微积分
极限、导数、最优化与函数性质。
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add. simplify if necessary. \\(\frac{1}{2} + \frac{2}{3} = ?\\) — enter…
1
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multiply. $-2\\frac{1}{3} \\times -3\\frac{3}{10} = $ submit
\(7\frac{7}{10}\) (or \(\frac{77}{10}\))
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graph the equation. $y = -3|x| - 4$
The graph is a downward-opening V with vertex at $(0, -4)$, passing through points $(\pm1, -7)$ and $(\pm2, -10)$, extending infinitely along the lines $y=-3x-4$ (for $x\geq0$) an…
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claytons family is going to the bahamas on vacation next week. the airl…
\( w \leq 50 \) ### Part 2: Graphing the Inequality
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solve the following logarithmic equation. be sure to reject any value o…
Exact answer: \(x = e^{-\frac{1}{8}}\) Decimal approximation: \(x\approx0.88\)
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graph this function: $y = x - 9$ click to select points on the graph.
Plot the points $(0, -9)$, $(9, 0)$, and $(5, -4)$, then draw a straight line through them to graph $y=x-9$.
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solve the logarithmic equation. be sure to reject any value of x that i…
$e^2=\sqrt{x + 7}$
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solve the following exponential equation. express the solution set in t…
In terms of natural logarithms, the solution is \( x = \frac{1-\ln(247)}{6} \), and the decimal approximation is \( x\approx - 0.753 \)
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this equation describes a relationship between x and y. y = x - 1 compl…
Completed table: | x | y | |---|---| | 1 | 0 | | 2 | 1 | | 3 | 2 | | 4 | 3 | Correct graph: The left graph (passing through (1,0), (2,1), etc.)
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function g can be thought of as a scaled version of f(x)=|x|. what is t…
C. $g(x) = -0.2|x|$
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h(x) = 3·4^x choose 1 answer: a graph a b graph b c graph c
A. <The graph with y-intercept at (0,3), passing through (1,12), approaching 0 as x approaches negative infinity>
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choose the graph of the function. $g(x) = 2 \\cdot 4^x$ choose 1 answer…
A. <The graph passing through (0, 2) and (1, 8), with exponential growth approaching 0 as x approaches negative infinity>
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choose the function that is graphed below. choose 1 answer: a ( y = 5 c…
C. $y = 5 \cdot 2^x$
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choose the graph of the function. $f(x) = 2 \\cdot 3^x$ choose 1 answer…
A. <The graph passing through (0,2), rising steeply for positive x, and approaching 0 for negative x>
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choose the function that is graphed below. choose 1 answer: a ( y = 6 c…
A. $y = 6 \cdot 2^x$
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formative assessment look to the graph below and identify the key featu…
- y - intercept: \((0, 5)\) - x - intercept: \((2, 0)\) - Slope: \(-\frac{5}{2}\) (mark 'Negative') - Domain: \((-\infty,\infty)\) (or all real numbers) - Range: \((-\infty,\infty…
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6. write the equation of the line shown on in slope - intercept form.
\( y = x + 5 \)
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ebukas monthly rent is $750. if ebuka pays the rent late, his landlord …
$R(t) = 750(1.04)^t$
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8. write the equation of the line shown on the grid in slope - intercep…
\(y = 2\) (assuming the lower horizontal line; if the upper one, but the graph shows the lower horizontal line with arrows. Wait, no, looking at the graph again, the horizontal li…
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algebra: concepts and connections - plc exponential growth functions wh…
2.50
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1. write the equation of the line shown on the grid in slope - intercep…
$y=\frac{2}{3}x + 4$
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what does the term new woman mean? (1 point) a woman who has recently b…
a woman who resists limitations of society
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which equation represents an exponential function that passes through t…
$f(x) = 4(3)^x$
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when the dragons have lost their most recent game, 200 fans buy tickets…
\( t(w) = 200(1.1)^w \)
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which is the graph of $f(x) = 2(3)^x$?
The bottom graph (with the marked point (1,6)) is the graph of $f(x)=2(3)^x$.
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which of these shows the graphs of $y = x$ and $y = x^2$? a) graph b) g…
A) The graph with the upward - opening parabola (\( y = x^2 \)) and the line passing through the origin (representing \( y = x \) or a line through the origin along with the parab…
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el agua debemos beber el agua para mantener la salud. 1. los tomates 2.…
1. Debemos comer los tomates para mantener la salud. 2. Debemos limitar las grasas para mantener la salud. 3. Debemos comer los plátanos para mantener la salud.
