微積分
極限、導関数、最適化、関数挙動。
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4) find the vertex of $y = -3x^2 - 24x - 46$
The vertex of the parabola \( y=-3x^{2}-24x - 46 \) is \( (-4,2) \)
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read a text about déjà vu. déjà vu is the strange feeling that an event…
- Research on déjà vu is limited because it is difficult to study in a controlled environment. - Déjà vu occurs randomly and without warning.
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x = log₉(3)
\( x = \frac{1}{2} \)
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4(3)?×17=87
\(x = 20\) (assuming the equation is \(4x + 7 = 87\) with a typo in the (3))
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given the function ( f(x) = -2x - 8 ), find the following values. a. ( …
$-2x - 2h - 8$
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complete the table of values for ( f(x) = 6x + 3 ) and ( g(x) = 5x^2 - …
### Completed Table: | $x$ | $f(x)$ | $g(x)$ | |-----|--------|--------| | 1 | 9 | 4 | | 2 | 15 | 18 | | 3 | 21 | 42 | | 4 | 27 | 76 | ### Growth Conclusion: $g(x) = 5x^2 - x$ eve…
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complete the table of values (for ( f(x) = 4x^2 - 6 ) and ( g(x) = 5x -…
### Completed Table: | $x$ | $f(x)$ | $g(x)$ | |-----|--------|--------| | 1 | -2 | 3 | | 2 | 10 | 8 | | 3 | 30 | 13 | | 4 | 58 | 18 | ### Growth Conclusion: $f(x) = 4x^2 - 6$ eve…
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find the product of $(-7.3) \\cdot (5)$. (lesson 5 - 9)
$-36.5$
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find the product of $(-7) \\cdot (-1.1)$. (lesson 5 - 9)
\(7.7\)
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find the product of (100)·(-0.09). (lesson 5-9)
\(-9\)
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6. (5pts) a car’s position, s, measured in feet, after t seconds is giv…
8.25 feet per second
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evaluate the limit, if it exists. (if an answer does not exist, enter d…
$\frac{2}{5}$
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école secondaire montcalm nom : mariana herrera gr. : cose mini - test …
2.00 mètres
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5. (11pts) evaluate each limit. show all work. (a) \\(\\lim\\limits_{x\…
(a) $\boldsymbol{-3}$ (b) $\boldsymbol{6}$ (c) $\boldsymbol{-\frac{1}{81}}$
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write the domain and range of the function using interval notation. not…
The domain is: \(\boldsymbol{[-2, 4]}\) The range is: \(\boldsymbol{[-5, -4]}\)
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name:math is life ©core______directions: find each sum or difference.1)…
1) $5$ (Positive) 2) $13$ (Positive) 3) $-11$ (Negative) 4) $-7$ (Negative) 5) $10$ (Positive) 6) $2$ (Positive) 7) D. 2,025 feet (Positive) 8) Expression: $-20 + 9 - 12 - 15$; An…
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question what is the slope of the line that passes through the points $…
$\boldsymbol{-\frac{1}{6}}$
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question what is an equation of the line that passes through the points…
$y = x - 2$
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limited ability to respond convinced many people that the nation needed…
- They felt a heavy responsibility to address the crisis facing the nation's failing government. - They felt the changes needed would be substantial and long-lasting.
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incorrect 1 try left. try once more write an exponential function for t…
$y=1(2)^x$ or simplified as $y=2^x$
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match each argument from the federalist papers with the concern it addr…
1. The federal government won't reflect the needs of people in different communities all across the country. → The Constitution creates a federal government to address national is…
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use the properties of radicals to simplify the expression. $\frac{sqrt5…
3
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some opponents of the constitution worried that separating powers would…
The branches are given the power to check, or resist, one another.
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fill in the equation for this function. ● = original start point $f(x) …
$f(x) = \boldsymbol{\frac{5}{2}}\cos(\boldsymbol{3}x) + \boldsymbol{-\frac{1}{2}}$
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some opponents of the constitution worried that requiring the federal g…
- The federal government only has certain listed powers. - State governments have broad powers over matters in their states.
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q7 (2 points) determine the exact value of $cos(\theta)$ given that $\t…
$-\frac{\sqrt{17}}{17}$
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question 2 true or false? brands and sizes of food products are much mo…
Question 2: False Question 3: - It can help avoid extra trips. - It can help save time. - It can help stick to the food budget.
