微積分
極限、導數、最優化與函數性質。
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questions: 1. a ______ is a share of ownership in a company. a. bond b.…
### First Section 1. b. Stock 2. c. A type of investment that invests in a mix of different types of investment 3. a. Bond ### Second Section 1. d. increasing your financial aware…
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2. write the equation of the line that is perpendicular to y = 8x + 4 a…
$y = -\frac{1}{8}x - 2$
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complete the table and then graph the function. $y = -5$ | x | y | | -1…
For \( x = -10 \), \( y = -5 \); for \( x = 6 \), \( y = -5 \); for \( x = 7 \), \( y = -5 \). So the completed table (filling the blanks) has \( y \)-values of -5, -5, -5 for \( …
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ol2: problem 3 (1 point) evaluate the indefinite integral. \\(\\int xe^…
$\frac{1}{2}xe^{2x} - \frac{1}{4}e^{2x}$
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complete the table and then graph the function. y = -4x x | y -2 | 0 | …
When \( x = -2 \), \( y = 8 \); when \( x = 0 \), \( y = 0 \); when \( x = 2 \), \( y = -8 \). So the completed table (for the \( y \)-values) is 8, 0, -8 respectively.
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ol2: problem 1 (1 point) use integration by parts to evaluate the integ…
$2x^2\ln(2x) - x^2$
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move at least one of the 5 guide points below to complete the graph of …
To complete the graph of \( y=(x - 5)^2 \): 1. Move the blue vertex point from \( (0,0) \) to \( (5,0) \). 2. Adjust the red points to be symmetric about \( x = 5 \): - For a poin…
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6. $y = \\frac{3}{4}x + 3$
To graph \(y=\frac{3}{4}x + 3\): 1. Plot the y - intercept \((0,3)\) (already marked). 2. Use the slope \(\frac{3}{4}\): from \((0,3)\), move 4 units right and 3 units up to get \…
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move at least one of the 5 guide points below to complete the graph of …
Move the blue vertex point to \( (6,0) \) and adjust the red points to lie on \( y=(x - 6)^2 \) (e.g., \( (5,1) \), \( (7,1) \), \( (4,4) \), \( (8,4) \)) to complete the graph.
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$\\sqrt3{648}+\\sqrt3{2000}$
Approximately 21.25 (or more precisely, $6\sqrt[3]{3}+10\sqrt[3]{2}$ or the decimal approximation as above).
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2. evaluate: 2 × (4^2 - 2) 3. evaluate: 12 ÷ (3^2 - 1) + 2 4. evaluate:…
Problem 2: 28 Problem 3: 3.5 Problem 4: 33 Problem 5: 6 Challenge Problem: 29
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set 3 decimal place value and rounding decimals fill in the blanks. 1 i…
0.7 2.
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¿qué ecuación tiene ceros reales correspondientes a la $x$-¿interseccio…
$y = \log_{3}(x) - 1$
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¿cómo explicarías la relación entre el cero real de la función y x-¿int…
Dado que el gráfico nunca cruza el $x$-eje, la función no tiene ceros reales.
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for the given polynomial p(x) and c = -3, use the remainder theore p(x)…
384
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use synthetic division and the remainder theorem to find p(a). p(x)=x³+…
$9$
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(\frac{1}{3} + \frac{2}{9})
$\frac{5}{9}$
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the function ( f(x) = 2x - 8 ) is shifted 3 units up. which equation co…
D. \( g(x) = 2x - 5 \)
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o $f(x) = -sqrt{x + 2} + 2$ o $f(x) = sqrt{x + 2} - 2$ o $f(x) = -sqrt{…
$f(x)=\sqrt{x+2}$
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c) \\( f(x) = \\sqrt{x + 2} - 2 \\) \\( f(x) = \\sqrt{x + 2} \\) \\( f(…
$\boldsymbol{f(x) = \sqrt{x+2} - 2}$
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in public discussions about automation, the conversation often swings b…
B. even-handed
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b) \\(\\boldsymbol{f(x) = \\sqrt{x + 2}}\\) \\(\\boldsymbol{f(x) = -\\s…
$\boldsymbol{f(x) = -\sqrt{x+2} + 2}$ (Option 4)
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solve for x, $\\log_4 x = 2$ options: $x = 12$, $x = 16$, $x = 4$
x = 16
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let $f(x) = \\sqrt{x + 1}$ and $g(x) = 3x - 3$. find $f \\circ g$ and $…
a) $(f \circ g)(x) = \sqrt{3x - 2}$ b) $(g \circ f)(x) = 3\sqrt{x+1} - 3$
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6. a. $f(-3) =$ b. $f(4) =$ c. $f(1) =$ d. $f(-1) =$ e. $f(0) =$
a. $f(-3) = -2$ b. $f(4) = 4$ c. $f(1) = 1$ d. $f(-1) = 1$ e. $f(0) = 1$
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which point is on the line that passes through (0, 6) and is parallel t…
(-12, 8)
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let $f(x) = 6x + 2$. which of the following is the inverse of $f(x)$? -…
$\boldsymbol{f^{-1}(x)=\frac{x-2}{6}}$ (the second option)
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5. a. $f(-1) =$ b. $f(2) =$ c. $f(1) =$ d. $f(-2) =$ e. $f(0) =$
a. $-1$ b. $1$ c. $1$ d. $0$ e. $1$
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suppose $f(x)=x^3 + 1$. a) find the inverse function $f^{-1}(x)$.
