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

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 circle and an ellipse; two points

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Question 201

Graph the function. Give the domain and range. - $f(x)=|x+3|$

(Multiple Choice)

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Question 202

Find the equation of a circle satisfying the given conditions. -Center: $(1,0)$ ; radius: 2

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Question 203

Evaluate the expression. - $\llbracket \frac{1}{7} \rrbracket$

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Question 204

Choose the equation that matches the graph. -

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Question 205

What is the domain of the greatest integer function, given by $f(x)=[[x]]$ ?

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Question 206

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

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Question 207

Graph the function. Give the domain and range. - $f(x)=|x-3|+1$

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Question 208

For the reciprocal function defined by $f(x)=\frac{1}{x^{\prime}}$ _______is the only real number not in the domain.

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Question 209

Identify the graph of the equation as a parabola, circle, ellipse, or hyperbola. - $5 x^{2}=16-5 y^{2}$

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Question 210

Graph the inequality. - $x^{2}+4 y^{2} \leq 16$ $Graph the inequality. - x^{2}+4 y^{2} \leq 16$

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Question 211

Solve the problem. -An elliptical riding path is to be built on a rectangular piece of property that measures $6 \mathrm{mi}$ by $4 \mathrm{mi}$ . Find an equation for the ellipse, where $\mathrm{x}$ and $\mathrm{y}$ are measured in $\mathrm{mi}$ , if the path is to touch the center of the property line on all 4 sides. $Solve the problem. -An elliptical riding path is to be built on a rectangular piece of property that measures 6 \mathrm{mi} by 4 \mathrm{mi} . Find an equation for the ellipse, where \mathrm{x} and \mathrm{y} are measured in \mathrm{mi} , if the path is to touch the center of the property line on all 4 sides.$

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Question 212

The graphing calculator screen shows the graphs of the two given functions, and the display gives the coordinates of one of the solutions. Find the other solution. - $The graphing calculator screen shows the graphs of the two given functions, and the display gives the coordinates of one of the solutions. Find the other solution. - y=-x^{2}+4 \mathrm{x}+\mathrm{y}=4$ $y=-x^{2}+4$ $\mathrm{x}+\mathrm{y}=4$

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Question 213

Graph the system of inequalities. - $\frac{x^{2}}{9}+\frac{y^{2}}{25} \leq 1$ $\frac{x^{2}}{25}+\frac{y^{2}}{9} \leq 1$ $Graph the system of inequalities. - \frac{x^{2}}{9}+\frac{y^{2}}{25} \leq 1 \frac{x^{2}}{25}+\frac{y^{2}}{9} \leq 1$

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Question 214

Solve the system by the elimination method or a combination of the elimination and substitution methods. - $5 x^{2}+3 x y-5 y^{2}=-9$ $x^{2}-x y-y^{2}=-5$

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Question 215

Solve the nonlinear system. - $x y=1$ $-8 x-y=9$

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Question 216

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

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Question 217

Graph the system of inequalities. - -\geq1 +\leq36 $Graph the system of inequalities. - \begin{array}{l}\frac{x^{2}}{9}-\frac{y^{2}}{16} \geq 1 \\ x^{2}+y^{2} \leq 36\end{array}$

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Question 218

Describe the graph of the solution set of the following inequality: $x< y^{2}+7$

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Question 219

Graph the function defined by a radical expression. - $y=4 \sqrt{\frac{16-x^{2}}{16}}$ $Graph the function defined by a radical expression. - y=4 \sqrt{\frac{16-x^{2}}{16}}$

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Question 220

Showing 201 - 220 of 233

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 circle and an ellipse; two points

Graph the function. Give the domain and range. - $f(x)=|x+3|$

Find the equation of a circle satisfying the given conditions. -Center: $(1,0)$ ; radius: 2

Evaluate the expression. - $\llbracket \frac{1}{7} \rrbracket$

Choose the equation that matches the graph. -

What is the domain of the greatest integer function, given by $f(x)=[[x]]$ ?

Graph the function. Give the domain and range. - $f(x)=|x-3|+1$

For the reciprocal function defined by $f(x)=\frac{1}{x^{\prime}}$ _______is the only real number not in the domain.

Identify the graph of the equation as a parabola, circle, ellipse, or hyperbola. - $5 x^{2}=16-5 y^{2}$

Graph the inequality. - $x^{2}+4 y^{2} \leq 16$ $Graph the inequality. - x^{2}+4 y^{2} \leq 16$

Graph the system of inequalities. - $\frac{x^{2}}{9}+\frac{y^{2}}{25} \leq 1$ $\frac{x^{2}}{25}+\frac{y^{2}}{9} \leq 1$ $Graph the system of inequalities. - \frac{x^{2}}{9}+\frac{y^{2}}{25} \leq 1 \frac{x^{2}}{25}+\frac{y^{2}}{9} \leq 1$

Solve the system by the elimination method or a combination of the elimination and substitution methods. - $5 x^{2}+3 x y-5 y^{2}=-9$ $x^{2}-x y-y^{2}=-5$

