微積分
極限、導數、最優化與函數性質。
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4. 3.6 ÷ 9 = 7. 3.01 ÷ 7 =
For 3.6 ÷ 9, the answer is 0.4. For 3.01 ÷ 7, the answer is 0.43.
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rewrite as an exponential equation. ln4 = y
\(e^{y}=4\)
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score: 27/30 penalty: 1 off question find the value of f(-8). y = f(x) …
\(-5\)
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divide. use base - ten blocks. 3. $4.9\\div7 = $ 6. $6.48\\div4 = $
For \(4.9\div7\), the answer is \(0.7\). For \(6.48\div4\), the answer is \(1.62\).
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divide. use base - ten blocks. 3. $4.9\\div7 = \\underline{\\quad\\quad…
3. \(0.7\) 4. \(0.4\) 5. \(0.3\) 6. \(1.62\) 7. \(0.43\) 8. \(1.42\)
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use the aleks graphing calculator to solve the equation. 3 log(4 - x) =…
\( x\approx - 1.13,3.00 \) (If we consider the problem's requirement to round to the nearest hundredth, and after using a graphing calculator, the solutions are \( \boldsymbol{-1.…
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score: 25/30 penalty: 1 off question find the value of f(8). y = f(x) (…
-4
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score: 24/30 penalty: 1 off question find the value of f(4). y = f(x) a…
5
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question find the value of f(-4). y = f(x) answer attempt 2 out of 2
6
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5. use your calculator to evaluate each expression. express answers to …
a) \(5.00\) b) \(-12.50\) c) \(-5.65\) d) \(8.00\) e) \(0.46\) f) \(1.14\)
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question find the value of $f(-2)$. $y = f(x)$
-3
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evaluate functions from a graph score: 19/30 penalty: 1 off question wa…
\(-6\)
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evaluate functions from a graph score: 17/30 penalty: 1 off question fi…
\(-1\)
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score: 16/30 penalty: 1 off question watch video show examples find the…
\( f(-8)=-5 \)
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score: 15/30 penalty: 1 off question find the value of f(-3). y = f(x) …
\( f(-3)=-9 \)
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score: 14/30 penalty: 1 off question find the value of f(7). y = f(x) (…
-8
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score: 13/30 penalty: 1 off question find the value of f(-3). y = f(x) …
3
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this question has two parts. first, answer part a. then, answer part b.…
\(y=\begin{cases}-x + 5, & x<3\\x - 1, & x\geq3\end{cases}\)
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question find the value of $f(7)$. $y = f(x)$ (graph of a piecewise fun…
\( 5 \)
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3. write as a single power. express answers with positive exponents. a)…
$a^{2}$ ### Part (b)
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evaluate functions from a graph score: 13/30 penalty: 1 off question fi…
\( 1 \)
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rational expressions evaluating a rational function: problem type 2 the…
Undefined
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evaluate functions from a graph score: 12/30 penalty: 1 off question fi…
\( 4 \)
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rational expressions evaluating a rational function: problem type 2 the…
\( -\dfrac{16}{3} \)
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score: 11/30 penalty: 1 off question watch video show examples find the…
\( 9 \)
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3. $f(x) = \\frac{x + 4}{-x + 4}$ vertical asymptote: horizontal asympt…
- Vertical Asymptote: \( x = 4 \) - Horizontal Asymptote: \( y=-1 \) - x - intercept: \( (-4,0) \) - y - intercept: \( (0,1) \) - Domain: \( \{x|x eq4\} \) - Range: \( \{y|y eq …
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score: 11/30 penalty: 1 off question watch video show examples find the…
6
