Question 1

Graph.
-$36 x^{2}-4 y^{2}=144$

Accepted Answer

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

Question 2

The range of $f(x)=\llbracket x \rrbracket$, the greatest integer function, is

Accepted Answer

A)  $\{\ldots,-4,-2,0,2,4, \ldots\}$ 
B)  $(-\infty, \infty)$ 
C)  $[0, \infty)$ 
D)  $\{\ldots,-2,-1,0,1,2, \ldots\}$ 
A)  $\{\ldots,-4,-2,0,2,4, \ldots\}$ 
B)  $(-\infty, \infty)$ 
C)  $[0, \infty)$ 
D)  $\{\ldots,-2,-1,0,1,2, \ldots\}$ D

Question 3

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.
- 
$y=\frac{1}{2} x^{2}-3$
$x+y=1$

Accepted Answer

A)  $(4,-3)$ 
B)  $(6,-5)$ 
C)  $(-4,5)$ 
D)  $(5,-4)$ 
A)  $(4,-3)$ 
B)  $(6,-5)$ 
C)  $(-4,5)$ 
D)  $(5,-4)$ C

Question 4

Graph the step function.
-$f(x)=\llbracket x-5 \rrbracket$

Accepted Answer

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

Question 5

The hyperbola with equation $\frac{x^{2}}{36}-\frac{y^{2}}{25}=1$ opens left and right.

Accepted Answer

A) True 
 B)False

Question 6

Graph the step function.
-$f(x)=\llbracket x+5 \rrbracket$

Accepted Answer

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

Question 7

Graph the function defined by a radical expression.
-$ f(x)=-\sqrt{4-x^{2}} $

Accepted Answer

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

Question 8

Graph the system of inequalities.
-$2 x+y \geq 4$
$x-1 \geq 0$

Accepted Answer

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

Question 9

Graph the inequality.
-$ 9 x^{2}-25 y^{2} \leq 225 $

Accepted Answer

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

Question 10

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

Accepted Answer

A) $y>-x^{2}-1$ $\mathrm{y} - 4$ C) $y>-x^{2}-1$ $y>-4$ D) $y<-x^{2}-1$ $\mathrm{y} < -4$ A) $y>-x^{2}-1$ $\mathrm{y} - 4$ C) $y>-x^{2}-1$ $y>-4$ D) $y<-x^{2}-1$ $\mathrm{y} < -4$

Question 11

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

Accepted Answer

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

Question 12

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

Accepted Answer

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

Question 13

Solve the problem by using a nonlinear system.
-A garden contains two square vegetable beds. Find the length of each bed if the sum of their areas is $1205 \mathrm{ft}^{2}$ and the difference of their areas is $147 \mathrm{ft}^{2}$.

Accepted Answer

A)  $26 \mathrm{ft}$; $23 \mathrm{ft}$ 
B)  $1352 \mathrm{ft} ; 1058 \mathrm{ft}$ 
C)  $7 \mathrm{ft} ; 7 \mathrm{ft}$ 
D)  $37 \mathrm{ft}$; $33 \mathrm{ft}$ 
A)  $26 \mathrm{ft}$; $23 \mathrm{ft}$ 
B)  $1352 \mathrm{ft} ; 1058 \mathrm{ft}$ 
C)  $7 \mathrm{ft} ; 7 \mathrm{ft}$ 
D)  $37 \mathrm{ft}$; $33 \mathrm{ft}$

Question 14

Solve the system by the elimination method or a combination of the elimination and substitution methods.
-$x^{2}+y^{2}=73$
$\mathrm{x}^{2}-\mathrm{y}^{2}=55$

Accepted Answer

A)  $\{(8,3),(-8,3),(8,-3),(-8,-3)\}$ 
B)  $\{(-8,-3),(-3,-8)\}$ 
C)  $\{(8,-3),(8,3)\}$ 
D)  $\{(8,3),(3,8),(-8,-3),(-3,-8)\}$ 
A)  $\{(8,3),(-8,3),(8,-3),(-8,-3)\}$ 
B)  $\{(-8,-3),(-3,-8)\}$ 
C)  $\{(8,-3),(8,3)\}$ 
D)  $\{(8,3),(3,8),(-8,-3),(-3,-8)\}$

Question 15

Identify the graph of the equation as a parabola, circle, ellipse, or hyperbola.
-$3 x^{2}-y=13$

Accepted Answer

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

Question 16

Solve the problem. Round your answer to the nearest tenth.
-The roof of a building is in the shape of the hyperbola $9 y^{2}-x^{2}=7$, where $x$ and $y$ are in meters. Refer to the figure and determine the height, $h$, of the outside walls.

