微積分
極限、導関数、最適化、関数挙動。
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question 18 (5 points) listen controls given to one branch of governmen…
Question 18: A) checks and balances. Question 19: D) Amendment VIII
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which of the following is the graph of this absolute value function? y …
The rightmost graph (with vertex at (4, 0), decreasing left of x=4 and increasing right of x=4)
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given the function $f(x) = -x^2 - 8x + 21$, determine the average rate …
\( 4 \)
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graph the inverse of the provided graph on the accompanying set of axes…
The inverse graph is formed by plotting the points $(4,0)$, $(6,0)$, $(7,1)$, $(2,10)$, $(8,10)$ and drawing a smooth curve connecting them, which is symmetric to the original gra…
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question $f(x)=\\begin{cases}-x + 3&\\text{for }x\\leq - 3\\\\-3x - 4&\…
\( 2 \)
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the graph shows g(x), which is a transformation of f(x) = |x|. write th…
\( g(x) = \frac{5}{2}|x| \) (or \( g(x) = 2.5|x| \), but as a fraction, \( \frac{5}{2}|x| \))
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the graph shows g(x), which is a translation of f(x) = x². write the fu…
\( g(x) = (x - 5)^2 + 4 \)
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what is the slope of this line? simplify your answer and write it as a …
\(2\)
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solve the following system of equations graphically on the set of axes …
The solution of the system of equations is \( x = 2,y = 1 \) (or the point \( (2,1) \)).
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sketch the graph of the quadratic function and the axis of symmetry. st…
Vertex: \((-1, 1)\) Axis of symmetry: \( x = -1 \) (For the graph, plot the vertex \((-1, 1)\), points like \((0, 2)\), \((-2, 2)\), draw the upward - opening parabola, and the da…
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solve this system of equations by graphing. first graph the equations, …
The solution is $(-3, 0)$
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write \\(\\frac{2}{5}\\) as a decimal. \\(\\frac{2}{5} = \\square\\)
0.4
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lesson 1.1 checkpoint complete the previous problems, check your soluti…
To obtain the graph of \( v(x)=-3|x + 1|+4 \) from \( f(x)=|x| \): 1. Reflect the graph of \( f(x)=|x| \) over the \( x \)-axis. 2. Vertically stretch the reflected graph by a fac…
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graph the following features: - y-intercept = 1 - slope = 3
# Explanation: ## Step1: Recall slope - intercept form The slope - intercept form of a linear equation is $y = mx + b$, where $m$ is the slope and $b$ is the y - intercept. Given …
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question given $f(x) = -x - 2$, find $f(-6)$.
4
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find the slope of the line that passes through (10, 8) and (1, 7). simp…
$\frac{1}{9}$
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use technology to find points and then graph the function $y = 2^x - 2$…
The four points with integer coordinates are (0, -1), (1, 0), (2, 2), (3, 6) (you can plot these on the graph).
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watch the video and then solve the problem given below. click here to w…
9
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5) 9 + 50 ÷ 10(3 + 9 - 4) 6) 6 + 28 ÷ 4(4 + 14 - 6)
For problem 5: 49 For problem 6: 64
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find the inverse of the following function. also list the domain restri…
The inverse function \( f^{-1}(x)=-\sqrt{x + 5}-3\)
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question use technology to find points and then graph the function ( y …
Plot the following points on the graph: $(2, 4)$, $(3, 2)$, $(4, 0)$, $(5, 2)$, $(6, 4)$ Connect the points to form a V-shaped graph with vertex at $(4,0)$.
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what are the domain and range of this function? domain: {-5, -3, -1, 0,…
domain: \(\{-5, - 3, - 1, 0, 3\}\) range: \(\{-4, - 3, - 2, 1, 5\}\) (corresponding to the first option among the given choices)
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write the inverse of $f(x) = 5x - 4$? $f^{-1}(x) = \\square \\square$
\( f^{-1}(x)=\frac{x + 4}{5} \) (or \( f^{-1}(x)=\frac{1}{5}x+\frac{4}{5} \))
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find the inverse of the function. \\( y = (x + 5)^2 \\) write your answ…
\( -5\pm\sqrt{x} \)
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7. which of the following would be an example of logos used in a persua…
The second option (Wearing school uniforms means that all students have the same clothes, easing parents’ task of choosing school cloth...)
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a(c) = 2c - 4 evaluate a(4) type answer here.
4
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f(x) = -2x + 5 evaluate f(-4)
13
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find the average rate of change of the function f(x)=8x from x₁=0 to x₂…
8
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r(x) = \\frac{4}{3}x - 2 evaluate r(-6)
\(-10\)
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b(t) = 4t³ - t² evaluate b(-2) type answer here.
