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

Graph the function defined by a radical expression. - $f(x)=\sqrt{9-x^{2}}$ $Graph the function defined by a radical expression. - f(x)=\sqrt{9-x^{2}}$

(Multiple Choice)

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Question 141

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; one point

(Essay)

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Question 142

Graph the inequality. - $y \geq \frac{1}{4} x^{2}+2 x+6$ $Graph the inequality. - y \geq \frac{1}{4} x^{2}+2 x+6$

(Multiple Choice)

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Question 143

Choose the equation that matches the graph. -

(Multiple Choice)

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Question 144

Graph the inequality. - $36x^2-16y^2 \leq 576$ $Graph the inequality. - 36x^2-16y^2 \leq 576$

(Multiple Choice)

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Question 145

Graph the function. -f(x)=3|x-5|-8

(Multiple Choice)

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Question 146

Which method should be used to solve the system? Explain your answer, including a description of the first step. - $\mathrm{x}^{2}+9 \mathrm{y}^{2}=49$ $-9 x^{2}+8 y^{2}=25$

(Essay)

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Question 147

Solve the problem by using a nonlinear system. -Find the dimensions of a rectangular enclosure with perimeter $40 \mathrm{yd}$ and area $75 \mathrm{yd}^{2}$ .

(Multiple Choice)

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Question 148

Choose the graph that matches the given function. - $f(x)=\sqrt{x-1}$

(Multiple Choice)

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Question 149

Choose the inequality that matches the graph. -

(Multiple Choice)

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Question 150

Graph the circle. - $x^{2}+y^{2}-8 x-8 y+7=0$ $Graph the circle. - x^{2}+y^{2}-8 x-8 y+7=0$

(Multiple Choice)

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Question 151

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 line and an ellipse; two points

(Essay)

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Question 152

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

(Multiple Choice)

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Question 153

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. - $The graphing calculator screen shows the graphs of the two given functions, and the display gives the coordinates of one of the solutions. Find the other solution. - y=\frac{1}{2} x^{2} x-y=-4$ $y=\frac{1}{2} x^{2}$ $x-y=-4$

(Multiple Choice)

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Question 154

Solve the system by the substitution method. - $x^{2}+y^{2}=85$ $\mathrm{x}-\mathrm{y}=1$

(Multiple Choice)

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Question 155

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

(Multiple Choice)

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Question 156

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; three points

(Essay)

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Question 157

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

(Multiple Choice)

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Question 158

The hyperbola with equation $\frac{y^{2}}{64}-\frac{x^{2}}{49}=1$ opens up and down.

(True/False)

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Question 159

What is the domain of the square root function, given by $f(x)=\sqrt{x}$ ?

(Multiple Choice)

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Question 160

Showing 141 - 160 of 233

Graph the function defined by a radical expression. - $f(x)=\sqrt{9-x^{2}}$ $Graph the function defined by a radical expression. - f(x)=\sqrt{9-x^{2}}$

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; one point

Graph the inequality. - $y \geq \frac{1}{4} x^{2}+2 x+6$ $Graph the inequality. - y \geq \frac{1}{4} x^{2}+2 x+6$

Choose the equation that matches the graph. -

Graph the inequality. - $36x^2-16y^2 \leq 576$ $Graph the inequality. - 36x^2-16y^2 \leq 576$

Graph the function. -f(x)=3|x-5|-8

Which method should be used to solve the system? Explain your answer, including a description of the first step. - $\mathrm{x}^{2}+9 \mathrm{y}^{2}=49$ $-9 x^{2}+8 y^{2}=25$

Solve the problem by using a nonlinear system. -Find the dimensions of a rectangular enclosure with perimeter $40 \mathrm{yd}$ and area $75 \mathrm{yd}^{2}$ .