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q6 (1 point) if $f(x) = \\int_{1}^{x} \\ln t^{2}dt$, then $f(2) =$ $\\l…
$\ln(2^2)$
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q5 (1 point) if $f(x) = |\\tan(e^x)|$, then $f(x) =$ $\tan(e^x)$ $e^x \…
$\frac{\tan(e^{x})}{|\tan(e^{x})|}e^{x}(\sec(e^{x}))^{2}$
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enter the result of $32.6669 \\div 0$
DNE
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q4 (1 point) on which interval is $\\sin(x)$ invertible? select all tha…
$(-\frac{\pi}{2}, \frac{\pi}{2})$, $[-\frac{\pi}{2}, \frac{\pi}{2}]$
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1) is the function linear or non-linear?the graph is a straight line.th…
1. Linear 2. $(0,10)$
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composition of functions (with x) score: 0/1 penalty: 1 off question ex…
$6x^2 - 12x + 17$
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what is the slope of the line?
25
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4. graph: $f(x) = -2x^2 + 4x + 8$ a. what is the parent function?
$g(x) = x^2$ Additionally, for reference to graph $f(x) = -2x^2 + 4x + 8$: 1. Convert to vertex form: ## Step1: Factor out -2 from first two terms $f(x) = -2(x^2 - 2x) + 8$ ## Ste…
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40 what is the slope of the line?(4) slope = $\frac{rise}{run}$
10
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after the due date, some assignments might still be available in review…
1. Getting exercises correct in Review Mode won't change the score in the gradebook. 2. (Select both applicable statements): - Your last attempt score reflects your performance on…
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3. graph: $f(x) = 3x^2 + 5x - 2$ a. what is the axis of symmetry?
$x=-\frac{5}{6}$
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9. $int \frac{3}{x^{2}+14x+49}dx$
$-\frac{3}{x+7} + C$
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7. $int \frac{1}{x^{2}-12x+37}dx$
$\arctan(x-6)+C$
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$k(x) = x^4 - 14x^3 + 69x^2 - 140x + 100$ $g(x) = 2x^4 + 4x^3 + 4x^2 + …
- $k(x)=x^4-14x^3+69x^2-140x+100$ → Top-left graph - $h(x)=x^4+11x^3+42x^2+64x+32$ → Top-right graph - $g(x)=2x^4+4x^3+4x^2+4x+2$ → Bottom-left graph - $f(x)=x^4+4x^2+3$ → Bottom-…
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a1.4.16 name: ____________ date _______ period ____ problems 1-3: write…
1. $4$ 2. $5$ 3. $7$ 4. Completed table: | $x$ | $g(x)$ | |-----|--------| | $-3$| $6$ | | $-1$| $4$ | | $0$ | $5$ | | $1$ | $6$ | | $2$ | $7$ | Graph: Plot the points and draw a …
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find the slope of the line graphed below.
$\frac{-4}{5}$
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unit 8 hw 2 - graphing quadratic functions directions: show all work in…
(Problem 1a): $x=-3$ and $x=1$ --- ### Problem 2: $f(x) = x^2 +4x +3$ ## Step1: Find x-coordinate of vertex For $ax^2+bx+c$, $x=-\frac{b}{2a} = -\frac{4}{2(1)} = -2$ ## Step2: Fin…
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multiple-choice question what is completed first for the expression $(3…
subtraction (inside the parentheses)
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spiral review 8. determine the average rate of change for each interval…
- $r=-2$ to $r=1$: $0$ - $r=-2$ to $r=5$: $-\frac{4}{7}$ - $r=-2$ to $r=8$: $0.2$ --- ### Problem 9
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1. how can i reason about the sum of two fractions with like denominato…
7
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name kuta software - infinite algebra 2 date_______ period____ graphing…
Maximum number of turns: 1 Real zeros: $x\approx1.4$, $x\approx-3.4$ Relative minimum: $(-1, -6)$ (Graph: Opens upward parabola with vertex at $(-1,-6)$, crossing x-axis at the ap…
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solve the following system of equations graphically on the set of axes …
The solution (intersection point) is $(-8, 2)$ To plot the lines: 1. For $y=\frac{1}{2}x+6$: plot $(0,6)$ and $(-12,0)$, then draw the line through them. 2. For $y=-\frac{5}{4}x-8…
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use the image to answer the question. $f(x)=\\log_{2}x$ $g(x)=\\log_{2}…
a shift down 3 units
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given the function $f(x)=\\log_{5}x$, which of the following functions …
$g(x) = -2\log_5(x - 6) + 3$
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which of the following exponential equations shows a horizontal stretch…
$y = 7^{\frac{1}{3}x}$
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which function is the inverse of $f(x)=\\log_{3}x$? (5 points)○ $f^{-1}…
$\boldsymbol{f^{-1}(x) = 3^x}$ (the second option)
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identify the inverse to the function $f(x)=\\frac{3x}{4}+\\frac{1}{2}$.…
$f^{-1}(x)=\frac{4x-2}{3}$
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the point (0.36, 2) lies on the graph of $f(x) = \\log_{0.6} x$. what i…
B. (2, 0.36)
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describe the horizontal and vertical asymptotes of $f(x)=\\log_{4}x$. (…
The function $f(x)$ has a vertical asymptote at $x = 0$ and no horizontal asymptote.
