Question 1

Graph the hyperbola.
-$\frac{x^{2}}{4}-\frac{y^{2}}{4}=1$

Accepted Answer

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

Question 2

Identify the graph of the equation as a parabola, circle, ellipse, or hyperbola.
-$11 y=3(x+3)^{2}$

Accepted Answer

A)  Ellipse 
B)  Hyperbola 
C)  Circle 
D)  Parabola 
A)  Ellipse 
B)  Hyperbola 
C)  Circle 
D)  Parabola

Question 3

Graph the function. Give the domain and range.
-$f(x)=|x+3|+6$

Accepted Answer

A)  Domain: $(-\infty, \infty)$; Range: $[6, \infty)$
  
B)  Domain: $(-\infty, \infty)$; Range: $[-6, \infty)$
  
C)  Domain: $(-\infty, \infty)$; Range: $[-6, \infty)$
  
D)  Domain: $(-\infty, \infty)$; Range: $[6, \infty)$
  
A)  Domain: $(-\infty, \infty)$; Range: $[6, \infty)$
  
B)  Domain: $(-\infty, \infty)$; Range: $[-6, \infty)$
  
C)  Domain: $(-\infty, \infty)$; Range: $[-6, \infty)$
  
D)  Domain: $(-\infty, \infty)$; Range: $[6, \infty)$

Question 4

Identify the graph of the equation as a parabola, circle, ellipse, or hyperbola.
-$x^{2}-y^{2}=36$

Accepted Answer

A)  Ellipse 
B)  Circle 
C)  Parabola 
D)  Hyperbola 
A)  Ellipse 
B)  Circle 
C)  Parabola 
D)  Hyperbola

Question 5

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?
-$\frac{y^{2}}{36}-\frac{x^{2}}{25}=1$

Accepted Answer

A)  $y_{1}=5 \sqrt{x^{2}+36}, y_{2}=-5 \sqrt{x^{2}+36}$ 
B)  $y_{1}=6 \sqrt{\frac{x^{2}}{25}-1}, y_{2}=-6 \sqrt{\frac{x^{2}}{25}-1}$ 
C)  $y_{1}=6 \sqrt{\frac{x^{2}}{25}+1}, y_{2}=-6 \sqrt{\frac{x^{2}}{25}+1}$ 
D)  $y_{1}=6 \sqrt{x^{2}-25}, y_{2}=-6 \sqrt{x^{2}-25}$ 
A)  $y_{1}=5 \sqrt{x^{2}+36}, y_{2}=-5 \sqrt{x^{2}+36}$ 
B)  $y_{1}=6 \sqrt{\frac{x^{2}}{25}-1}, y_{2}=-6 \sqrt{\frac{x^{2}}{25}-1}$ 
C)  $y_{1}=6 \sqrt{\frac{x^{2}}{25}+1}, y_{2}=-6 \sqrt{\frac{x^{2}}{25}+1}$ 
D)  $y_{1}=6 \sqrt{x^{2}-25}, y_{2}=-6 \sqrt{x^{2}-25}$

Question 6

Identify the graph of the equation as a parabola, circle, ellipse, or hyperbola.
-$(x-2)^{2}=9-y^{2}$

Accepted Answer

A)  Hyperbola 
B)  Ellipse 
C)  Parabola 
D)  Circle 
A)  Hyperbola 
B)  Ellipse 
C)  Parabola 
D)  Circle

Question 7

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

Accepted Answer

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

Question 8

Graph the hyperbola with center shifted away from the origin.
-$\frac{(x+3)^{2}}{25}-\frac{(y-3)^{2}}{16}=1$

Accepted Answer

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

Question 9

The equation of a circle centered at the origin with radius 5 is $x^{2}+y^{2}=5$.

Accepted Answer

A) True 
 B)False

Question 10

Identify the graph of the equation as a parabola, hyperbola, ellipse, or circle.
-$25 y^{2}+36 x^{2}=900$

Accepted Answer

A)  ellipse 
B)  parabola 
C)  circle 
D)  hyperbola 
A)  ellipse 
B)  parabola 
C)  circle 
D)  hyperbola

Question 11

A student thinks that the graphs of the equations
$\frac{x^{2}}{81}-\frac{y^{2}}{25}=1$ and $\frac{y^{2}}{25}-\frac{x^{2}}{81}=1$
are identical. Is the student correct? Explain.

