Question 1

Describe the graph of the solution set of the following inequality:
$25 x^{2}+36 y^{2}>16$

Accepted Answer

The graph of the reg

Question 2

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

Accepted Answer

A) $\begin{aligned} y & >x^{2}-4 \ y & >3\end{aligned}$ B) $\begin{aligned} y & >x^{2}-4 \ y & 3\end{aligned}$ D) $y< x^{2}-4$ $\mathrm{y}<3$ A) $\begin{aligned} y & >x^{2}-4 \ y & >3\end{aligned}$ B) $\begin{aligned} y & >x^{2}-4 \ y & 3\end{aligned}$ D) $y< x^{2}-4$ $\mathrm{y}<3$

Question 3

Solve the system by the substitution method.
-$6 x^{2}-y^{2}=30$
$\mathrm{y}=\mathrm{x}^{2}-5$

Accepted Answer

A)  $\{(-\sqrt{5}, 0),(\sqrt{5}, 0)\}$ 
B)  $\{\{-\sqrt{11}, 6),(\sqrt{11}, 6)\}$ 
C)  $\{(-\sqrt{5}, 0),(\sqrt{5}, 0),(-\sqrt{11}, 6),(\sqrt{11}, 6)\}$ 
D)  $\{(0,-\sqrt{5}),(0, \sqrt{5}),(6,-\sqrt{11}),(6, \sqrt{11})\}$ 
A)  $\{(-\sqrt{5}, 0),(\sqrt{5}, 0)\}$ 
B)  $\{\{-\sqrt{11}, 6),(\sqrt{11}, 6)\}$ 
C)  $\{(-\sqrt{5}, 0),(\sqrt{5}, 0),(-\sqrt{11}, 6),(\sqrt{11}, 6)\}$ 
D)  $\{(0,-\sqrt{5}),(0, \sqrt{5}),(6,-\sqrt{11}),(6, \sqrt{11})\}$

Question 4

Choose the inequality that matches the graph.
-

Accepted Answer

A) $y>x^{2}+2 x+6$ B) $y< x^{2}+2 x+6$ C) $y \leq x^{2}+2 x+6$ D) $y \geq x^{2}+2 x+6$ A) $y>x^{2}+2 x+6$ B) $y< x^{2}+2 x+6$ C) $y \leq x^{2}+2 x+6$ D) $y \geq x^{2}+2 x+6$

Question 5

Find the center and radius of the circle whose equation is given. Graph the circle.
-$(x+5)^{2}+(y+1)^{2}=9$

Accepted Answer

A)  center: $(-5,-1)$; radius: 9
  
B)  center: $(5,1)$; radius: 9
  
C)  center: $(-5,-1)$; radius: 3
  
D)  center: $(5,1)$; radius: 3
  
A)  center: $(-5,-1)$; radius: 9
  
B)  center: $(5,1)$; radius: 9
  
C)  center: $(-5,-1)$; radius: 3
  
D)  center: $(5,1)$; radius: 3

Question 6

Find the center and radius of the circle.
-$x^{2}+y^{2}+8 x+12 y+16=0$

Accepted Answer

A)  $(4,6) ; r=36$ 
B)  $(6,4) ; r=36$ 
C)  $(-4,-6) ; \mathrm{r}=6$ 
D)  $(-6,-4) ; r=6$ 
A)  $(4,6) ; r=36$ 
B)  $(6,4) ; r=36$ 
C)  $(-4,-6) ; \mathrm{r}=6$ 
D)  $(-6,-4) ; r=6$

Question 7

Graph the circle.
-$2 y^{2}=32-2 x^{2}$

Accepted Answer

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

Question 8

Solve the problem by using a nonlinear system.
-In 1982, City $\# 1$ and City $\# 2$ had the same population. The population of City $\# 2$ continued to increase steadily, while the rate of population growth of City $\# 1$ (although initially less than that of City \#2) eventually overtook the growth rate of City \#2. The populations of two cities are modeled by the following equations: City $\# 1: y=2 x^{2}+15 x+1192$; City $\# 2: y=25 x+1192$, where $x=0$ corresponds to the year 1982. In what year after 1982 did the cities have the same population?

