Question 1

The $y$-intercepts of the hyperbola with equation $\frac{x^{2}}{36}-\frac{y^{2}}{9}=1$ are $(6,0)$ and $(-6,0)$.

Accepted Answer

A) True 
 B)False

Question 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.
-Two parabolas; four points

Accepted Answer

The answer of Suppose that a nonlinear system is composed...

Question 3

Graph the rational function.
-f(x) = $\frac{4}{ x }$ + 3

Accepted Answer

A)    
B)    
C)    
D)    
A)    
B)    
C)    
D)

Question 4

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?
-$\frac{x^{2}}{9}-\frac{y^{2}}{36}=1$

Accepted Answer

A)  $y_{1}=6 \sqrt{x^{2}-9}, y_{2}=-6 \sqrt{x^{2}-9}$ 
B)  $y_{1}=3 \sqrt{x^{2}+6}, y_{2}=-3 \sqrt{x^{2}+6}$ 
C)  $y_{1}=6 \sqrt{\frac{x^{2}}{9}+1}, y_{2}=-6 \sqrt{\frac{x^{2}}{9}+1}$ 
D)  $y_{1}=6 \sqrt{\frac{x^{2}}{9}-1}, y_{2}=-6 \sqrt{\frac{x^{2}}{9}-1}$ 
A)  $y_{1}=6 \sqrt{x^{2}-9}, y_{2}=-6 \sqrt{x^{2}-9}$ 
B)  $y_{1}=3 \sqrt{x^{2}+6}, y_{2}=-3 \sqrt{x^{2}+6}$ 
C)  $y_{1}=6 \sqrt{\frac{x^{2}}{9}+1}, y_{2}=-6 \sqrt{\frac{x^{2}}{9}+1}$ 
D)  $y_{1}=6 \sqrt{\frac{x^{2}}{9}-1}, y_{2}=-6 \sqrt{\frac{x^{2}}{9}-1}$

Question 5

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 a parabola; one point

Accepted Answer

The answer of Suppose that a nonlinear system is composed...

Question 6

Graph the function.
-$f(x)=\sqrt{x+5}+2$

Accepted Answer

A)    
B)    
C)    
D)    
A)    
B)    
C)    
D)

Question 7

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 $y^{2}-10 x^{2}=70$, where $x$ and $y$ are in meters. Refer to the figure and determine the height, $h$, of the outside walls.

Accepted Answer

A)  $74.0 \mathrm{~m}$ 
B)  $8.6 \mathrm{~m}$ 
C)  $710.0 \mathrm{~m}$ 
D)  $26.6 \mathrm{~m}$ 
A)  $74.0 \mathrm{~m}$ 
B)  $8.6 \mathrm{~m}$ 
C)  $710.0 \mathrm{~m}$ 
D)  $26.6 \mathrm{~m}$

Question 8

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.
- 
$y=-x^{2}$
$x+y=-2$

Accepted Answer

A)  $(-4,2)$ 
B)  $(2,-4)$ 
C)  $(1,1)$ 
D)  $(-2,4)$ 
A)  $(-4,2)$ 
B)  $(2,-4)$ 
C)  $(1,1)$ 
D)  $(-2,4)$

Question 9

The $x$-intercepts of the hyperbola with equation $\frac{x^{2}}{16}-\frac{y^{2}}{25}=1$ are $(4,0)$ and $(-4,0)$.