\(-36\)
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the function $f(x)$ is shown on the coordinate plane below. graph of $y…
C. \(f(x)=-x(x - 2)^2(x - 1)(x + 1)\)
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find the average rate of change of the function $f(x)=\\sqrt{x}$ from $…
$\frac{1}{7}$
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graph the following features: • y-intercept = -3 • slope = 3
The graph is a straight line with a y - intercept at the point $(0,-3)$ and a slope of 3. To construct it, plot $(0,-3)$, then use the slope (rise 3, run 1) to find other points (…
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find the average rate of change of the function $f(x)=x^{2}+2x$ from $x…
10
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g(n) = -n² - 3 evaluate g(-2)
\( -7 \)
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what is the slope of a line that is perpendicular to the line whose equ…
$\frac{B}{A}$
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graph the following features: - slope = \\(\\frac{5}{3}\\) - y-intercep…
The graph is a straight line with a y - intercept at $(0, - 3)$ and a slope of $\frac{5}{3}$, passing through points like $(3,2)$ (obtained by moving 3 units right and 5 units up …
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g(y) = y² - 3y evaluate g(6) type answer here
\( 18 \)
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f(x) = \\frac{3}{4}x - 3 evaluate f(-8)
-9
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(\frac{sqrt3{9}}{sqrt3{4}})
$\boxed{\dfrac{\sqrt[3]{18}}{2}}$ (or $\boxed{\sqrt[3]{\dfrac{9}{4}}}$ depending on the preferred form)
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the graph of a linear function passes through the points (-10, -14) and…
slope = 1.25 y-intercept = -1.25
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graph the following features: • y-intercept = 1 • slope = -3
To graph the line with y - intercept 1 and slope - 3: 1. Plot the point \((0,1)\) (the y - intercept). 2. Use the slope \(-3=\frac{-3}{1}\): from \((0,1)\), move 3 units down and …
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part of a linear function passes through the points shown in this x | y…
$-3$
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use the given conditions to write an equation for the line in point - s…
Point-slope form: $y+4 = -8(x-1)$ General form: $8x+y-4=0$
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5. 2(3 + 1)² + 10
\(42\)
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4. $3^2×8 - 5 - 1$
66
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3²×8 - 5 - 1 6. ((5 - 3)²)/(2×7 - 5) friend so they can better understa…
\( 66 \) ### Solving \( \frac{(5 - 3)^2}{2\times7-5} \)
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3. 100 - 3(2 + 1)^2
\(73\)
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37 + 5² × 2
\(87\)
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1. $2×3^{2}-5$
13
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you can log out once you get a sticker! what is f(x) when x=6?
\( 4.4 \) (or \( \frac{22}{5} \))
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find the solutions of the quadratic equation $2x^2 + 6x - 2 = 0$. choos…
B. \(-\frac{3}{2}\pm\frac{\sqrt{13}}{2}\)
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multiply and simplify the following complex numbers: (1 + 2i)·(1 - 4i)
\(9 - 2i\)
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write a number that makes this equation true. \\(\\square\\) hundreds =…
4
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when is the vertex a minimum? when is it a maximum?
For a quadratic function (parabola) with equation \( y = ax^{2}+bx + c \) (or vertex form \( y=a(x - h)^{2}+k \)): - The vertex is a minimum when the coefficient of \( x^{2} \) (i…
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evaluate the function for the given value of x. #1 $y = 2(4)^x$ $x = -2…
\( 7 \)
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use the aleks calculator to approximate \\(\\sqrt{95}\\). round your an…
9.75
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fix the inequality below to correctly show the range of the function.
\(-1.67814\leq y\leq2\)
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fix the inequality below to correctly show the range of the function.
-2 ≤ y ≤ 2
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what is the domain of the function? enter your answer as an inequality …
\( -6 \leq x \leq 8 \)
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what is the domain of the function? enter your answer in inequality not…
\( -5\leq x < 10 \)
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what was the greatest challenge the ancestral pueblo people faced when …
C. They depended on farming, and a lack of rain could lead to food shortages.
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fix the inequality below to correctly show the domain of the function. …
\(-1.5\leq x<1\) (or \(-\frac{3}{2}\leq x<1\))
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limits quiz a \\(\\lim\\limits_{x \\to 2} (8 - 3x + 12x^2)\\) b \\(\\li…
A. $\boldsymbol{50}$ B. $\boldsymbol{-15}$ C. $\boldsymbol{0}$ D. $\boldsymbol{10}$ E. $\text{Does not exist}$ F. $\boldsymbol{6}$ G. $\boldsymbol{0}$ H. $\boldsymbol{2}$ I. $\bol…
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which of the following factors most influenced the adoption of largely …
D. The arid Great Basin limited farming opportunities close to major waterways, making permanent settlements undesirable.
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of two quadratic functions, f(x) and g(x) are shown below
If finding the equation of \( f(x) \): \( f(x) = x^2 \) If finding the equation of \( g(x) \): \( g(x) = (x - 3)^2 - 3 \) (or \( x^2 - 6x + 6 \)) If comparing leading coefficients…
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topic review vocabulary choose the best term from the box to complete e…
1. fraction 2. numerator 3. denominator 4. $0.4$ 5. $0.75$ 6. $2.5$ 7. $1.5$ 8. $0.375$ 9. $4.\overline{3}$ 10. $2.5$ 11. $20$ 12. $30.5$ 13. $(0, 5)$ 14. $(4, 3)$ 15. $(6, 8)$ 16…
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b) use words to describe the transformations
To transform \( f(x) = x^2 \) into \( g(x) \), we apply a **horizontal shift 3 units to the right** and a **vertical shift 3 units down**.
