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

Question 1

Graph the function.

-f(x)=|-1-x|

A)
B)
C)
D)

Answer 1

Question 2

Graph the function.

-f(x)=4|x|-9

A)
B)
C)
D)

Answer 2

Question 3

Graph the function.

-f(x)=|x-8|-6

A)

B)
C)

D)

Answer 3

Question 4

Graph the function.

-f(x)=3|x-5|-8

A)


B)

C)

D)

Question 5

Graph the rational function.

-f(x) = $\frac{1}{ x - 3}$

A)
B)

C)
D)

Question 6

Graph the rational function.

-f(x) = $\frac{1}{ x }$

A)

B)
C)
D)

Question 7

Graph the rational function.

-f(x) = - $\frac{2}{ x }$

A)

B)
C)

D)

Question 8

Graph the rational function.

-f(x) = - $\frac{1}{ x+1 }$

A)


B)


C)


D)

Question 9

Graph the rational function.

-f(x) = $\frac{1}{ x }$ + 3

A)


B)

C)


D)

Question 10

Graph the rational function.

-f(x) = $\frac{4}{ x }$ + 3

A)
B)
C)
D)

Question 11

Graph the function.

- $f(x)=\sqrt{x+4}$

A)

B)

C)

D)

Question 12

Graph the function.

- $f(x)=\sqrt{x+5}+2$

A)

B)

C)

D)

Question 13

Graph the function. Give the domain and range.

- $f(x)=|x+3|$

A) Domain: $(-\infty, \infty)$ ; Range: $[0, \infty)$


B) Domain: $(-\infty, \infty)$ ; Range: $[3, \infty)$

C) Domain: $(-\infty, \infty)$ ; Range: $[-3, \infty)$

D) Domain: $(-\infty, \infty)$ ; Range: $[0, \infty)$

Question 14

Graph the function. Give the domain and range.

- $f(x)=|x-4|$

A) Domain: $(-\infty, \infty)$ ; Range: $[0, \infty)$


B) Domain: $(-\infty, \infty)$ ; Range: $[-4, \infty)$

C) Domain: $(-\infty, \infty)$ ; Range: $[4, \infty)$


D) Domain: $(-\infty, \infty)$ ; Range: $[0, \infty)$

Question 15

Graph the function. Give the domain and range.

- $f(x)=|x-3|+1$

A) Domain: $(-\infty, \infty)$ ; Range: $[1, \infty)$

B) Domain: $(-\infty, \infty)$ ; Range: $[1, \infty)$

C) Domain: $(-\infty, \infty)$ ; Range: $[-1, \infty)$

D) Domain: $(-\infty, \infty)$ ; Range: $[-1, \infty)$

Question 16

Graph the function. Give the domain and range.

- $f(x)=|x+3|+6$

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 17

Evaluate the expression.

- $[[5]]$

A) 4
B) -5
C) 5
D) 6

Question 18

Evaluate the expression.

- $[[7.6]]$

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

Question 19

Evaluate the expression.

-[[-18]]

A) -17
B) -18
C) -19
D) 18

Question 20

Evaluate the expression.

- $[[-20.7]]$

A) -19
B) -21
C) -20
D) -8

Question 21

Evaluate the expression.

- $\llbracket \frac{1}{7} \rrbracket$

A) 1
B) 0
C) $\frac{1}{7}$
D) 7

Question 22

Graph the step function.

- $f(x)=\llbracket x+5 \rrbracket$

A)

B)

C)


D)

Question 23

Graph the step function.

- $f(x)=\llbracket x-5 \rrbracket$

A)
B)
C)
D)

Question 24

Graph the step function.

-Assume it costs 25 cents to mail a letter weighing one ounce or less, and then 20 cents for each additional ounce or fraction of an ounce. Let $\mathrm{L}(\mathrm{x})$ be the cost of mailing a letter weighing $\mathrm{x}$ ounces. Graph $y=L(x)$ . Use the interval $(0,4]$ .

A)

B)

C)

D)

Question 25

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

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

Question 26

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

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

Question 27

What is the domain of the greatest integer function, given by $f(x)=[[x]]$ ?