Accepted Answer

A)  1987 
B)  1988 
C)  1986 
D)  1985 
A)  1987 
B)  1988 
C)  1986 
D)  1985

Question 9

Graph the system of inequalities.
-$ \begin{array}{c}x-2 y \leq 2 \ x+y \leq 0\end{array} $

Accepted Answer

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

Question 10

Solve the system by the substitution method.
-$x^{2}-y^{2}=39$
$\mathrm{x}-\mathrm{y}=3$

Accepted Answer

A)  $\{(-8,-5)\}$ 
B)  $\{(8,5)\}$ 
C)  $\{(8,-5)\}$ 
D)  $\{(-8,5)\}$ 
A)  $\{(-8,-5)\}$ 
B)  $\{(8,5)\}$ 
C)  $\{(8,-5)\}$ 
D)  $\{(-8,5)\}$

Question 11

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

Accepted Answer

A) 
  
B) 
  
C)

D) 
  
A) 
  
B) 
  
C)

D)

Question 12

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.
- 
$$\begin{aligned}
& y=-\frac{1}{2} x^{2} \
& x+y=-4
\end{aligned}$$

Accepted Answer

A)  $(-8,4)$ 
B)  $(4,-6)$ 
C)  $(4,-8)$ 
D)  $(4,8)$ 
A)  $(-8,4)$ 
B)  $(4,-6)$ 
C)  $(4,-8)$ 
D)  $(4,8)$

Question 13

The lowest point on the graph of $f(x)=|x|+18$ has what coordinates?

Accepted Answer

A)  $(18,18)$ 
B)  $(0,0)$ 
C)  $(18,0)$ 
D)  $(0,18)$ 
A)  $(18,18)$ 
B)  $(0,0)$ 
C)  $(18,0)$ 
D)  $(0,18)$

Question 14

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.
- 
$$\begin{aligned}
& y=-\frac{1}{3} x^{2}+5 \
& x-y=1 \
\end{aligned}$$

Accepted Answer

A)  $(-7,-6)$ 
B)  $(-6,-7)$ 
C)  $(6,7)$ 
D)  $(-5,-8)$ 
A)  $(-7,-6)$ 
B)  $(-6,-7)$ 
C)  $(6,7)$ 
D)  $(-5,-8)$

Question 15

Graph the inequality.
-$ y \leq-x^{2}-4 x-5 $

Accepted Answer

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

Question 16

Solve the system by the elimination method or a combination of the elimination and substitution methods.
-$x^{2}+3 x y+y^{2}=4$
$x^{2}-3 x y-y^{2}=4$

Accepted Answer

A)  $\{(2,0),(-2,0)\}$ 
B)  $\{(2,0),(-2,0),(2,-6),(-2,6)\}$ 
C)  $\{(0,2),(0,-2),(2,-6),(-2,6)\}$ 
D)  $\{(2,-6),(-2,6)\}$ 
A)  $\{(2,0),(-2,0)\}$ 
B)  $\{(2,0),(-2,0),(2,-6),(-2,6)\}$ 
C)  $\{(0,2),(0,-2),(2,-6),(-2,6)\}$ 
D)  $\{(2,-6),(-2,6)\}$

Question 17

The range of the square root function, given by $f(x)=\sqrt{x}$, is__________

Accepted Answer

A)  $(-\infty, 0]$ 
B)  $[0, \infty)$ 
C)  $(-\infty, \infty)$ 
D)  $[0, \infty)$. 
A)  $(-\infty, 0]$ 
B)  $[0, \infty)$ 
C)  $(-\infty, \infty)$ 
D)  $[0, \infty)$.