Accepted Answer

A)  $16.0 \mathrm{~m}$ 
B)  $1.8 \mathrm{~m}$ 
C)  $1.3 \mathrm{~m}$ 
D)  $4.0 \mathrm{~m}$ 
A)  $16.0 \mathrm{~m}$ 
B)  $1.8 \mathrm{~m}$ 
C)  $1.3 \mathrm{~m}$ 
D)  $4.0 \mathrm{~m}$

Question 17

Evaluate the expression.
-$[[7.6]]$

Accepted Answer

A)  7 
B)  8 
C)  -7 
D)  6 
A)  7 
B)  8 
C)  -7 
D)  6

Question 18

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

Accepted Answer

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

Question 19

Find the equation of a circle satisfying the given conditions.
-Center: $(0,-2)$; radius: $\sqrt{10}$

Accepted Answer

A)  $x^{2}+(y+2)^{2}=10$ 
B)  $(x+2)^{2}+y^{2}=100$ 
C)  $(x-2)^{2}+y^{2}=100$ 
D)  $x^{2}+(y-2)^{2}=10$ 
A)  $x^{2}+(y+2)^{2}=10$ 
B)  $(x+2)^{2}+y^{2}=100$ 
C)  $(x-2)^{2}+y^{2}=100$ 
D)  $x^{2}+(y-2)^{2}=10$

Question 20

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?
-$\frac{x^{2}}{4}-\frac{y^{2}}{25}=1$

Accepted Answer

A)  $y_{1}=5 \sqrt{\frac{x^{2}}{4}+1}, y_{2}=-5 \sqrt{\frac{x^{2}}{4}+1}$ 
B)  $y_{1}=5 \sqrt{\frac{x^{2}}{4}-1}, y_{2}=-5 \sqrt{\frac{x^{2}}{4}-1}$ 
C)  $y_{1}=5 \sqrt{x^{2}-4}, y_{2}=-5 \sqrt{x^{2}-4}$ 
D)  $y_{1}=2 \sqrt{x^{2}+5}, y_{2}=-2 \sqrt{x^{2}+5}$ 
A)  $y_{1}=5 \sqrt{\frac{x^{2}}{4}+1}, y_{2}=-5 \sqrt{\frac{x^{2}}{4}+1}$ 
B)  $y_{1}=5 \sqrt{\frac{x^{2}}{4}-1}, y_{2}=-5 \sqrt{\frac{x^{2}}{4}-1}$ 
C)  $y_{1}=5 \sqrt{x^{2}-4}, y_{2}=-5 \sqrt{x^{2}-4}$ 
D)  $y_{1}=2 \sqrt{x^{2}+5}, y_{2}=-2 \sqrt{x^{2}+5}$

Graph. - $36 x^{2}-4 y^{2}=144$ $Graph. - 36 x^{2}-4 y^{2}=144$

The range of $f(x)=\llbracket x \rrbracket$ , the greatest integer function, is

Graph the step function. - $f(x)=\llbracket x-5 \rrbracket$ $Graph the step function. - f(x)=\llbracket x-5 \rrbracket$

The hyperbola with equation $\frac{x^{2}}{36}-\frac{y^{2}}{25}=1$ opens left and right.

Graph the step function. - $f(x)=\llbracket x+5 \rrbracket$ $Graph the step function. - f(x)=\llbracket x+5 \rrbracket$

Graph the function defined by a radical expression. - $f(x)=-\sqrt{4-x^{2}}$ $Graph the function defined by a radical expression. - f(x)=-\sqrt{4-x^{2}}$

Graph the system of inequalities. - $2 x+y \geq 4$ $x-1 \geq 0$ $Graph the system of inequalities. - 2 x+y \geq 4 x-1 \geq 0$

Graph the inequality. - $9 x^{2}-25 y^{2} \leq 225$ $Graph the inequality. - 9 x^{2}-25 y^{2} \leq 225$

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

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

Graph the system of inequalities. - -\leq1 +\leq36 $Graph the system of inequalities. - \begin{array}{l}\frac{x^{2}}{9}-\frac{y^{2}}{16} \leq 1 \\ x^{2}+y^{2} \leq 36\end{array}$

Solve the problem by using a nonlinear system. -A garden contains two square vegetable beds. Find the length of each bed if the sum of their areas is $1205 \mathrm{ft}^{2}$ and the difference of their areas is $147 \mathrm{ft}^{2}$ .