Accepted Answer

A) True 
 B)False

Question 10

Which method should be used to solve the system? Explain your answer, including a description of the first step.
-$\quad 6 x^{2}-6 y^{2}=81$
$10 x+10 y=5$

Accepted Answer

Substitution should be used, b

Question 11

Graph the inequality.
-$ \left\{\begin{array}{l}x^{2}+y^{2} \leq 16 \ \frac{x^{2}}{9}+\frac{y^{2}}{49} \geq 1\end{array}\right. $

Accepted Answer

A)    
B)    
C)    
D)    
A)    
B)    
C)    
D)

Question 12

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?
-$\frac{x^{2}}{25}+\frac{y^{2}}{25}=1$

Accepted Answer

A)  $y_{1}=\sqrt{25-x^{2}}, y_2=-\sqrt{25-x^{2}}$ 
B)  $y_{1}=\sqrt{25+x^{2}}, y_{2}=-\sqrt{25+x^{2}}$ 
C)  $y_{1}=\sqrt{5+x^{2}}, y_{2}=-\sqrt{5+x^{2}}$ 
D)  $y_{1}=\sqrt{5-x^{2}}, y_{2}=-\sqrt{5-x^{2}}$ 
A)  $y_{1}=\sqrt{25-x^{2}}, y_2=-\sqrt{25-x^{2}}$ 
B)  $y_{1}=\sqrt{25+x^{2}}, y_{2}=-\sqrt{25+x^{2}}$ 
C)  $y_{1}=\sqrt{5+x^{2}}, y_{2}=-\sqrt{5+x^{2}}$ 
D)  $y_{1}=\sqrt{5-x^{2}}, y_{2}=-\sqrt{5-x^{2}}$

Question 13

Graph the function defined by a radical expression.
-$ f(x)=\sqrt{x+7} $

Accepted Answer

A)    
B)    
C)    
D)    
A)    
B)    
C)    
D)

Question 14

Solve the problem.
-A rectangular board is 8 by 20 . How far from the center of the board will the foci be located to determine the largest elliptical tabletop? Round your answer to the nearest tenth.

Accepted Answer

A)  9.2 
B)  .8 
C)  4.0 
D)  6.0 
A)  9.2 
B)  .8 
C)  4.0 
D)  6.0

Question 15

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.
-An ellipse and a hyperbola; four points

Accepted Answer

The answer of Suppose that a nonlinear system is composed...

Question 16

Solve the problem.
-A rectangular board is 8 by 14 . The foci of an ellipse are located to produce the largest area. A string is connected to the foci and pulled taut by a pencil in order to draw the ellipse. Find the length of the string.

Accepted Answer

A)  16 
B)  8 
C)  28 
D)  14 
A)  16 
B)  8 
C)  28 
D)  14

Question 17

Graph the function defined by a radical expression.
-$f(x)=-\sqrt{3-x}$

Accepted Answer

A)    
B)    
C)    
D)    
A)    
B)    
C)    
D)

Question 18

Graph.
-$\frac{\mathrm{y}}{8}=-\sqrt{\frac{4-\mathrm{x}^{2}}{4}}$

Accepted Answer

A)    
B)    
C)    
D)    
A)    
B)    
C)    
D)

Question 19

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?
-$\frac{y^{2}}{36}-x^{2}=1$

Accepted Answer

A)  $y_{1}=\sqrt{\frac{x^{2}}{36}+1}, y_{2}=-\sqrt{\frac{x^{2}}{36}+1}$ 
B)  $y_{1}=6 \sqrt{x^{2}+1}, y_{2}=-6 \sqrt{x^{2}+1}$ 
C)  $y_{1}=\sqrt{\frac{x^{2}}{36}-1}, y_{2}=-\sqrt{\frac{x^{2}}{36}-1}$ 
D)  $y_{1}=\sqrt{x^{2}+36}, y_{2}=-\sqrt{x^{2}+36}$ 
A)  $y_{1}=\sqrt{\frac{x^{2}}{36}+1}, y_{2}=-\sqrt{\frac{x^{2}}{36}+1}$ 
B)  $y_{1}=6 \sqrt{x^{2}+1}, y_{2}=-6 \sqrt{x^{2}+1}$ 
C)  $y_{1}=\sqrt{\frac{x^{2}}{36}-1}, y_{2}=-\sqrt{\frac{x^{2}}{36}-1}$ 
D)  $y_{1}=\sqrt{x^{2}+36}, y_{2}=-\sqrt{x^{2}+36}$