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

Question 28

What is the only real number not in the domain of $f(x)=\frac{1}{x-3}$ ?

A) -3
B) $x-3$
C) 3
D) 0

Question 29

Choose the equation that matches the graph.

-

A) $(x-1)^{2}+(y-3)^{2}=9$
B) $(x-1)^{2}-(y-3)^{2}=9$
C) $(x-1)^{2}-(y-3)^{2}=3$
D) $(x-1)^{2}+(y-3)^{2}=3$

Question 30

Choose the equation that matches the graph.

-

A) $(x+5)^{2}+(y-5)^{2}=9$
B) $(x-5)^{2}+(y+5)^{2}=9$
C) $(x+5)^{2}+(y+5)^{2}=9$
D) $(x-5)^{2}+(y-5)^{2}=9$

Question 31

Find the equation of a circle satisfying the given conditions.

-Center: $(1,-1)$ ; radius: 12

A) $(x+1)^{2}+(y-1)^{2}=12$
B) $(x-1)^{2}+(y+1)^{2}=144$
C) $(x-1)^{2}+(y+1)^{2}=12$
D) $(x+1)^{2}+(y-1)^{2}=144$

Question 32

Find the equation of a circle satisfying the given conditions.

-Center: $(1,0)$ ; radius: 2

A) $x^{2}+(y-1)^{2}=2$
B) $(x-1)^{2}+y^{2}=4$
C) $(x+1)^{2}+y^{2}=4$
D) $x^{2}+(y+1)^{2}=2$

Question 33

Find the equation of a circle satisfying the given conditions.

-Center: $(0,4)$ ; radius: 10

A) $x^{2}+(y+4)^{2}=10$
B) $(x-4)^{2}+y^{2}=100$
C) $x^{2}+(y-4)^{2}=100$
D) $(x+4)^{2}+y^{2}=100$

Question 34

Find the equation of a circle satisfying the given conditions.

-Center: $(0,-2)$ ; radius: $\sqrt{10}$

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 35

Find the equation of a circle satisfying the given conditions.

-Center: $(10,0)$ ; radius: $\sqrt{13}$

A) $x^{2}+(y+10)^{2}=169$
B) $(x+10)^{2}+y^{2}=13$
C) $x^{2}+(y-10)^{2}=169$
D) $(x-10)^{2}+y^{2}=13$

Question 36

Find the center and radius of the circle.

- $x^{2}+y^{2}+8 x+12 y+16=0$

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

Question 37

Find the center and radius of the circle.

- $x^{2}+y^{2}+18 x+4 y+4=0$

A) $(-9,-2) ; r=9$
B) $(2,9) ; \mathrm{r}=81$
C) $(9,2) ; \mathrm{r}=81$
D) $(-2,-9) ; \mathrm{r}=9$

Question 38

Find the center and radius of the circle.

- $x^{2}+y^{2}-4 x+2 y-20=0$

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

Question 39

Graph the circle.

- $x^{2}+y^{2}=100$

A)
B)
C)
D)

Question 40

Graph the circle.

- $(x-6)^{2}+(y-2)^{2}=16$

A)
B)
C)
D)

Question 41

Graph the circle.

- $x^{2}+(y-3)^{2}=16$

A)
B)
C)
D)

Question 42

Graph the circle.

- $(x-5)^{2}+y^{2}=9$

A)

B)

C)

D)

Question 43

Graph the circle.

- $x^{2}+y^{2}-8 x-8 y+7=0$

A)

B)
C)

D)

Question 44

Graph the circle.

- $x^{2}+y^{2}+2 x+8 y+8=0$

A)
B)
C)
D)

Question 45

Graph the circle.

- $2 y^{2}=32-2 x^{2}$

A)
B)
C)
D)

Question 46

Graph the ellipse.

- $\frac{x^{2}}{4}+\frac{y^{2}}{49}=1$

A)
B)
C)
D)

Question 47

Graph the ellipse.

- $\frac{(x+5)^{2}}{9}+\frac{(y-1)^{2}}{4}=1$

A)
B)
C)
D)

Question 48

Graph the ellipse.

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

A)
B)
C)
D)

Question 49

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?