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find $f(f^{-1}(-2)).$
$-2$
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question find $f(f^{-1}(-5))$. | $x$ | $f(x)$ || --- | --- || $-7$ | $-…
$-5$
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4 part a give an example of a nonlinear function. you may represent the…
### Part A A nonlinear function: $y = x^2$ (the output is the square of the input value) ### Part B Table representing the function: | $x$ | $y$ | |-----|-----| | -2 | 4 | | -1 | …
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lesson 9: the distributive property, part 1 lets use the distributive p…
$5 \cdot 102 = 510$ $5 \cdot 98 = 490$ $5 \cdot 999 = 4995$
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graph the piecewise function given below. $f(x)=\\begin{cases}-x & \\te…
1. For $-3 < x < 4$: A straight line with open circles at $(-3, 3)$ and $(4, -4)$, passing through the origin $(0,0)$. 2. For $4 < x < 7$: A V-shaped graph with open circles at $(…
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which statement best describes how the authors purpose differs in chapt…
Nature portrays the world of nature as superior to the social world, while Society and Solitude argues that nature can help individuals be more content within society.
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question 22 0/1 pt use a calculator to approximate the following square…
a. $1.871$ b. $5.916$ c. $18.708$ d. $59.161$
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question for the function $f(x) = \\frac{3x+10}{4-5x}$, find $f^{-1}(x)…
$f^{-1}(x)=\frac{4x-10}{5x+3}$
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7. what is $4\\frac{4}{8}-\\frac{7}{8}$? a. $3\\frac{3}{8}$ b. $3\\frac…
7. B. $3\frac{5}{8}$ 8. C. $2\frac{1}{2}$ 9. C. $6\frac{1}{2}$ pounds
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a piecewise function $f(x)$ is defined as shown.$f(x)=\begin{cases}-\fr…
The correct table is: | x | y | |----|----| | 40 | 60 | | 160| 15 | | 200| 0 |
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sample response: you would graph the equation $f(x) = -x + 3$ for input…
- There would be an open circle at (2, 1). - There would be a closed circle at (2, 3). - There would be an open circle at (4, 3). - There would be a closed circle at (4, -4).
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question 1 of 25 which of the following values are in the range of the …
A. 2 B. -6
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explain how to graph the given piecewise-defined function. be sure to s…
1. For $f(x) = -x + 3$ where $x<2$: - Graph the line with slope $-1$, y-intercept $(0,3)$. The endpoint at $x=2$ is $(2,1)$, drawn as an **open circle** because $x=2$ is not inclu…
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homework: introduction to functions question 9, *11.1.35 hw score: 5 po…
$(0, 18)$ $(2, -2)$ $(-6, 78)$
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graphing a piecewise-defined function which graph represents the piecew…
The fourth graph (bottom-right option: decreasing line with closed dot at (0,4), open dot at (3,1); horizontal line with closed dot at (3,6) extending right)
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divide whole numbers, part 1 -- instruction -- level d rowan collects 9…
2 tens Additionally, for the full problem context: Each class gets 23 books, with 2 books left over.