Question 20

Find the center and radius of the circle whose equation is given.
-$x^{2}+y^{2}+12 x+8 y+52=81$

Accepted Answer

A)  center: $(4,6)$; radius: 81 
B)  center: $(6,4)$; radius: 81 
C)  center: $(-6,-4)$; radius: 9 
D)  center: $(-4,-6)$; radius: 9 
A)  center: $(4,6)$; radius: 81 
B)  center: $(6,4)$; radius: 81 
C)  center: $(-6,-4)$; radius: 9 
D)  center: $(-4,-6)$; radius: 9

The $y$ -intercepts of the hyperbola with equation $\frac{x^{2}}{36}-\frac{y^{2}}{9}=1$ are $(6,0)$ and $(-6,0)$ .

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. -Two parabolas; four points

Graph the rational function. -f(x) = $\frac{4}{ x }$ + 3 $Graph the rational function. -f(x) = \frac{4}{ x } + 3$

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 a parabola; one point

Graph the function. - $f(x)=\sqrt{x+5}+2$ $Graph the function. - f(x)=\sqrt{x+5}+2$

The $x$ -intercepts of the hyperbola with equation $\frac{x^{2}}{16}-\frac{y^{2}}{25}=1$ are $(4,0)$ and $(-4,0)$ .

Which method should be used to solve the system? Explain your answer, including a description of the first step. - $\quad 6 x^{2}-6 y^{2}=81$ $10 x+10 y=5$

Graph the inequality. - $\left\{\begin{array}{l}x^{2}+y^{2} \leq 16 \\ \frac{x^{2}}{9}+\frac{y^{2}}{49} \geq 1\end{array}\right.$ $Graph the inequality. - \left\{\begin{array}{l}x^{2}+y^{2} \leq 16 \\ \frac{x^{2}}{9}+\frac{y^{2}}{49} \geq 1\end{array}\right.$

Graph the function defined by a radical expression. - $f(x)=\sqrt{x+7}$ $Graph the function defined by a radical expression. - f(x)=\sqrt{x+7}$

Solve the problem. -A rectangular board is 8 by 20 . How far from the center of the board will the foci be located to determine the largest elliptical tabletop? Round your answer to the nearest tenth.

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. -An ellipse and a hyperbola; four points

Solve the problem. -A rectangular board is 8 by 14 . The foci of an ellipse are located to produce the largest area. A string is connected to the foci and pulled taut by a pencil in order to draw the ellipse. Find the length of the string.

Graph the function defined by a radical expression. - $f(x)=-\sqrt{3-x}$ $Graph the function defined by a radical expression. - f(x)=-\sqrt{3-x}$

Graph. - $\frac{\mathrm{y}}{8}=-\sqrt{\frac{4-\mathrm{x}^{2}}{4}}$ $Graph. - \frac{\mathrm{y}}{8}=-\sqrt{\frac{4-\mathrm{x}^{2}}{4}}$

Find the center and radius of the circle whose equation is given. - $x^{2}+y^{2}+12 x+8 y+52=81$

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 yyy -intercepts of the hyperbola with equation x236−y29=1\frac{x^{2}}{36}-\frac{y^{2}}{9}=136x2​−9y2​=1 are (6,0)(6,0)(6,0) and (−6,0)(-6,0)(−6,0) .

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. -Two parabolas; four points

Graph the rational function. -f(x) = 4x\frac{4}{ x }x4​ + 3

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? - x29−y236=1\frac{x^{2}}{9}-\frac{y^{2}}{36}=19x2​−36y2​=1

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 a parabola; one point

Graph the function. - f(x)=x+5+2f(x)=\sqrt{x+5}+2f(x)=x+5​+2

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 y2−10x2=70y^{2}-10 x^{2}=70y2−10x2=70 , where xxx and yyy are in meters. Refer to the figure and determine the height, hhh , of the outside walls.