Question 18

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

Accepted Answer

A)  $\mathrm{y}_{1}=2+\sqrt{1+(\mathrm{x}-2)^{2}}, \mathrm{y}_{2}=2-\sqrt{1+(\mathrm{x}-2)^{2}}$ 
B)  $\mathrm{y}_{1}=\sqrt{1-(\mathrm{x}-2)^{2}}, \mathrm{y}_2=-\sqrt{1-(\mathrm{x}-2)^{2}}$ 
C)  $\mathrm{y}_{1}=2+\sqrt{1-(\mathrm{x}-2)^{2}}, \mathrm{y}_{2}=2-\sqrt{1-(\mathrm{x}-2)^{2}}$ 
D)  $y_{1}=2+\sqrt{(x-2)^{2}-1}, y_{2}=2-\sqrt{(x-2)^{2}-1}$ 
A)  $\mathrm{y}_{1}=2+\sqrt{1+(\mathrm{x}-2)^{2}}, \mathrm{y}_{2}=2-\sqrt{1+(\mathrm{x}-2)^{2}}$ 
B)  $\mathrm{y}_{1}=\sqrt{1-(\mathrm{x}-2)^{2}}, \mathrm{y}_2=-\sqrt{1-(\mathrm{x}-2)^{2}}$ 
C)  $\mathrm{y}_{1}=2+\sqrt{1-(\mathrm{x}-2)^{2}}, \mathrm{y}_{2}=2-\sqrt{1-(\mathrm{x}-2)^{2}}$ 
D)  $y_{1}=2+\sqrt{(x-2)^{2}-1}, y_{2}=2-\sqrt{(x-2)^{2}-1}$

Question 19

Solve the system by the substitution method.
-$y=x^{2}-8 x+16$
$\mathrm{x}+\mathrm{y}=6$

Accepted Answer

A)  $\{(5,1),(2,4)\}$ 
B)  $\{(4,2)\}$ 
C)  $\{(-5,11),(-2,8)\}$ 
D)  $\{(5,11),(2,4)\}$ 
A)  $\{(5,1),(2,4)\}$ 
B)  $\{(4,2)\}$ 
C)  $\{(-5,11),(-2,8)\}$ 
D)  $\{(5,11),(2,4)\}$

Question 20

Find the center and radius of the circle.
-$x^{2}+y^{2}-4 x+2 y-20=0$

Accepted Answer

A)  $(1,-2) ; r=25$ 
B)  $(2,-1) ; r=5$ 
C)  $(-1,2) ; \mathrm{r}=5$ 
D)  $(-2,1) ; r=25$ 
A)  $(1,-2) ; r=25$ 
B)  $(2,-1) ; r=5$ 
C)  $(-1,2) ; \mathrm{r}=5$ 
D)  $(-2,1) ; r=25$

Describe the graph of the solution set of the following inequality: $25 x^{2}+36 y^{2}>16$

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

Solve the system by the substitution method. - $6 x^{2}-y^{2}=30$ $\mathrm{y}=\mathrm{x}^{2}-5$

Choose the inequality that matches the graph. -

Find the center and radius of the circle whose equation is given. Graph the circle. - $(x+5)^{2}+(y+1)^{2}=9$ $Find the center and radius of the circle whose equation is given. Graph the circle. - (x+5)^{2}+(y+1)^{2}=9$

Find the center and radius of the circle. - $x^{2}+y^{2}+8 x+12 y+16=0$

Graph the circle. - $2 y^{2}=32-2 x^{2}$ $Graph the circle. - 2 y^{2}=32-2 x^{2}$

Graph the system of inequalities. - x-2y\leq2 x+y\leq0 $Graph the system of inequalities. - \begin{array}{c}x-2 y \leq 2 \\ x+y \leq 0\end{array}$

Solve the system by the substitution method. - $x^{2}-y^{2}=39$ $\mathrm{x}-\mathrm{y}=3$

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

The lowest point on the graph of $f(x)=|x|+18$ has what coordinates?