$f^{-1}(x) = \sqrt[3]{x - 1}$
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there are many situations that have a minimum or maximum value and many…
1. Word Problem: A part-time job pays $12 per hour, plus a $50 weekly bonus for showing up on time every day. You need to earn at least $230 this week to pay your phone bill. How …
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how many zeros does this polynomial have? options: 3, 2, 0, 5
5
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4. $f(x) = \\begin{cases} |2x + 7|, & x \\leq -4 \\\\ 1 + x^2, & -4 < x…
a. $\frac{29}{3}$ b. $2$ c. $1$ d. $6$
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given $f(x) = x^2 + 3$ for $x \\geq 0$, find $f^{-1}(x)$. $f^{-1}(x) = $
$f^{-1}(x) = \sqrt{x - 3}$ (for $x \geq 3$)
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use synthetic substitution to evaluate the given value and determine th…
The remainder when \( f(x)=-4x^{4}+9x^{3}+8x^{2}+9x - 13 \) is evaluated at \( x = 3 \) using synthetic substitution is \( 5 \).
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2. $f(x)=\\begin{cases}x^3 - 7x, & x\\leq - 3\\\\8, & - 3 < x\\leq 3\\\…
a. $f(-5) = -90$ b. $f(11) = 5$ c. $f(0) = 8$ d. $f(3) = 8$
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use synthetic substitution to evaluate the given value and determine th…
The remainder is \(5\), so the value of \(f(3)\) is \(5\).
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3. $f(x)=\\begin{cases}\\ \\dfrac{3}{x + 4},&x < -5\\\\x^2 - 3x,&-5 < x…
a. $4$ b. $249$ c. $-\frac{1}{2}$ d. $0$
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obergefell v. hodges by justice anthony m. kennedy applying these estab…
The changing social climate may reverse earlier Court assumptions.
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use technology to find points and then graph the function $y = -(x - 2)…
Five points are (0, -2), (1, 1), (2, 2), (3, 1), (4, -2). Plot these on the graph.
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use the passage to answer the question. which word has a connotation th…
The word with a connotation suggesting disapproval is related to the negative context of unhealthy diets. Among the options, "exposure" (in the context of exposure to unhealthy di…
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© bridgeman art library / universal images group/ image quest 2015 whic…
Low prices made automobiles available to many Americans.
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k5 learning mixed addition and subtraction (2 - digits) math practice w…
s (row-wise): 14, 19, 141, 1, 126 115, 28, 12, 71, 35 28, 50, 7, 65, 45 110, 40, 140, 67, 170 80, 115, 45, 169, 71
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mals 176.81 5.32 0.92 + 0.8 ------ oge hundred eig ceight hundred six t…
\( 172.94 \)
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if \\(log_{4} x = 12\\), then \\(x = ?\\)
$16777216$
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18. which statement is true? a the product of $5 \\times \\frac{2}{5}$ …
D. The product of \( 5\times\frac{2}{5} \) is less than the whole number in the problem because \( \frac{2}{5} \) is less than one.