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copy the important definitions and examples onto your notes sheet: stan…
All of the above examples must include a squared term (a term with \( x^{2} \), where the coefficient of \( x^{2} \) is non - zero) to be a quadratic function.
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student name: class period: date: activity overview: you will explore t…
| Park | Year Founded | Founder | Description of Park | Why was the area important to protect? | |---------------|--------------|---------|---------------------|------------------…
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11. select the mathematical symbol that makes this number sentence true…
C. < (assuming the third option's symbol is '<' to represent "less than" as 1.5 < 2)
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learning check given the equation or graph, classify the function type …
1. $y=-3x^2+5$: Quadratic function 2. $y=5^x$: Exponential function 3. Provided graph: Cubic function 4. $y=\sqrt[3]{x+2}$: Cube root (radical) function
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the two graphs represent either an exponential function or logarithmic …
A. The logarithmic parent function was shifted right 1 unit and the exponential function was shifted down 2 units.
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what is the equation of the horizontal asymptote of the graph for the f…
C. $y=9$
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which graph appears to belong to the family of radical functions? a gra…
A. <The S-shaped graph in option A>
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the figure above shows the graph of the differentiable function ( g ) a…
# Explanation: ## Step1: Find \( f'(3) \) using Fundamental Theorem of Calculus By the Fundamental Theorem of Calculus, if \( f(x)=\int_{0}^{x}g(t)dt \), then \( f'(x) = g(x) \). …
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a pump allows water to flow into a tank at the rate of $r(t) = 3t$ lite…
D. \( f(x)=\int_{1}^{x}3t\ dt \)
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find the y-coordinate of the y-intercept of the polynomial function def…
-2
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find the y-coordinate of the y-intercept of the polynomial function def…
-4
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what is the y-intercept of the polynomial $f(x)$ defined below? write t…
-1
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f(x) = \\begin{cases} (x - 9)^2 - 3 & \\text{for } x \ eq 3 \\\\ 4 & \\…
\( 6 \)
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f(x) = \\begin{cases} -\\frac{2}{3}x - 3 & \\text{for } x < -3 \\\\ x +…
\( 5 \)
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f(x) = \\begin{cases} 3x + 6 & \\text{for } x \ eq -1 \\\\ -5 & \\text{…
\( f(-1)=-5 \)
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f(x)=\begin{cases}dfrac{(x + 5)^2 - 6}{4}&\text{for }x < -4\\dfrac{3}{2…
\( \boxed{-5} \)
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question $f(x)=\\begin{cases}\\frac{4}{3}x + 4&\\text{for } -6 < x < 0\…
\( 5 \)
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question $f(x)=\\begin{cases}6&\\text{for }x<2\\\\-5&\\text{for }x = 2\…
\(-5\)
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the function $y = f(x)$ is graphed below. plot a line segment connectin…
The average rate of change of \( f(x) \) on the interval \( 1\leq x\leq2 \) is \( 30 \).
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the function $y = f(x)$ is graphed below. what is the average rate of c…
\(\frac{40}{11}\) (or approximately \(3.64\))
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this is the graph of an exponential function. write an equation for the…
$f(x) = -1(3)^x$ or $f(x) = -(3)^x$
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give the slope and y-intercept of the line whose equation is given. the…
For the \(y\) - intercept: The correct choice is A. The \(y\) - intercept is \(4\).
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give the slope and y-intercept of the line whose equation is given. the…
The \(y\) - intercept is \(-1\).
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give the slope and y-intercept of the line whose equation is given. the…
For the slope: A. The slope is - 2. For the y - intercept: A. The y - intercept is 7.
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find the slope of the line passing through the points given below or st…
s: - The slope is \( \boldsymbol{4} \). - The line rises from left to right (Option B).
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use intercepts and a checkpoint to graph the linear function below. 6x …
The x - intercept is \((2,0)\), the y - intercept is \((0,-12)\), and a checkpoint is \((1,-6)\). The line can be graphed by plotting these points and drawing a straight line thro…
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plot the intercepts to graph the equation. x + 4y = 4 use the graphing …
To graph \( x + 4y = 4 \), plot the x - intercept \( (4, 0) \) and y - intercept \( (0, 1) \), then draw a line through these two points.
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use the figure below to list the slopes ( m_1 ), ( m_2 ), ( m_3 ), and …
B. \( m_4, m_1, m_2, m_3 \)
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write the equation of the line in fully simplified slope - intercept fo…
$y=\frac{2}{5}x + 6$
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25. why do you think oral and written histories disagree? do you think …
1. Oral and written histories disagree because oral accounts evolve through retelling and carry cultural context, while written records are fixed but may have biased or limited fr…
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error analysis describe and correct the error in graphing the function.…
The error is that the graph of \( y = - 3|x| \) is opening upwards, but it should open downwards (because \( a=-3<0\) for the absolute - value function \( y=a|x|\), and a negative…
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y = \\frac{7}{4}x - 4 slope: y-intercept:
Slope: \(\frac{7}{4}\) y - intercept: \(-4\)