Accepted Answer

No, the student is incorrect. Although b

Question 12

Identify the graph of the equation as a parabola, hyperbola, ellipse, or circle.
-$36 y^{2}=144+4 x^{2}$

Accepted Answer

A)  ellipse 
B)  circle 
C)  hyperbola 
D)  parabola 
A)  ellipse 
B)  circle 
C)  hyperbola 
D)  parabola

Question 13

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

Accepted Answer

A)  $\{(0,-1),(-1,0)\}$ 
B)  $\{(0,1),(1,0)\}$ 
C)  $\{(0,-1),(1,0)\}$ 
D)  $\{(0,1),(-1,0)\}$ 
A)  $\{(0,-1),(-1,0)\}$ 
B)  $\{(0,1),(1,0)\}$ 
C)  $\{(0,-1),(1,0)\}$ 
D)  $\{(0,1),(-1,0)\}$

Question 14

Graph the function defined by a radical expression.
-$y=8 \sqrt{\frac{9+x^{2}}{9}}$

Accepted Answer

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

Question 15

Graph the hyperbola.
-$\frac{y^{2}}{25}-\frac{x^{2}}{64}=1$

Accepted Answer

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

Question 16

Identify the graph of the equation as a parabola, circle, ellipse, or hyperbola.
-$x^{2}+y^{2}=9$

Accepted Answer

A)  Parabola 
B)  Hyperbola 
C)  Circle 
D)  Ellipse 
A)  Parabola 
B)  Hyperbola 
C)  Circle 
D)  Ellipse

Question 17

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?
-$(x-1)^{2}+(y-1)^{2}=1$

Accepted Answer

A)  $y_{1}=-1+\sqrt{1-(x-1)^{2}}, y_{2} =-1-\sqrt{1-(x-1)^{2}}$ 
B)  $y_{1}=-1+\sqrt{1-(x-1)^{2}}, y_{2}=1-\sqrt{1-(x-1)^{2}}$ 
C)  $\mathrm{y}_{1}=1+\sqrt{1-(\mathrm{x}-1)^{2}}, \mathrm{y}_{2}=1-\sqrt{1-(\mathrm{x}-1)^{2}}$ 
D)  $y_{1}=1+\sqrt{1-(x-1)^{2}}, y_{2}=-1-\sqrt{1-(x-1)^{2}}$ 
A)  $y_{1}=-1+\sqrt{1-(x-1)^{2}}, y_{2} =-1-\sqrt{1-(x-1)^{2}}$ 
B)  $y_{1}=-1+\sqrt{1-(x-1)^{2}}, y_{2}=1-\sqrt{1-(x-1)^{2}}$ 
C)  $\mathrm{y}_{1}=1+\sqrt{1-(\mathrm{x}-1)^{2}}, \mathrm{y}_{2}=1-\sqrt{1-(\mathrm{x}-1)^{2}}$ 
D)  $y_{1}=1+\sqrt{1-(x-1)^{2}}, y_{2}=-1-\sqrt{1-(x-1)^{2}}$

Question 18

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

Accepted Answer

A) $\begin{aligned} y & >-x^{2}+5 \ y & -x^{2}+5$ $y>2$ C) $\begin{aligned} y & 2\end{aligned}$ D) $y<-x^{2}+5$ $\mathrm{y}<2$ A) $\begin{aligned} y & >-x^{2}+5 \ y & -x^{2}+5$ $y>2$ C) $\begin{aligned} y & 2\end{aligned}$ D) $y<-x^{2}+5$ $\mathrm{y}<2$

Question 19

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

Accepted Answer

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

Question 20

Graph the hyperbola.
-$\frac{y^{2}}{16}-\frac{x^{2}}{16}=1$

Accepted Answer

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

Graph the hyperbola. - $\frac{x^{2}}{4}-\frac{y^{2}}{4}=1$ $Graph the hyperbola. - \frac{x^{2}}{4}-\frac{y^{2}}{4}=1$

Identify the graph of the equation as a parabola, circle, ellipse, or hyperbola. - $11 y=3(x+3)^{2}$

Graph the function. Give the domain and range. - $f(x)=|x+3|+6$

Identify the graph of the equation as a parabola, circle, ellipse, or hyperbola. - $x^{2}-y^{2}=36$

Identify the graph of the equation as a parabola, circle, ellipse, or hyperbola. - $(x-2)^{2}=9-y^{2}$

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

Graph the hyperbola with center shifted away from the origin. - $\frac{(x+3)^{2}}{25}-\frac{(y-3)^{2}}{16}=1$ $Graph the hyperbola with center shifted away from the origin. - \frac{(x+3)^{2}}{25}-\frac{(y-3)^{2}}{16}=1$

The equation of a circle centered at the origin with radius 5 is $x^{2}+y^{2}=5$ .

Identify the graph of the equation as a parabola, hyperbola, ellipse, or circle. - $25 y^{2}+36 x^{2}=900$

A student thinks that the graphs of the equations $\frac{x^{2}}{81}-\frac{y^{2}}{25}=1$ and $\frac{y^{2}}{25}-\frac{x^{2}}{81}=1$ are identical. Is the student correct? Explain.