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question find the value of f(-3). y = f(x) (graph of a parabola with ax…
-7
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11. directions drag and drop the correct answer choice to each answer b…
-7
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score: 13/30 penalty: 1 off question watch video show examples find the…
\(-1\)
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find the functions average rate of change over each interval. a. from x…
s: a. \( \boldsymbol{6} \) b. \( \boldsymbol{-2} \) c. \( \boldsymbol{-1} \) d. \( \boldsymbol{4} \) e. \( \boldsymbol{-3} \) f. \( \boldsymbol{0} \)
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graphs and functions finding slope given two points on a line find the …
\(-\frac{7}{8}\)
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5. the graph of a function is shown below. based on the graph, what is …
\( -3 < x \leq 1 \) (corresponding to the option: \( -3 < x \leq 1 \))
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graphs and functions finding slope given two points on a line find the …
\(\frac{7}{4}\)
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question find the value of f(-4). y = f(x) answer attempt 1 out of 2
\( - 3 \)
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question find the value of f(7). y = f(x) (graph of a piecewise linear …
\( 5 \)
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question find the value of f(2). y = f(x) answer attempt 1 out of 2
2
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exponential and logarithmic functions using a calculator to evaluate na…
\( \log\sqrt{7}\approx\boldsymbol{0.423} \), \( \log\frac{25}{3}\approx\boldsymbol{0.921} \)
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score: 8/30 penalty: 1 off question find the value of f(-2). y = f(x) (…
\( f(-2)=-5 \)
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question find the value of f(2). y = f(x) answer attempt 1 out of 2
7
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question find the value of f(-2). y = f(x) (graph of the function y = f…
-5
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which is the graph of $f(x) = 100(0.7)^x$? four graphs with coordinate …
The top - right graph (the third graph in the top row) with points \( (0,100) \) and \( (2,49) \)
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question find the value of f(9). y = f(x) answer attempt 1 out of 2
\( f(9)=-7 \)
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a population of bacteria is treated with an antibiotic. it is estimated…
B. \( f(x) = 5000(0.4)^x \), with a horizontal asymptote of \( y = 0 \)
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quadratic and polynomial functions simplifying a quotient of square roo…
5
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which graph represents exponential decay?
The graph on the Top - Right (the third graph in the top row)
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compare the rate of change for the function ( f(x) = x^3 - 2x^2 + x + 1…
The average rate of change over \([0, 2]\) is \(1\), over \([2, 4]\) is \(17\), so it's greater over \([2, 4]\).
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find the value of $f(7)$. $y = f(x)$
\(-2\)
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does the function have a minimum x - value? does the function have a ma…
Domain is a subset of all real numbers
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using the rate of change to complete an exponential decay pattern domai…
18
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mathematics i a-g cr sem a aguirre exponential decay functions writing …
The three correct statements are: - The range values, in the context of the situation, are limited to whole numbers. - The domain values, in the context of the situation, are limi…
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solve for x. 3 ln(5x) = 12 do not round any intermediate computations, …
\(x\approx10.92\)
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how do quotas help domestic producers? quotas facilitate the sale of mo…
Quotas limit the number of producers that compete in a sector.
