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Domain and range of absolute value functions: equations

x

.\begin{align*}x^{2}+12x+36&=0\newline x&=\square\end{align*}

7

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a=\left(\begin{array}{l}2 \\ 3\end{array}\right),|a|=

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\sqrt{ }(13)

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5

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13

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4

\begin{array}{l}y=-2 x+19 \\ -2 x+4 y=16\end{array}

\begin{array}{l}\quad A=\left[\begin{array}{lll}1 & 2 & 3 \\ 4 & 5 & 6 \\ 7 & 8 & 9\end{array}\right] \quad B=\left[\begin{array}{ccc}2 & 4 & 6 \\ 8 & 10 & 12 \\ 14 & 16 & 18\end{array}\right] \quad C=\left[\begin{array}{ccc}1 & 3 & 5 \\ 7 & 9 & 11 \\ 13 & 15 & 17\end{array}\right] \\ 2 A-3 B+4 C\end{array}

1

. Fungsi Tujuan : Meminimumkan

\mathrm{C}=3 \times 1+4 \mathrm{X} 2

Fungsi Batasan :

1

2 X 1+X 2 \geq 6.000

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2

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\begin{array}{l} x 1+3 x 2 \geq 9.000 \\ x 1 \geq 0, x 2 \geq 0 \end{array}

\begin{array}{rr} 4 \\ 4^{2}+4^{2}=x^{2} & \\ 16+16=x^{2} & x=\sqrt{x^{2}}=\sqrt{32} \\ 32=x^{2} & \text { or } 4 \sqrt{2} \\ & \text { or } 5.656 \ldots \end{array}

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3

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\mathrm{U}=1,5,6,8,10,12

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=8

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What is the complement of Set B in Set U?

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\{8\}

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\{1,5,6,10,12\}

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\{1,8,10,12\}

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\{1,5,6,8,10,12\}

Which of the following are integers?

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Multi-select Choices:

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3

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8

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\pi

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\frac{2}{7}

Utilizar la calculadora gráfica de ALEKS para resolver el sistema de ecuaciones.

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\begin{array}{l} 6-0.9 x=0.4 y \\ -y+0.2 x=3.6 \end{array}

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Redondear a la centésima más cercana.

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(x, y)=(\square, \square)

Suppose that the functions

f

g

are defined as follows.

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f(x)=\frac{4}{x+7}\quad g(x)=\frac{5}{x}

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\frac{f}{g}

. Then, give its domain using an interval or union of intervals.

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Simplify your answers.

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\left(\frac{f}{g}\right)(x)=\prod2

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\frac{f}{g}

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\left[\left(\frac{\square}{\square},\square^{\square},(\square,\square)\right),\left[\square,\square\right],\square\cup\square,(\square,\square]\right),\left[\square,\square\right),\mathcal{O}/,\infty\right),\left[-\infty,\square\right),\left[\times,\(5\right]:\}

f(x)=\cos[e^x–\sin(x)]

\begin{cases} g(1) = -5 \\ g(2) = 3 \\ g(n) = g(n-2) + g(n-1) \end{cases}

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g(3)=\square

v

\begin{align*} -\frac{9}{8} &= v - \frac{1}{2}, \ v &= \Box \end{align*}

r

\begin{array}{l} -10-5r=-6r-1 \ r=\dots \end{array}

Find the value of

A

that makes the following equation true for all values of

x

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\begin{array}{l} 3^{x}-3^{x-2}=A \cdot 3^{x} \\ A= \end{array}

Find the value of

A

that makes the following equation true for all values of

x

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\begin{array}{l} 5^{x}+5^{x+3}=A \cdot 5^{x} \\ A= \end{array}

Find the expression for

f(x)

that makes the following equation true for all values of

x

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\begin{array}{l} \frac{81^{x}}{9^{5 x-8}}=9^{f(x)} \\ f(x)=\square \end{array}

Which of the following functions are continuous for all real numbers?

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\begin{array}{l} g(x)=\sqrt[5]{x} \\ h(x)=\sqrt[3]{x} \end{array}

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1

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g

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h

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g

h

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g

h

Which of the following functions are continuous at

x=-2

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\begin{array}{l} h(x)=\sqrt[3]{x+1} \\ f(x)=\sqrt[4]{x+1} \end{array}

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1

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h

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f

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h

f

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h

f

Which of the following functions are continuous at

x=0

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\begin{array}{l} f(x)=\tan (x) \\ g(x)=\cot (x) \end{array}

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1

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f

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g

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f

g

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f

g

Which of the following functions are continuous at

x=1

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\begin{array}{l} f(x)=e^{x}-1 \\ g(x)=\ln \left(e^{x}-1\right) \end{array}

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1

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f

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g

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f

g

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f

g

Which of the following functions are continuous at

x=3

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\begin{array}{l} g(x)=\ln (x-3) \\ f(x)=e^{x-3} \end{array}

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1

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g

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f

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g

f

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g

f

f(x)=\left\{\begin{array}{ll} x^{2} & \text { for } x \leq 0 \\ \ln (x) & \text { for } x>0 \end{array}\right.