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question 12 0/1 pt 100 99 details use a calculator to approximate the f…
a. $18.521$ b. $14.248$ c. $18.521$ d. $18.521$
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q4 1 point compute the derivative of $f(x)$ algebraically. $f(x)=x^2 - …
$f'(x)=2x$ (matches the last option)
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q4 1 point compute the derivative of $f(x)$ algebraically. $f(x)=x^2 - …
$f'(x)=2x$ (matches the option: $f'(x)=2x$)
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q3 1 point compute $f(a)$ algebraically for $a = -4.2$ if $f(x) = 7.2x …
7.2
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q2 1 point compute $f(a)$ algebraically for $a = 3$ if $f(x) = 8x^2 + x…
49
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1 point calculate the average rate of change of the given function over…
9
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solve for c. approximate by rounding your answer to three decimal place…
$c = 1.809$ $n = 2.046$
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read the quotation from abigail adams. it is from a letter she wrote he…
Truth would agree with Adams's sentiment that women deserve to be represented in the Constitution.
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question the graph of $y = f(x)$ is shown below. find all values of $x$…
$x < -3$ or $x > 5$
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t this graph: hat is the equation of the line in point-slope form? se t…
$y - (-60) = \frac{1}{5}(x - (-10))$ (or simplified as $y + 60 = \frac{1}{5}(x + 10)$)
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18 mark for review the functions $f$ and $g$ are given by $f(\\theta)=\…
D. $\frac{3\pi}{2} < \theta < 2\pi$
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the functions $f(x)$ and $g(x)$ are both continuous functions. the func…
The maximum value of $f(x)$ is equal to the maximum value of $g(x)$ (both are 6).
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question the graph of $y = f(x)$ is shown below. find all values of $x$…
All real numbers $x$ such that $x < -2$ or $x > 5$, or in interval notation: $(-\infty, -2) \cup (5, \infty)$
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is the inverse a function? $h(x) = \\sqrt{x + 7}$ yes no
yes
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1) find the inverse of the function. $g(x) = \\frac{2x - 8}{4x + 5}$ 2)…
$\boldsymbol{\frac{-5x - 8}{4x - 2}}$ (or equivalent $\boldsymbol{\frac{5x + 8}{-4x + 2}}$)
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question determine the domain on which the following graph of $f(x)$ is…
The domain where $f(x)$ is negative is $3 < x < 7$ (or in interval notation, $(3, 7)$)
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13 mark for review the function $h$ is defined by $h(\\theta)=a\\cos(b\…
D. $a = 4$ and $b = 2$
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12 mark for review the functions $f$ and $g$ are given by $f(\\theta)=2…
B. $\frac{2\pi}{b} = \frac{1}{2}(2\pi)$
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4 the periodic function $y = g(x)$ has a period of 6. it is known that …
D. \(g(5)=g(23)\)
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the graph of $f(x)$ is shown. which graph represents $g(x)=f(2x)$?
The third option (the graph with a narrow "W" shape, vertices at $x=-1, 0, 1$ with the same vertical range as $f(x)$)
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multiply: 3.7 × 0.1
0.37
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add. 34.4 + 30.28 \\overline{\\square}
64.68
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inverse of rational functions score: 0/2 penalty: none question for the…
$\frac{9}{4 - 2x}$
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multiply. write your answer as a fraction or as a whole or mixed number…
$42\frac{7}{12}$ or $\frac{511}{12}$
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writing equations of linear functions to write the equation of a linear…
1. $y = \frac{1}{3}x + 14$ 2. $y = -5x + 3$ 3. $y = 1.75x - 1$ 4. $y = \frac{2}{5}x - 2$ 5. Yes, because the point $(0, -7)$ is the y-intercept ($b = -7$). Since the slope $m = -7…
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$y=mx+b$ 4) $y=-\frac{2}{3}x-1$ 5) $y=-x-1$ 6) $y=-2x-4$ 7) $y=-\frac{1…
1. For $y=-\frac{2}{3}x-1$: Line through $(0,-1)$ and $(-1.5, 0)$ 2. For $y=-x-1$: Line through $(0,-1)$ and $(-1, 0)$ 3. For $y=-2x-4$: Line through $(0,-4)$ and $(-2, 0)$ 4. For…
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graph the line. $y=3x$
The line $y=3x$ is a straight line passing through the origin $(0,0)$ with a slope of 3, passing through points like $(1,3)$ and $(-1,-3)$, extending infinitely in both directions…
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omar wants to use a graph to solve the equation below.$log_{6}x = log_{…
$y_1 = \frac{\log x}{\log 6}, y_2 = \frac{\log(x+4)}{\log 2}$ (the fourth option)