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rewrite as a logarithmic equation. $e^{2}=y$
\(\ln y = 2\)
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evaluate each expression using the graphs of y = f(x) and y = g(x) show…
7
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what is the purpose of quotas? to limit how much of a good can be impor…
to limit how much of a good can be imported
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hematics i a-g cr sem a aguirre ponential decay functions which graph r…
The Middle Graph (Top - middle graph)
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does the function have a minimum x - value? yes no does the function ha…
For "Does the function have a minimum x - value?": Yes For "Does the function have a maximum x - value?": No For "Does the function have a minimum y - value?": Yes
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use the graph to answer all of the questions: select the number of y in…
- Number of y - intercepts: 1 - Number of x - intercepts: 1 - Does the function have a minimum x - value? Yes - Does the function have a maximum x - value? No
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what is the governments aim in setting quotas? to create more competiti…
to increase sales of domestic goods
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ue functions and translations on each coordinate plane, the parent func…
The graph with dashed V at (0,0) and solid V at (0,-4) (specific position depends on clear option visibility; typically the one with solid line vertex below origin)
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use the aleks graphing calculator to solve the equation. 2 log(x - 2) =…
\( 3.73 \) (Note: The actual value from a graphing calculator or more precise calculation might be slightly adjusted, but the key is to use the graphing tool to find the intersect…
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solve for x. \\(3^{-2x} = 17^{x - 5}\\) write the exact answer using ei…
\(x = \frac{5\ln(17)}{2\ln(3)+\ln(17)}\) (or an equivalent expression using base - 10 logarithms, e.g., \(x=\frac{5\log(17)}{2\log(3)+\log(17)}\))
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use the change of base formula to compute \\(\\log_{4} 3\\). round your…
\(0.792\)
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jason estimates that his car loses 12% of its value every year. the ini…
\( f(x) = 12,000(0.88)^x \), with a horizontal asymptote of \( y = 0 \)
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solve for x. \\log_{5}(x - 8) = \\log_{5}(x - 4) + 1 if there is more t…
No solution
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if n stands for number sold and c stands for cost per item, in which co…
A. column D
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integrated ii > chapter 4: solving quadratic equations with complex sol…
\(x = 5 + 2i\) and \(x = 5 - 2i\)
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4) graph the following piecewise function. (4pts) $f(x) \\begin{cases} …
To graph the piecewise function: 1. For \( x < -1 \): Draw a horizontal line at \( y = -5 \) (open dot at \( x = -1 \) since \( x < -1 \) does not include \( x = -1 \)). 2. For \(…
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for $f(x) = x^2 + 8$ and $g(x) = \\sqrt{x - 2}$, find the following com…
\(\sqrt{\sqrt{x - 2}-2}\)
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during the gilded age, working women had limited work opportunities and…
A. limited work opportunities and were paid less than men.
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13.) $g(5) = -5^2 + 3(5) + 2$ $g(5) = $ $g(-3) = -(-3)^2 + 3(-3) + 2$ $…
\( G(5) = -8 \), \( G(-3) = -16 \), \( G(0) = 2 \)
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2. select the system of inequalities that is represented by the graph b…
A. \( y < -4x + 5 \) \( y < x - 4 \)
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for $f(x) = x^2 + 8$ and $g(x) = \\sqrt{x - 2}$, find the following com…
For the domain of \(f\circ g\), we have \(x\geq2\), so the inequality to fill in the box is \(x\geq2\)
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12.) $f(4) = \\frac{4^{2}+2(4)}{4 - 5}$ $f(4) = $
\(-24\)
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question 5 which events were used in an attempt to limit people from vo…
The events used to limit people from voting are: - Grandfather clause - Poll Taxes - Literacy Tests
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f(7) = \\frac{7^2 + 2(7)}{7 - 5} f(7) = \\underline{\\quad\\quad}
\(31.5\)
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use the complete, weighted graph on the right and the brute force metho…
For the total weights: - A, B, C, D, A: 105 - A, B, D, C, A: 127 - A, C, B, D, A: 136 - A, C, D, B, A: 127 - A, D, B, C, A: 136 - A, D, C, B, A: 105 The optimal solutions are A, B…
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f(-2) = \\frac{(-2)^2 + 2(-2)}{-2 - 5} f(-2) = \\underline{\\quad\\quad}
\(0\)
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which of the following statements explains the relationship between soc…
d. Social Security is applied to all wages up to the maximum taxable earnings. Medicare is applied to all wages without limit.
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what is the following quotient? \\(\frac{9 + sqrt{2}}{4 - sqrt{7}}\\) \…
\(\frac{36 + 9\sqrt{7} + 4\sqrt{2} + \sqrt{14}}{9}\) (the third option)
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analyzing exponential decay graphs analyze the graph of the exponential…
Initial value: 1; Base: \( \frac{1}{3} \); Domain: All real numbers (\( (-\infty, \infty) \)) (Assuming the first dropdown is for initial value, the second for base, and the third…
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which statements are true about exponential decay functions? choose thr…
- The domain is all real numbers. - The function has a constant multiplicative rate of change. - The base must be less than 1 and greater than 0.