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\lim _{x \rightarrow 1} f(x)

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1

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0

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1

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e

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(D) The limit doesn't exist.

h(x)=\left\{\begin{array}{ll} \cos (x) & \text { for } x<\pi \\ \sin (x) & \text { for } x \geq \pi \end{array}\right.

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\lim _{x \rightarrow \pi^{+}} h(x)

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1

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-1

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0

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1

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(D) The limit doesn't exist.

f(x)=\left\{\begin{array}{ll} 2^{x} & \text { for } 0<x \leq 4 \\ 8 \sqrt{x} & \text { for } x>4 \end{array}\right.

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\lim _{x \rightarrow 4} f(x)

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1

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4

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8

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16

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(D) The limit doesn't exist.

g(x)=\left\{\begin{array}{ll} 2^{x}-1 & \text { for }-8 \leq x \\ \sqrt{x} & \text { for } x \geq 1 \end{array}\right.

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\lim _{x \rightarrow 4} g(x)

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1

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1

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2

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\mathbf{1 5}

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(D) The limit doesn't exist.

\begin{array}{l} g(x)=\frac{8 x-1}{x+4} \\ h(x)=3 x+10 \end{array}

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(g \circ h)(x)

as an expression in terms of

x

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(g \circ h)(x)=

\begin{array}{l} f(x)=\frac{2-x}{x+1} \\ g(x)=18-3 x \end{array}

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(f \circ g)(x)

as an expression in terms of

x

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(f \circ g)(x)=

What is the midline equation of the function

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\begin{array}{l} g(x)=-6 \sin (3 \pi x+4)-2 ? \\ y=\square \end{array}

What is the midline equation of the function

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\begin{array}{l} h(x)=-4 \cos (5 x-9)-7 ? \\ y=\square \end{array}

What is the midline equation of the function

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\begin{array}{l} g(x)=3 \sin (2 x-1)+4 ? \\ y=\square \end{array}

What is the midline equation of the function

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\begin{array}{l} g(x)=-\sin (8 x-3)+5 ? \\ y=\square \end{array}

What is the midline equation of

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\begin{array}{l} y=7 \sin \left(\frac{3 \pi}{4} x-\frac{\pi}{4}\right)+6 ? \\ y=\square \end{array}

What is the midline equation of the function

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\begin{array}{l} h(x)=5 \sin (4 x-2)-3 ? \\ y=\square \end{array}

What is the midline equation of

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\begin{array}{l} y=2 \sin \left(\frac{\pi}{2} x+3\right) ? \\ y=\square \end{array}

What is the midline equation of

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\begin{array}{l} y=-8 \cos \left(\frac{3 \pi}{2} x+1\right) ? \\ y=\square \end{array}

\begin{array}{l}z=-60-12 i \\ \operatorname{Re}(z)= \\ \operatorname{Im}(z)=\end{array}

\begin{array}{l} f(x)=\frac{1}{x-1} \\ g(x)=5 x+8 \end{array}

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f

g

are defined. What is the value of

f(g(-1))

\begin{aligned} a y & =\frac{3}{4} x \\ x-5 y & =0 \end{aligned}

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For what value of

a

does the system of linear equations in the variables

x

y

have infinitely many solutions?

\begin{array}{r} a y=2 x+1 \\ y=2 x+2 \end{array}

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Consider the system of equations, where

a

is a constant. For what value of

a

(x, y)

y=|x|

is shifted up by

7

units and to the left by

8

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What is the equation of the new graph?

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1

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y=|x+8|-7

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y=|x+8|+7

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y=|x-8|+7

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y=|x-8|-7

y=|x|

is shifted down by

6

units and to the left by

9

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What is the equation of the new graph?

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1

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y=|x+9|-6

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y=|x-9|+6

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y=|x+9|+6

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y=|x-9|-6

y=|x|

is shifted up by

4

units and to the right by

5

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What is the equation of the new graph?

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1

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y=|x+4|-5

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y=|x+5|+4

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y=|x-5|+4

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y=|x+4|+5

y=|x|

is shifted down by

9

units and to the right by

4

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What is the equation of the new graph?

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1

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y=|x-4|-9

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y=|x-9|+4

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y=|x-9|-4

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y=|x-4|+9

y=|x|

is reflected across the

x

-axis and then scaled vertically by a factor of

\frac{3}{8}

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What is the equation of the new graph?

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1

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y=\frac{8}{3}|x|

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y=-\frac{8}{3}|x|

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y=\frac{3}{8}|x|

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y=-\frac{3}{8}|x|

y=|x|

is scaled vertically by a factor of

\frac{7}{2}

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What is the equation of the new graph?

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1

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y=-\frac{2}{7}|x|

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y=-\frac{7}{2}|x|

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y=\frac{2}{7}|x|

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y=\frac{7}{2}|x|

y=|x|

is scaled vertically by a factor of

\frac{1}{5}

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What is the equation of the new graph?

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1

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y=\frac{1}{5}|x|

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y=-5|x|

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y=|x+5|

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y=|x-5|

What is the range of this function?

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\text{all real numbers}

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\{y \mid y \geq 0\}

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\{y \mid y \leq 0\}

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\{y \mid y > 0\}