -63x−2y≤−6 x−1<0x - 1 < 0x−1<0

Graph the circle. - x2+(y−3)2=16x^{2}+(y-3)^{2}=16x2+(y−3)2=16

Identify the graph of the equation as a parabola, hyperbola, ellipse, or circle. - 5y2−2x=25 y^{2}-2 x=25y2−2x=2

The yyy -intercepts of the ellipse with equation x236+y264=1\frac{x^{2}}{36}+\frac{y^{2}}{64}=136x2​+64y2​=1 are (0,6)(0,6)(0,6) and (0,−6)(0,-6)(0,−6) .

Suppose that a nonlinear system is composed of equations whose graphs are those described, and the number of points of intersection of the two graphs is as given. Make a sketch satisfying these conditions. -A parabola and a hyperbola; four points

Graph the system of inequalities. - y\geq- y\leqx+1 y\geq-5 x\geq-4

Choose the graph that matches the given function. - f(x)=x−2f(x)=\sqrt{x}-2f(x)=x​−2

Graph the function. -f(x)=|-1-x|

Choose the inequality that matches the graph. -

Graph the nonlinear inequality with restrictions. - 9x2+16y2≥144,x≥0,y≤09 x^{2}+16 y^{2} \geq 144, \quad x \geq 0, y \leq 09x2+16y2≥144,x≥0,y≤0

Choose the inequality that matches the graph. -

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

Graph the inequality. - $4 y^{2}-16 x^{2} \geq 64$ $Graph the inequality. - 4 y^{2}-16 x^{2} \geq 64$

Which method should be used to solve the system? Explain your answer, including a description of the first step. - $-5 x^{2}-10 y^{2}=1$ $-6 x^{2}+3 y^{2}=49$

Solve the system by the elimination method or a combination of the elimination and substitution methods. - $x^{2}-x y+y^{2}=3$ $2 x^{2}+x y+2 y^{2}=12$

Which method should be used to solve the system? Explain your answer, including a description of the first step. - $-3 x^{2}-3 y^{2}=49$ $x-5 y=1$

Graph the system of inequalities. - x+2y\leq2 x+y\geq0 $Graph the system of inequalities. - \begin{array}{c}x+2 y \leq 2 \\ x+y \geq 0\end{array}$

Graph the hyperbola. - $\frac{y^{2}}{36}-\frac{x^{2}}{25}=1$ $Graph the hyperbola. - \frac{y^{2}}{36}-\frac{x^{2}}{25}=1$

Graph the system of inequalities. - $3x - 2y \leq -6$ $x - 1 < 0$ $Graph the system of inequalities. - 3x - 2y \leq -6 x - 1 < 0$

Graph the circle. - $x^{2}+(y-3)^{2}=16$ $Graph the circle. - x^{2}+(y-3)^{2}=16$

Identify the graph of the equation as a parabola, hyperbola, ellipse, or circle. - $5 y^{2}-2 x=2$

The $y$ -intercepts of the ellipse with equation $\frac{x^{2}}{36}+\frac{y^{2}}{64}=1$ are $(0,6)$ and $(0,-6)$ .

Graph the system of inequalities. - y\geq- y\leqx+1 y\geq-5 x\geq-4 $Graph the system of inequalities. - \begin{array}{l}y \geq-x^{2} \\ y \leq x+1 \\ y \geq-5 \\ x \geq-4\end{array}$

Choose the graph that matches the given function. - $f(x)=\sqrt{x}-2$

Graph the nonlinear inequality with restrictions. - $9 x^{2}+16 y^{2} \geq 144, \quad x \geq 0, y \leq 0$ $Graph the nonlinear inequality with restrictions. - 9 x^{2}+16 y^{2} \geq 144, \quad x \geq 0, y \leq 0$