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8. graph the system of equations and determine the solution. $y = -3x -…
\((-2,1)\)
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(e) 1.8 × 0.23 = (f) 7.3 × 0.045 = (g) 0.07 × 4.2 = (h) 5.05 × 0.00039 …
Un paquet de 1000 feuilles coûte 25. ### Question 4:
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find the square root of the number.\\(\\sqrt{-64}\\)\ the square root i…
\( 8i \)
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what is the following quotient? \\(\frac{sqrt3{60}}{sqrt3{20}}\\) \\(\\…
$\sqrt[3]{3}$ (corresponding to the option $\boldsymbol{\sqrt[3]{3}}$)
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4.) $f(3) = 4(3) - 7$ $f(3) = \\underline{\\quad\\quad}$ $f(-5) = 4(-5)…
4. \( f(3)=\boldsymbol{5} \), \( f(-5)=\boldsymbol{-27} \) 5. \( f(4)=\boldsymbol{-2} \), \( f(-9)=\boldsymbol{37} \) 6. \( g(6)=\boldsymbol{65} \), \( g(-4)=\boldsymbol{-5} \) 7.…
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2 y = 2x + 4 y = 2x + \\frac{1}{3}
The equation that should correspond to the graph (assuming a possible mis - mark in the y - intercept) is \(y = 2x + 4\)
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which of the exponential growth functions has a multiplicative rate of …
The first table (with \( x \) values \(-1, 0, 1, 2\) and \( f(x) \) values \(\frac{1}{4}, 1, 4, 16\))
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the function f is graphed below. determine the intervals on which f inc…
The function is decreasing on the interval \( -6 < x < -2 \) (segment 1), increasing on the interval \( -2 < x < 3 \) (segment 2), and increasing on the interval \( 3 < x < 7 \) (…
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the function f is graphed below. determine the intervals on which f is …
The function is increasing on the interval \( -6 < x < -1 \) (segment 1), decreasing on the interval \( -1 < x < 5 \) (segment 2), and increasing on the interval \( 5 < x < 9 \) (…
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construct a table of values for the function. (round your answers to th…
| \( x \) | \( -3 \) | \( -2 \) | \( -1 \) | \( 0 \) | \( 1 \) | | --- | --- | --- | --- | --- | --- | | \( f(x) \) | \( 1.249 \) | \( 1.677 \) | \( 2.840 \) | \( 6.000 \) | \( 14…
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the function f is graphed below. determine the intervals on which f inc…
The function is \(\boldsymbol{\text{increasing}}\) on the interval \(\boldsymbol{-8}<x<\boldsymbol{-5}\) (segment 1), \(\boldsymbol{\text{decreasing}}\) on the interval \(\boldsym…
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25 nso.4.1 add integers with the same sign and with opposite signs usin…
For \(-7 + 4=-3\), \(8 + (-5)=3\), \(-6 + (-2)=-8\), \(-3 + 7 = 4\), \(5 + (-9)=-4\), \(-4 + (-3)=-7\) (and the number - line models involve starting at the first integer and movi…
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all exponential functions take the form of $y = a(b)^x$ what does the $…
- For "What does the a value represent?": Initial value, starting point, or y - intercept - For "What does the b value represent?": Growth/decay factor - For "What does the x valu…
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a professional baseball player throws a baseball from the outfield near…
The domain of the function in this context is \(0\leq t\leq4\) (or the interval \([0, 4]\) where \(t\) is in seconds).
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2/15 e expression be after you perform th 5 - 3 × 2 + 9 × 2 + 9 5 - 15 …
The middle option (the one with \(5 - 15\))
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31 select all exponential functions: a $y = \\frac{3}{2}x + 3$ b $y = 3…
B. \( y = 3 \cdot (2)^x \), C. \( f(x) = 0.5 \cdot (3)^x \), E. \( f(x) = 2 \cdot (2)^x \)
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solve. -10.6 × -8.05 = □ options: 85.33, -90.10, 81.3, -85.33
85.33