Graph the inequality. - $y \leq-x^{2}-4 x-5$ $Graph the inequality. - y \leq-x^{2}-4 x-5$

Solve the system by the elimination method or a combination of the elimination and substitution methods. - $x^{2}+3 x y+y^{2}=4$ $x^{2}-3 x y-y^{2}=4$

The range of the square root function, given by $f(x)=\sqrt{x}$ , is__________

Solve the system by the substitution method. - $y=x^{2}-8 x+16$ $\mathrm{x}+\mathrm{y}=6$

Find the center and radius of the circle. - $x^{2}+y^{2}-4 x+2 y-20=0$

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

Describe the graph of the solution set of the following inequality: 25x2+36y2>1625 x^{2}+36 y^{2}>1625x2+36y2>16

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

Solve the system by the substitution method. - 6x2−y2=306 x^{2}-y^{2}=306x2−y2=30 y=x2−5\mathrm{y}=\mathrm{x}^{2}-5y=x2−5

Choose the inequality that matches the graph. -

Find the center and radius of the circle whose equation is given. Graph the circle. - (x+5)2+(y+1)2=9(x+5)^{2}+(y+1)^{2}=9(x+5)2+(y+1)2=9

Find the center and radius of the circle. - x2+y2+8x+12y+16=0x^{2}+y^{2}+8 x+12 y+16=0x2+y2+8x+12y+16=0

Graph the circle. - 2y2=32−2x22 y^{2}=32-2 x^{2}2y2=32−2x2

Graph the system of inequalities. - x-2y\leq2 x+y\leq0

Solve the system by the substitution method. - x2−y2=39x^{2}-y^{2}=39x2−y2=39 x−y=3\mathrm{x}-\mathrm{y}=3x−y=3

Graph the rational function. -f(x) = - 1x+1\frac{1}{ x+1 }x+11​

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+y=-4

The lowest point on the graph of f(x)=∣x∣+18f(x)=|x|+18f(x)=∣x∣+18 has what coordinates?

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=-+5 x-y=1

Graph the inequality. - y≤−x2−4x−5 y \leq-x^{2}-4 x-5 y≤−x2−4x−5

Solve the system by the elimination method or a combination of the elimination and substitution methods. - x2+3xy+y2=4x^{2}+3 x y+y^{2}=4x2+3xy+y2=4 x2−3xy−y2=4x^{2}-3 x y-y^{2}=4x2−3xy−y2=4

The range of the square root function, given by f(x)=xf(x)=\sqrt{x}f(x)=x​ , is__________

Solve the system by the substitution method. - y=x2−8x+16y=x^{2}-8 x+16y=x2−8x+16 x+y=6\mathrm{x}+\mathrm{y}=6x+y=6

Find the center and radius of the circle. - x2+y2−4x+2y−20=0x^{2}+y^{2}-4 x+2 y-20=0x2+y2−4x+2y−20=0

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

Describe the graph of the solution set of the following inequality: $25 x^{2}+36 y^{2}>16$

Solve the system by the substitution method. - $6 x^{2}-y^{2}=30$ $\mathrm{y}=\mathrm{x}^{2}-5$

Find the center and radius of the circle whose equation is given. Graph the circle. - $(x+5)^{2}+(y+1)^{2}=9$ $Find the center and radius of the circle whose equation is given. Graph the circle. - (x+5)^{2}+(y+1)^{2}=9$

Find the center and radius of the circle. - $x^{2}+y^{2}+8 x+12 y+16=0$

Graph the circle. - $2 y^{2}=32-2 x^{2}$ $Graph the circle. - 2 y^{2}=32-2 x^{2}$

Graph the system of inequalities. - x-2y\leq2 x+y\leq0 $Graph the system of inequalities. - \begin{array}{c}x-2 y \leq 2 \\ x+y \leq 0\end{array}$

Solve the system by the substitution method. - $x^{2}-y^{2}=39$ $\mathrm{x}-\mathrm{y}=3$

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

The lowest point on the graph of $f(x)=|x|+18$ has what coordinates?

Graph the inequality. - $y \leq-x^{2}-4 x-5$ $Graph the inequality. - y \leq-x^{2}-4 x-5$

Solve the system by the elimination method or a combination of the elimination and substitution methods. - $x^{2}+3 x y+y^{2}=4$ $x^{2}-3 x y-y^{2}=4$

The range of the square root function, given by $f(x)=\sqrt{x}$ , is__________

Solve the system by the substitution method. - $y=x^{2}-8 x+16$ $\mathrm{x}+\mathrm{y}=6$

Find the center and radius of the circle. - $x^{2}+y^{2}-4 x+2 y-20=0$