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if: \\(\\log(a) + \\log(b) = 0\\) then \\(ab =?\\)
$ab = 1$
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iply decimals 86.47 × 2.4
\( 207.528 \)
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consider the function $g(x)=|x + 4|+6$. complete the statements. the gr…
- The graph of \(g(x)\) is the V - shaped graph (the first/blue one) opening upwards. - The vertex of \(g(x)\) is \((-4,6)\). - \(g(x)\) is increasing on the interval \((-4,+\inft…
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a function is shown. $f(x) = -\frac{7}{8}x + 11$ complete the statement…
The function's x - intercept occurs at \(\boldsymbol{(\frac{88}{7},0)}\) The function's y - intercept occurs at \(\boldsymbol{(0,11)}\)
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a quadratic function is shown. $h(r) = -2(r + 3)(r - 1)$ complete the s…
The function is \(\boldsymbol{\text{negative and increasing}}\) on the interval \( r < -3 \). The function is positive and decreasing on the interval \(\boldsymbol{-1 < r < 1}\).
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multiplying a positive number and a negative number gives you a negativ…
$8 \times 5$ pairs with $40$ $8 \times (-5)$ pairs with $-40$
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Question was provided via image upload.
\( x = -7 \) and \( x = -1 \)
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which of the following represents the graph of $f(x) = 3^x - 2$?
The second graph (with a horizontal asymptote at $y = -2$ and a y-intercept at $(0, -1)$).
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which is the graph of $f(x) = 5^x$.\ \ \\(\\bigcirc\\) a.\ \ \\(\\bigci…
A. The graph of \( f(x) = 5^x \) (the first graph)
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identify the key features of the exponential function f(x) = 6^x and it…
- The domain is \( (-\infty, \infty) \) (or all real numbers). - The range is \( y>0 \). - The asymptote is \( y = 0 \). - The y - intercept is \( 1 \).
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13. a football is kicked from the ground with an initial vertical veloc…
A. 3 seconds #### Part B
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compare using >, <, or =. 417 + 10 + 10 437
$417 + 10 + 10 = 437$
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the sinusoidal function ( y = g(x) ) has a period of ( \frac{6pi}{5} ) …
B. The first maximum value for $x > -\frac{3\pi}{2}$ occurs at $x = -\frac{\pi}{4}$, because the smallest interval of input values between the maximum and minimum output values is…
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24. graph each function as a vertical compression of its parent functio…
Graph is a vertical compression of $y=|x|$ by factor $\frac{1}{4}$; key points: $(0,0), (4,1), (-4,1)$ --- ### Problem 25: $g(x) = 3x^2$
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compare using >, <, or =. 483 283 + 100 + 10
$483 > 283 + 100 + 10$
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use the graph to state the number of real zeros of the function.
4
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jerry has a part time job at a supermarket. the ordered pairs show the …
1. Yes, the ordered pairs are a relation. By definition, any set of ordered pairs that connects inputs to outputs is a relation. 2. - Left oval (inputs, empty boxes top to bottom)…
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order of operations - part i use the order of operations to evaluate th…
31
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use the order of operations to evaluate this expression. enter the numb…
1
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compare using >, <, or =. 483 283 + 100 + 10
$483 > 283 + 100 + 10$
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use synthetic division and the remainder theorem to find p(a). p(x) = x…
114
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use the order of operations to evaluate this expression. enter the numb…
2
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question 7 what are the typical money market account (mma) features? hi…
All of the above
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i do not surrender my treasures, nor do i share them. the fortune of my…
economics ### For the question "Based on the passage, which type of government would Rand most likely support?"
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read the excerpt from \the storyteller.\ the smaller girl created a div…
A. Whoever it was who had made the wager was likely to lose his bet. E. In a low, confidential voice, interrupted at frequent intervals by loud, petulant questionings from her lis…
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i can identify functions as linear or non - linear. 9. classify each of…
a. Linear b. Non-linear c. Non-linear d. Linear --- ### Second Section: Slope-Intercept Form ($y=mx+b$)
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quiz: functions for questions 1-2, determine whether the representation…
1. Yes 2. No 3. A. Its graph must pass through the origin. 4. D. (-3, -4) 5. $y=-5x-2$
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a pool is being filled with water. it starts with 2 gallons of water an…
12
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a container starts with 8 milliliters of water in it. chloe is dropping…
The vertical distance is 4, the horizontal distance is 1, and the slope of the line is 4.
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the graph shows the relationship between the number of marbles and the …
8
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the graph shows the relationship between the number of marbles and the …
Slope: $\frac{1}{2}$ Line equation: $y = \frac{1}{2}x + 8$
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function 3 graph of function 3 ○ linear ○ not linear function 4 graph o…
Function 3: Not linear Function 4: Not linear
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add. $-dfrac{1}{4}+dfrac{5}{7}$ write your answer in simplest form.