Choose the graph that matches the given function. - $f(x)=\sqrt{x-1}$

Choose the inequality that matches the graph. -

Graph the circle. - $x^{2}+y^{2}-8 x-8 y+7=0$ $Graph the circle. - x^{2}+y^{2}-8 x-8 y+7=0$

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 line and an ellipse; two points

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

Solve the system by the substitution method. - $x^{2}+y^{2}=85$ $\mathrm{x}-\mathrm{y}=1$

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

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; three points

The hyperbola with equation $\frac{y^{2}}{64}-\frac{x^{2}}{49}=1$ opens up and down.

What is the domain of the square root function, given by $f(x)=\sqrt{x}$ ?

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

Graph the function defined by a radical expression. - f(x)=9−x2f(x)=\sqrt{9-x^{2}}f(x)=9−x2​

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; one point

Graph the inequality. - y≥14x2+2x+6y \geq \frac{1}{4} x^{2}+2 x+6y≥41​x2+2x+6

Choose the equation that matches the graph. -

Graph the inequality. - 36x2−16y2≤57636x^2-16y^2 \leq 57636x2−16y2≤576

Graph the function. -f(x)=3|x-5|-8

Which method should be used to solve the system? Explain your answer, including a description of the first step. - x2+9y2=49\mathrm{x}^{2}+9 \mathrm{y}^{2}=49x2+9y2=49 −9x2+8y2=25-9 x^{2}+8 y^{2}=25−9x2+8y2=25

Solve the problem by using a nonlinear system. -Find the dimensions of a rectangular enclosure with perimeter 40yd40 \mathrm{yd}40yd and area 75yd275 \mathrm{yd}^{2}75yd2 .

Choose the graph that matches the given function. - f(x)=x−1f(x)=\sqrt{x-1}f(x)=x−1​

Choose the inequality that matches the graph. -

Graph the circle. - x2+y2−8x−8y+7=0x^{2}+y^{2}-8 x-8 y+7=0x2+y2−8x−8y+7=0

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 line and an ellipse; two points

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

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=12x2y=\frac{1}{2} x^{2}y=21​x2 x−y=−4x-y=-4x−y=−4

Solve the system by the substitution method. - x2+y2=85x^{2}+y^{2}=85x2+y2=85 x−y=1\mathrm{x}-\mathrm{y}=1x−y=1

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

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; three points

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? - x249−y2=1\frac{x^{2}}{49}-y^{2}=149x2​−y2=1

The hyperbola with equation y264−x249=1\frac{y^{2}}{64}-\frac{x^{2}}{49}=164y2​−49x2​=1 opens up and down.

What is the domain of the square root function, given by f(x)=xf(x)=\sqrt{x}f(x)=x​ ?

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 defined by a radical expression. - $f(x)=\sqrt{9-x^{2}}$ $Graph the function defined by a radical expression. - f(x)=\sqrt{9-x^{2}}$

Graph the inequality. - $y \geq \frac{1}{4} x^{2}+2 x+6$ $Graph the inequality. - y \geq \frac{1}{4} x^{2}+2 x+6$

Graph the inequality. - $36x^2-16y^2 \leq 576$ $Graph the inequality. - 36x^2-16y^2 \leq 576$

Which method should be used to solve the system? Explain your answer, including a description of the first step. - $\mathrm{x}^{2}+9 \mathrm{y}^{2}=49$ $-9 x^{2}+8 y^{2}=25$

Solve the problem by using a nonlinear system. -Find the dimensions of a rectangular enclosure with perimeter $40 \mathrm{yd}$ and area $75 \mathrm{yd}^{2}$ .

Choose the graph that matches the given function. - $f(x)=\sqrt{x-1}$

Graph the circle. - $x^{2}+y^{2}-8 x-8 y+7=0$ $Graph the circle. - x^{2}+y^{2}-8 x-8 y+7=0$

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

Solve the system by the substitution method. - $x^{2}+y^{2}=85$ $\mathrm{x}-\mathrm{y}=1$

The hyperbola with equation $\frac{y^{2}}{64}-\frac{x^{2}}{49}=1$ opens up and down.

What is the domain of the square root function, given by $f(x)=\sqrt{x}$ ?