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=−x2y=-x^{2}y=−x2 x+y=−2x+y=-2x+y=−2

The xxx -intercepts of the hyperbola with equation x216−y225=1\frac{x^{2}}{16}-\frac{y^{2}}{25}=116x2​−25y2​=1 are (4,0)(4,0)(4,0) and (−4,0)(-4,0)(−4,0) .

Which method should be used to solve the system? Explain your answer, including a description of the first step. - 6x2−6y2=81\quad 6 x^{2}-6 y^{2}=816x2−6y2=81 10x+10y=510 x+10 y=510x+10y=5

Graph the inequality. - {x2+y2≤16x29+y249≥1 \left\{\begin{array}{l}x^{2}+y^{2} \leq 16 \\ \frac{x^{2}}{9}+\frac{y^{2}}{49} \geq 1\end{array}\right. {x2+y2≤169x2​+49y2​≥1​

Graph the function defined by a radical expression. - f(x)=x+7 f(x)=\sqrt{x+7} f(x)=x+7​

Solve the problem. -A rectangular board is 8 by 20 . How far from the center of the board will the foci be located to determine the largest elliptical tabletop? Round your answer to the nearest tenth.

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. -An ellipse and a hyperbola; four points

Solve the problem. -A rectangular board is 8 by 14 . The foci of an ellipse are located to produce the largest area. A string is connected to the foci and pulled taut by a pencil in order to draw the ellipse. Find the length of the string.

Graph the function defined by a radical expression. - f(x)=−3−xf(x)=-\sqrt{3-x}f(x)=−3−x​

Graph. - y8=−4−x24\frac{\mathrm{y}}{8}=-\sqrt{\frac{4-\mathrm{x}^{2}}{4}}8y​=−44−x2​​

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? - y236−x2=1\frac{y^{2}}{36}-x^{2}=136y2​−x2=1

Find the center and radius of the circle whose equation is given. - x2+y2+12x+8y+52=81x^{2}+y^{2}+12 x+8 y+52=81x2+y2+12x+8y+52=81

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

The $y$ -intercepts of the hyperbola with equation $\frac{x^{2}}{36}-\frac{y^{2}}{9}=1$ are $(6,0)$ and $(-6,0)$ .

Graph the rational function. -f(x) = $\frac{4}{ x }$ + 3 $Graph the rational function. -f(x) = \frac{4}{ x } + 3$

Graph the function. - $f(x)=\sqrt{x+5}+2$ $Graph the function. - f(x)=\sqrt{x+5}+2$

The $x$ -intercepts of the hyperbola with equation $\frac{x^{2}}{16}-\frac{y^{2}}{25}=1$ are $(4,0)$ and $(-4,0)$ .

Which method should be used to solve the system? Explain your answer, including a description of the first step. - $\quad 6 x^{2}-6 y^{2}=81$ $10 x+10 y=5$

Graph the inequality. - $\left\{\begin{array}{l}x^{2}+y^{2} \leq 16 \\ \frac{x^{2}}{9}+\frac{y^{2}}{49} \geq 1\end{array}\right.$ $Graph the inequality. - \left\{\begin{array}{l}x^{2}+y^{2} \leq 16 \\ \frac{x^{2}}{9}+\frac{y^{2}}{49} \geq 1\end{array}\right.$

Graph the function defined by a radical expression. - $f(x)=\sqrt{x+7}$ $Graph the function defined by a radical expression. - f(x)=\sqrt{x+7}$

Graph the function defined by a radical expression. - $f(x)=-\sqrt{3-x}$ $Graph the function defined by a radical expression. - f(x)=-\sqrt{3-x}$

Graph. - $\frac{\mathrm{y}}{8}=-\sqrt{\frac{4-\mathrm{x}^{2}}{4}}$ $Graph. - \frac{\mathrm{y}}{8}=-\sqrt{\frac{4-\mathrm{x}^{2}}{4}}$

Find the center and radius of the circle whose equation is given. - $x^{2}+y^{2}+12 x+8 y+52=81$