- $x^{2}+y^{2}=25$

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

B) $\mathrm{y}_{1}=\sqrt{25-\mathrm{x}^{2}}, \mathrm{y}_2=-\sqrt{25-\mathrm{x}^{2}}$

C) $y_{1}=\sqrt{x^{2}-25}, y_{2}=-\sqrt{x^{2}-25}$

D) $y_{1}=\sqrt{25+x^{2}}, y_{2}=-\sqrt{25-x^{2}}$

Question 50

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?

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

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 51

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?

- $\frac{x^{2}}{16}+\frac{y^{2}}{25}=1$

A) $y_1=5 \sqrt{1+\frac{x^{2}}{16}}, y_2=-5 \sqrt{1+\frac{x^{2}}{16}}$

B) $\mathrm{y}_{1}=5 \sqrt{1-\frac{\mathrm{x}}{4}}, \mathrm{y}_{2}=-5 \sqrt{1-\frac{\mathrm{x}}{4}}$

C) $y_{1}=5 \sqrt{1-\frac{x^{2}}{16}}, y_{2}=-5 \sqrt{1-\frac{x^{2}}{16}}$

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

Question 52

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?

- $(x-5)^{2}+y^{2}=25$

A) $y_{1}=\sqrt{25-(x-5)^{2}}, y_{2}=-\sqrt{25-(x-5)^{2}}$

B) $y_{1}=5+\sqrt{x-5}, y_{2}=5-\sqrt{x-5}$

C) $y_{1}=25+\sqrt{x-5}, y_{2}=25-\sqrt{x-5}$

D) $y 1=\sqrt{25+(x-5)^{2}}, y 2=-\sqrt{25+(x-5)^{2}}$

Question 53

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?

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

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 54

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?

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

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 55

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?

- $x^{2}+\frac{(y+5)^{2}}{25}=1$

A) $y_{1}=5+5 \sqrt{1+x^{2}}, y_{2}=5-5 \sqrt{1+x^{2}}$

B) $y_{1}=-5+5 \sqrt{1+x^{2}}, y_{2}=-5-5 \sqrt{1+x^{2}}$

C) $y_{1}=5+5 \sqrt{1-x^{2}}, y_{2}=5-5 \sqrt{1-x^{2}}$

D) $y_{1}=-5+5 \sqrt{1-x^{2}}, y_{2}=-5-5 \sqrt{1-x^{2}}$

Question 56

Solve the problem.

-An elliptical riding path is to be built on a rectangular piece of property that measures $6 \mathrm{mi}$ by $4 \mathrm{mi}$ . Find an equation for the ellipse, where $\mathrm{x}$ and $\mathrm{y}$ are measured in $\mathrm{mi}$ , if the path is to touch the center of the property line on all 4 sides.

A) $\frac{x^{2}}{4}+\frac{y^{2}}{9}=1$

B) $\frac{x^{2}}{9}+\frac{y^{2}}{4}=1$

C) $\frac{x^{2}}{4}+\frac{y^{2}}{36}=1$

D) $\frac{x^{2}}{36}+\frac{y^{2}}{4}=1$

Question 57

Solve the problem.

-A railroad tunnel has the shape of half an ellipse. The height of the tunnel at the center is $52 \mathrm{ft}$ and the vertical clearance must be $26 \mathrm{ft}$ at a point $24 \mathrm{ft}$ from the center. Find an equation for the ellipse, where $\mathrm{x}$ and $\mathrm{y}$ are measured in $\mathrm{ft}$ .

A) $\frac{x^{2}}{768}+\frac{y^{2}}{676}=1$

B) $\frac{x^{2}}{576}+\frac{y^{2}}{2704}=1$

C) $\frac{x^{2}}{2704}+\frac{y^{2}}{768}=1$

D) $\frac{x^{2}}{768}+\frac{y^{2}}{2704}=1$

Question 58

Solve the problem.

-A satellite is to be put into an elliptical orbit around a moon. The moon is a sphere with radius 589 $\mathrm{km}$ . Determine an equation for the ellipse, where $\mathrm{x}$ and $\mathrm{y}$ are measured in $\mathrm{km}$ , if the distance of the satellite from the surface of the moon varies from $864 \mathrm{~km}$ to $174 \mathrm{~km}$ .