Identify the graph of the equation as a parabola, hyperbola, ellipse, or circle. - $36 y^{2}=144+4 x^{2}$

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

Graph the function defined by a radical expression. - $y=8 \sqrt{\frac{9+x^{2}}{9}}$ $Graph the function defined by a radical expression. - y=8 \sqrt{\frac{9+x^{2}}{9}}$

Graph the hyperbola. - $\frac{y^{2}}{25}-\frac{x^{2}}{64}=1$ $Graph the hyperbola. - \frac{y^{2}}{25}-\frac{x^{2}}{64}=1$

Identify the graph of the equation as a parabola, circle, ellipse, or hyperbola. - $x^{2}+y^{2}=9$

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

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

Graph the hyperbola. - $\frac{y^{2}}{16}-\frac{x^{2}}{16}=1$ $Graph the hyperbola. - \frac{y^{2}}{16}-\frac{x^{2}}{16}=1$

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 hyperbola. - x24−y24=1\frac{x^{2}}{4}-\frac{y^{2}}{4}=14x2​−4y2​=1

Identify the graph of the equation as a parabola, circle, ellipse, or hyperbola. - 11y=3(x+3)211 y=3(x+3)^{2}11y=3(x+3)2

Graph the function. Give the domain and range. - f(x)=∣x+3∣+6f(x)=|x+3|+6f(x)=∣x+3∣+6

Identify the graph of the equation as a parabola, circle, ellipse, or hyperbola. - x2−y2=36x^{2}-y^{2}=36x2−y2=36

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−x225=1\frac{y^{2}}{36}-\frac{x^{2}}{25}=136y2​−25x2​=1

Identify the graph of the equation as a parabola, circle, ellipse, or hyperbola. - (x−2)2=9−y2(x-2)^{2}=9-y^{2}(x−2)2=9−y2

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

Graph the hyperbola with center shifted away from the origin. - (x+3)225−(y−3)216=1\frac{(x+3)^{2}}{25}-\frac{(y-3)^{2}}{16}=125(x+3)2​−16(y−3)2​=1

The equation of a circle centered at the origin with radius 5 is x2+y2=5x^{2}+y^{2}=5x2+y2=5 .

Identify the graph of the equation as a parabola, hyperbola, ellipse, or circle. - 25y2+36x2=90025 y^{2}+36 x^{2}=90025y2+36x2=900

A student thinks that the graphs of the equations x281−y225=1\frac{x^{2}}{81}-\frac{y^{2}}{25}=181x2​−25y2​=1 and y225−x281=1\frac{y^{2}}{25}-\frac{x^{2}}{81}=125y2​−81x2​=1 are identical. Is the student correct? Explain.

Identify the graph of the equation as a parabola, hyperbola, ellipse, or circle. - 36y2=144+4x236 y^{2}=144+4 x^{2}36y2=144+4x2

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

Graph the function defined by a radical expression. - y=89+x29y=8 \sqrt{\frac{9+x^{2}}{9}}y=899+x2​​

Graph the hyperbola. - y225−x264=1\frac{y^{2}}{25}-\frac{x^{2}}{64}=125y2​−64x2​=1

Identify the graph of the equation as a parabola, circle, ellipse, or hyperbola. - x2+y2=9x^{2}+y^{2}=9x2+y2=9

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

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

Graph the hyperbola. - y216−x216=1\frac{y^{2}}{16}-\frac{x^{2}}{16}=116y2​−16x2​=1

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 hyperbola. - $\frac{x^{2}}{4}-\frac{y^{2}}{4}=1$ $Graph the hyperbola. - \frac{x^{2}}{4}-\frac{y^{2}}{4}=1$

Identify the graph of the equation as a parabola, circle, ellipse, or hyperbola. - $11 y=3(x+3)^{2}$

Graph the function. Give the domain and range. - $f(x)=|x+3|+6$

Identify the graph of the equation as a parabola, circle, ellipse, or hyperbola. - $x^{2}-y^{2}=36$

Identify the graph of the equation as a parabola, circle, ellipse, or hyperbola. - $(x-2)^{2}=9-y^{2}$

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

Graph the hyperbola with center shifted away from the origin. - $\frac{(x+3)^{2}}{25}-\frac{(y-3)^{2}}{16}=1$ $Graph the hyperbola with center shifted away from the origin. - \frac{(x+3)^{2}}{25}-\frac{(y-3)^{2}}{16}=1$

The equation of a circle centered at the origin with radius 5 is $x^{2}+y^{2}=5$ .

Identify the graph of the equation as a parabola, hyperbola, ellipse, or circle. - $25 y^{2}+36 x^{2}=900$

A student thinks that the graphs of the equations $\frac{x^{2}}{81}-\frac{y^{2}}{25}=1$ and $\frac{y^{2}}{25}-\frac{x^{2}}{81}=1$ are identical. Is the student correct? Explain.

Identify the graph of the equation as a parabola, hyperbola, ellipse, or circle. - $36 y^{2}=144+4 x^{2}$

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

Graph the function defined by a radical expression. - $y=8 \sqrt{\frac{9+x^{2}}{9}}$ $Graph the function defined by a radical expression. - y=8 \sqrt{\frac{9+x^{2}}{9}}$

Graph the hyperbola. - $\frac{y^{2}}{25}-\frac{x^{2}}{64}=1$ $Graph the hyperbola. - \frac{y^{2}}{25}-\frac{x^{2}}{64}=1$

Identify the graph of the equation as a parabola, circle, ellipse, or hyperbola. - $x^{2}+y^{2}=9$

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

Graph the hyperbola. - $\frac{y^{2}}{16}-\frac{x^{2}}{16}=1$ $Graph the hyperbola. - \frac{y^{2}}{16}-\frac{x^{2}}{16}=1$