Solve the nonlinear system. - $x y=1$ $-8 x-y=9$

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

Graph the system of inequalities. - -\geq1 +\leq36 $Graph the system of inequalities. - \begin{array}{l}\frac{x^{2}}{9}-\frac{y^{2}}{16} \geq 1 \\ x^{2}+y^{2} \leq 36\end{array}$

Describe the graph of the solution set of the following inequality: $x< y^{2}+7$

Graph the function defined by a radical expression. - $y=4 \sqrt{\frac{16-x^{2}}{16}}$ $Graph the function defined by a radical expression. - y=4 \sqrt{\frac{16-x^{2}}{16}}$

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

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 circle and an ellipse; two points

Graph the function. Give the domain and range. - f(x)=∣x+3∣f(x)=|x+3|f(x)=∣x+3∣

Find the equation of a circle satisfying the given conditions. -Center: (1,0)(1,0)(1,0) ; radius: 2

Evaluate the expression. - ⟦17⟧\llbracket \frac{1}{7} \rrbracket[[71​]]

Choose the equation that matches the graph. -

What is the domain of the greatest integer function, given by f(x)=[[x]]f(x)=[[x]]f(x)=[[x]] ?

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? - x2+y2=25x^{2}+y^{2}=25x2+y2=25

Graph the function. Give the domain and range. - f(x)=∣x−3∣+1f(x)=|x-3|+1f(x)=∣x−3∣+1

For the reciprocal function defined by f(x)=1x′f(x)=\frac{1}{x^{\prime}}f(x)=x′1​ _______is the only real number not in the domain.

Identify the graph of the equation as a parabola, circle, ellipse, or hyperbola. - 5x2=16−5y25 x^{2}=16-5 y^{2}5x2=16−5y2

Graph the inequality. - x2+4y2≤16x^{2}+4 y^{2} \leq 16x2+4y2≤16

The graphing calculator screen shows the graphs of the two given functions, and the display gives the coordinates of one of the solutions. Find the other solution. - y=−x2+4y=-x^{2}+4y=−x2+4 x+y=4\mathrm{x}+\mathrm{y}=4x+y=4

Graph the system of inequalities. - x29+y225≤1\frac{x^{2}}{9}+\frac{y^{2}}{25} \leq 19x2​+25y2​≤1 x225+y29≤1\frac{x^{2}}{25}+\frac{y^{2}}{9} \leq 125x2​+9y2​≤1

Solve the system by the elimination method or a combination of the elimination and substitution methods. - 5x2+3xy−5y2=−95 x^{2}+3 x y-5 y^{2}=-95x2+3xy−5y2=−9 x2−xy−y2=−5x^{2}-x y-y^{2}=-5x2−xy−y2=−5

Solve the nonlinear system. - xy=1x y=1xy=1 −8x−y=9-8 x-y=9−8x−y=9

Graph the rational function. -f(x) = 1x−3\frac{1}{ x - 3}x−31​

Graph the system of inequalities. - -\geq1 +\leq36

Describe the graph of the solution set of the following inequality: x<y2+7x< y^{2}+7x<y2+7

Graph the function defined by a radical expression. - y=416−x216y=4 \sqrt{\frac{16-x^{2}}{16}}y=41616−x2​​

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 function. Give the domain and range. - $f(x)=|x+3|$

Find the equation of a circle satisfying the given conditions. -Center: $(1,0)$ ; radius: 2

Evaluate the expression. - $\llbracket \frac{1}{7} \rrbracket$

What is the domain of the greatest integer function, given by $f(x)=[[x]]$ ?

Graph the function. Give the domain and range. - $f(x)=|x-3|+1$

For the reciprocal function defined by $f(x)=\frac{1}{x^{\prime}}$ _______is the only real number not in the domain.

Identify the graph of the equation as a parabola, circle, ellipse, or hyperbola. - $5 x^{2}=16-5 y^{2}$

Graph the inequality. - $x^{2}+4 y^{2} \leq 16$ $Graph the inequality. - x^{2}+4 y^{2} \leq 16$

Graph the system of inequalities. - $\frac{x^{2}}{9}+\frac{y^{2}}{25} \leq 1$ $\frac{x^{2}}{25}+\frac{y^{2}}{9} \leq 1$ $Graph the system of inequalities. - \frac{x^{2}}{9}+\frac{y^{2}}{25} \leq 1 \frac{x^{2}}{25}+\frac{y^{2}}{9} \leq 1$

Solve the system by the elimination method or a combination of the elimination and substitution methods. - $5 x^{2}+3 x y-5 y^{2}=-9$ $x^{2}-x y-y^{2}=-5$

Solve the nonlinear system. - $x y=1$ $-8 x-y=9$

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

Graph the system of inequalities. - -\geq1 +\leq36 $Graph the system of inequalities. - \begin{array}{l}\frac{x^{2}}{9}-\frac{y^{2}}{16} \geq 1 \\ x^{2}+y^{2} \leq 36\end{array}$

Describe the graph of the solution set of the following inequality: $x< y^{2}+7$

Graph the function defined by a radical expression. - $y=4 \sqrt{\frac{16-x^{2}}{16}}$ $Graph the function defined by a radical expression. - y=4 \sqrt{\frac{16-x^{2}}{16}}$