A) $\frac{x^{2}}{1453}+\frac{y^{2}}{763}=1$

B) $\frac{x^{2}}{763^{2}}+\frac{y^{2}}{1453^{2}}=1$

C) $\frac{x^{2}}{864^{2}}+\frac{y^{2}}{174^{2}}=1$

D) $\frac{x^{2}}{174}+\frac{y^{2}}{864}=1$

Question 59

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.

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

Question 60

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.

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

Question 61

The circle with equation $x^{2}+y^{2}=25$ has center at $(5,5)$ .

Question 62

The circle with equation $(x+7)^{2}+(y+5)^{2}=49$ has center at $(7,5)$ .

Question 63

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

Question 64

The equation of a semicircle that is the upper half of the circle centered at the origin with radius 2 is $y=\sqrt{4-x^{2}}$ .

Question 65

The $x$ -intercepts of the ellipse with equation $\frac{x^{2}}{4}+\frac{y^{2}}{36}=1$ are $(2,0)$ and $(-2,0)$ .

Question 66

The $y$ -intercepts of the ellipse with equation $\frac{x^{2}}{36}+\frac{y^{2}}{64}=1$ are $(0,6)$ and $(0,-6)$ .

Question 67

The $y$ -intercepts of the ellipse with equation $\frac{x^{2}}{16}+\frac{y^{2}}{81}=1$ are $(0,81)$ and $(0,-81)$ .

Question 68

The graph of the equation $\frac{x}{16}+\frac{y}{25}=1$ is an ellipse.

Question 69

Choose the equation that matches the graph.

-

A) $\frac{x^{2}}{49}+\frac{y^{2}}{16}=1$

B) $\frac{y^{2}}{49}-\frac{x^{2}}{16}=1$

C) $\frac{x^{2}}{16}+\frac{y^{2}}{49}=1$

D) $\frac{x^{2}}{16}-\frac{y^{2}}{49}=1$

Question 70

Choose the equation that matches the graph.

-

A) $\frac{(x+3)^{2}}{9}+\frac{(y-1)^{2}}{25}=1$

B) $\frac{(x+3)^{2}}{9}-\frac{(y-1)^{2}}{25}=1$

C) $\frac{(x+3)^{2}}{25}+\frac{(y-1)^{2}}{9}=1$

D) $\frac{(y-1)^{2}}{25}-\frac{(x+3)^{2}}{9}=1$

Question 71

Choose the equation that matches the graph.

-

A) $\frac{x^{2}}{4}+\frac{y^{2}}{16}=1$

B) $\frac{x^{2}}{4}-\frac{y^{2}}{16}=1$

C) $\frac{x^{2}}{16}-\frac{y^{2}}{4}=1$

D) $\frac{x^{2}}{16}+\frac{y^{2}}{4}=1$

Question 72

Choose the equation that matches the graph.

-

A) $\frac{x^{2}}{36}+\frac{y^{2}}{9}=1$

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

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

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

Question 73

Graph the hyperbola.

- $\frac{y^{2}}{25}-\frac{x^{2}}{64}=1$

A)


B)

C)

D)

Question 74

Graph the hyperbola.

- $\frac{x^{2}}{16}-\frac{y^{2}}{36}=1$

A)
B)
C)
D)

Question 75

Graph the hyperbola.

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

A)
B)
C)
D)

Question 76

Graph the hyperbola.

- $\frac{x^{2}}{9}-\frac{y^{2}}{25}=1$

A)

B)

C)
D)

Question 77

Graph the hyperbola.

- $\frac{y^{2}}{16}-\frac{x^{2}}{16}=1$

A)
B)
C)
D)

Question 78

Graph the hyperbola.

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

A)

B)

C)
D)

Question 79

Identify the graph of the equation as a parabola, circle, ellipse, or hyperbola.

- $x^{2}+y^{2}=9$

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

Question 80

Identify the graph of the equation as a parabola, circle, ellipse, or hyperbola.

- $3 x^{2}-y=13$

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