Solve the system by the elimination method or a combination of the elimination and substitution methods. - $x^{2}+y^{2}=73$ $\mathrm{x}^{2}-\mathrm{y}^{2}=55$

Identify the graph of the equation as a parabola, circle, ellipse, or hyperbola. - $3 x^{2}-y=13$

Evaluate the expression. - $[[7.6]]$

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

Find the equation of a circle satisfying the given conditions. -Center: $(0,-2)$ ; radius: $\sqrt{10}$

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. - 36x2−4y2=14436 x^{2}-4 y^{2}=14436x2−4y2=144

The range of f(x)=⟦x⟧f(x)=\llbracket x \rrbracketf(x)=[[x]] , the greatest integer function, is

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=12x2−3y=\frac{1}{2} x^{2}-3y=21​x2−3 x+y=1x+y=1x+y=1

Graph the step function. - f(x)=⟦x−5⟧f(x)=\llbracket x-5 \rrbracketf(x)=[[x−5]]

The hyperbola with equation x236−y225=1\frac{x^{2}}{36}-\frac{y^{2}}{25}=136x2​−25y2​=1 opens left and right.

Graph the step function. - f(x)=⟦x+5⟧f(x)=\llbracket x+5 \rrbracketf(x)=[[x+5]]

Graph the function defined by a radical expression. - f(x)=−4−x2 f(x)=-\sqrt{4-x^{2}} f(x)=−4−x2​

Graph the system of inequalities. - 2x+y≥42 x+y \geq 42x+y≥4 x−1≥0x-1 \geq 0x−1≥0

Graph the inequality. - 9x2−25y2≤225 9 x^{2}-25 y^{2} \leq 225 9x2−25y2≤225

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

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

Graph the system of inequalities. - -\leq1 +\leq36

Solve the problem by using a nonlinear system. -A garden contains two square vegetable beds. Find the length of each bed if the sum of their areas is 1205ft21205 \mathrm{ft}^{2}1205ft2 and the difference of their areas is 147ft2147 \mathrm{ft}^{2}147ft2 .

Solve the system by the elimination method or a combination of the elimination and substitution methods. - x2+y2=73x^{2}+y^{2}=73x2+y2=73 x2−y2=55\mathrm{x}^{2}-\mathrm{y}^{2}=55x2−y2=55

Identify the graph of the equation as a parabola, circle, ellipse, or hyperbola. - 3x2−y=133 x^{2}-y=133x2−y=13

Solve the problem. Round your answer to the nearest tenth. -The roof of a building is in the shape of the hyperbola 9y2−x2=79 y^{2}-x^{2}=79y2−x2=7 , where xxx and yyy are in meters. Refer to the figure and determine the height, hhh , of the outside walls.

Evaluate the expression. - [[7.6]][[7.6]][[7.6]]

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} \geq 125x2​+9y2​≥1

Find the equation of a circle satisfying the given conditions. -Center: (0,−2)(0,-2)(0,−2) ; radius: 10\sqrt{10}10​

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? - x24−y225=1\frac{x^{2}}{4}-\frac{y^{2}}{25}=14x2​−25y2​=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. - $36 x^{2}-4 y^{2}=144$ $Graph. - 36 x^{2}-4 y^{2}=144$

The range of $f(x)=\llbracket x \rrbracket$ , the greatest integer function, is

Graph the step function. - $f(x)=\llbracket x-5 \rrbracket$ $Graph the step function. - f(x)=\llbracket x-5 \rrbracket$

The hyperbola with equation $\frac{x^{2}}{36}-\frac{y^{2}}{25}=1$ opens left and right.

Graph the step function. - $f(x)=\llbracket x+5 \rrbracket$ $Graph the step function. - f(x)=\llbracket x+5 \rrbracket$

Graph the function defined by a radical expression. - $f(x)=-\sqrt{4-x^{2}}$ $Graph the function defined by a radical expression. - f(x)=-\sqrt{4-x^{2}}$

Graph the system of inequalities. - $2 x+y \geq 4$ $x-1 \geq 0$ $Graph the system of inequalities. - 2 x+y \geq 4 x-1 \geq 0$

Graph the inequality. - $9 x^{2}-25 y^{2} \leq 225$ $Graph the inequality. - 9 x^{2}-25 y^{2} \leq 225$

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

Graph the system of inequalities. - -\leq1 +\leq36 $Graph the system of inequalities. - \begin{array}{l}\frac{x^{2}}{9}-\frac{y^{2}}{16} \leq 1 \\ x^{2}+y^{2} \leq 36\end{array}$

Solve the problem by using a nonlinear system. -A garden contains two square vegetable beds. Find the length of each bed if the sum of their areas is $1205 \mathrm{ft}^{2}$ and the difference of their areas is $147 \mathrm{ft}^{2}$ .

Solve the system by the elimination method or a combination of the elimination and substitution methods. - $x^{2}+y^{2}=73$ $\mathrm{x}^{2}-\mathrm{y}^{2}=55$

Identify the graph of the equation as a parabola, circle, ellipse, or hyperbola. - $3 x^{2}-y=13$

Evaluate the expression. - $[[7.6]]$

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

Find the equation of a circle satisfying the given conditions. -Center: $(0,-2)$ ; radius: $\sqrt{10}$