$\frac{13}{28}$
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characteristics of french and british colonies instructions political g…
### Políticas: - Británicas: Royal officials had most power - Francesas: Colonists had more self - government ### Geográficas: - Británicas: Along Atlantic seaboard; varied climat…
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which of the statements about the graph of the function $y = 2^x$ are t…
- The domain is all real numbers \( x \) because the exponent of 2 can be any real number - When the \( x \)-values increases by 1 unit, the \( y \)-value multiplies by 2. - The \…
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youre trying to write an equation that represents this line by finding …
6
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youre trying to write an equation that represents this line by finding …
$4$
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youre trying to write an equation that represents this line by finding …
Labeled points: $(0.6, 6)$ and $(1.10, 10)$ Slope: $8$ Vertical intercept: $1.2$ Line equation: $y = 8x + 1.2$
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youre trying to write an equation that represents this line by finding …
$\frac{10}{3}$
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youre trying to write an equation that represents this line by finding …
$\frac{10}{3}$
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find the value of $f(9)$. $y = f(x)$
\( 8 \) (Wait, there is a mistake in the previous step. Let's re - examine the graph. Let's find two points on the right - hand line. Let's take \( x = 0\), \( y=- 1\)? No, wait, …
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question find the value of $f(-2)$. $y = f(x)$ answer attempt 1 out of 2
\( 0 \)
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find the value of $f(-3)$. $y = f(x)$ answer attempt 1 out of 2 submit …
-8
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question find the value of $f(5)$. $y = f(x)$ answer attempt 1 out of 2
9
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find the value of $f(-3)$. $y = f(x)$ answer attempt 1 out of 2 submit …
\(-2\)
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explaining function notation using words the function $h(x) = \\frac{1}…
After 2 hours of the snowstorm, the total amount of snow on the ground is 9 feet.
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consider the function shown to the left. $g(x) = -\frac{1}{2}x + 5$ eva…
s: - \( g(6)=\boldsymbol{2} \) - \( g(-14)=\boldsymbol{12} \) - The value of \( x \) when \( g(x) = 7 \) is \( \boldsymbol{-4} \)
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this rule can be represented by the function: $f(x) = 2x - 7$ now that …
| x (input) | f(x) - output | | --- | --- | | -3 | -13 | | 0 | -7 | | 4 | 1 | | -6 | -19 |
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evaluating functions given the graph of $f(x)$, find each of the follow…
| Function Notation | Answer | Result | | --- | --- | --- | | \( f(-4) = \) | 3 | | | \( f(0) = \) | 0 | | | \( f(2) = \) | -2 | | | \( f(5) = \) | -1 | |
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consider the three functions $f(x) = 6 - 2x$ $g(x) = \\frac{4}{5}x - 2$…
| Function Notation | Answer | Result | | --- | --- | --- | | \( f(6)= \) | \( 6-2\times6 \) | \( -6 \) | | \( g(-10)= \) | \( \frac{4}{5}\times(-10)-2 \) | \( -10 \) | | \( r(3)=…
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given the function $f(x)=x^2 - 4$ complete the table.\ | $x$ | $f(x)$ |…
| \( x \) | \( f(x) \) | | ---- | ---- | | -4 | 12 | | -2 | 0 | | 0 | -4 | | 3 | 5 |
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functions & tables - linear given the function $f(x) = -3x - 2$ complet…
When \( x = -3 \), \( f(x) = 7 \); when \( x = -2 \), \( f(x) = 4 \); when \( x = 0 \), \( f(x) = -2 \); when \( x = 2 \), \( f(x) = -8 \) Filling the table: | \( x \) | \( f(x) \…
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functions & tables - linear given the function $f(x) = -3x - 2$ complet…
When \( x = -1 \), \( f(x) = 1 \); when \( x = -2 \), \( f(x) = 4 \); when \( x = 0 \), \( f(x) = -2 \); when \( x = 2 \), \( f(x) = -8 \) The completed table (rows in order of \(…
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20) $g(x)=\frac{-x - 5}{3}$
The graph of $g(x)=\frac{-x-5}{3}$ is a straight line passing through the points $(-5, 0)$ and $(0, -\frac{5}{3})$, with a slope of $-\frac{1}{3}$.
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daniella manages a flower shop. the fixed costs are $500 per month, and…
$C(x) = 5x + 500$ $R(x) = -x(x - 120)$