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which was not one of the problems cities experienced as a result of rap…
B. limited recreation options
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$\\sqrt3{216} = \\square$
6
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slope: -3 y - intercept: 0
$y = -3x$
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compare using >, <, or =. 236 + 10 + 10 98
$236 + 10 + 10 > 98$
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post-world war i treaties a. ways these actions attempted to prevent wa…
s: - **A. Ways these actions attempted to prevent war**: - Limit of naval arms - Limit territorial expansion - **B. U.S. policy that these actions reflect**: - Isolationist Policy
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$\\sqrt{1.69} = \\square$
1.3
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name the excerpt. so it is enacted that this act may be cited as, \an a…
C. build an unlimited arsenal of weapons to fight Japan
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compare using >, <, or =. 942 842 + 100 + 10
$942 < 842 + 100 + 10$
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in the years following world war i, the united states adopted isolation…
- Decision not to join the League of Nations - Limiting territorial expansion in the Nine - Power Treaty - Signing the Kellogg - Briand Pact to stop war as “an instrument of natio…
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select all of the odd functions. $g(x) = -x^3 + 7$ $w(x) = x^4 + 2x^2 -…
- \( p(x) = -x^5 + 2x^3 + 8x \) (select this) - \( m(x) = -4x^5 + x^3 \) (select this) - Deselect \( g(x) = -x^3 + 7 \) and \( w(x) = x^4 + 2x^2 - 9 \).
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select all of the even functions.
The even functions are \( g(x) \) and \( k(x) \) (assuming the graphs: \( g(x) \) (top - left) and \( k(x) \) (bottom - right) are symmetric about the \( y \)-axis, while \( m(x) …
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algebra: concepts and connections - plc exponential growth functions re…
The graph will show an initial value that is lower on the y-axis.
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which graph represents the function $f(x) = \\frac{3}{2}(2)^x$?
The top graph (first graph shown) represents the function $f(x) = \frac{3}{2}(2)^x$.
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which statements are true of the function ( f(x) = 3(2.5)^x )? choose t…
1. The domain of the function is all real numbers. 2. The function is exponential. 3. The function increases by a factor of 2.5 for each unit increase in $x$.
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algebra: concepts and connections - plc exponential growth functions de…
3
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d. \\(\\log_{6}(x^{2} - 9) + \\log_{6}(3) = 3\\)\\(\\log_{4}(10) - \\lo…
For $\log_{6}(x^2 - 9)+\log_{6}(3)=3$, $x = 9$ or $x=-9$; for $\log_{4}(10)-\log_{4}(x + 3)=\log_{4}(x)$, $x = 2$
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(sqrt{\frac{9}{100}}=square)
$\frac{3}{10}$
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$\\sqrt{1.44} = \\square$
1.2
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sqrt{\frac{225}{16}} = square
$\frac{15}{4}$ or $3.75$
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8. an exponential function is graphed on the grid. draw the asymptote a…
- y-intercept: $(0, -3)$ - Asymptote: $y=-4$ - Growth or Decay?: Decay
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$\\sqrt3{1000} = \\square$
10
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$\\sqrt3{1728} = \\square$
12
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identify key features of an exponential function. 3. identify the key f…
$a = 1$ $b = 0.99$ Growth or Decay? Decay
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$\\sqrt3{729} = \\square$
9
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copy - identify key features of an exponential function. 2. identify th…
a = 20 b = 1.01 Growth or Decay? Growth
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$\\sqrt{3.24} = \\square$
1.8
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$\\sqrt{0.64} = \\square$
0.8
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warm-up #31 intro to exp fct possible points: 2 identify key features o…
Growth
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$\\sqrt{4.84} = \\square$
2.2
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what type of roots does the polynomial have? three imaginary; one real,…
D. Three real
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multiply by moving the decimal point. 37 × 1,000 select one of four 37,…
37,000
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multiply by moving the decimal point. 24.6 × 10 select one of four 24.6…
246 (corresponding to the option with value 246, assuming the options include one with 246 as the correct result of \(24.6\times10\))
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what kind of transformation converts the graph of $f(x) = 10|x + 5| + 8…
B. translation 2 units right
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f(x) = 3x³ + 5x² - 11x + 3; q. find all zeros. (hint: graph)
$x=1$, $x=-3$, $x=\frac{1}{3}$
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divide. 8.16 ÷ 1,000
0.00816
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what kind of transformation converts the graph of f(x) = |x + 8| + 4 in…
translation 1 unit down
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38/55 all imaginary roots comes in pairs. true false
True
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when you multiply a number by 10, 100, 1,000 and so forth, do you move …
To the right
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how many real zero(s) exist for the polynomial? f(x)=-x⁴ -x³ + 3x² - 3
0
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given ( p(x) = x^3 + x^2 - x - 9 ), what is the value of ( p(4) )? 14 6…
67
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how many zeros does the following function have? f(x)=x⁵ - 5x³ + x
5
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if under 21, new jersey law states that you may be under the influence …
more than.01% but less than.05% ### Second Question (Factors Affecting BAC)
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when looking at a quadratic graph, the solution(s) are always the _____…
x-intercept(s)
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identifying exponential growth functions which is an exponential growth…
$f(x)=0.25(5.25)^x$
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algebra: concepts and connections - plc exponential growth functions id…
$\frac{9}{2}$
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can you find the slope and type the correct code? please remember to ty…
DAHB
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f(x) = \\begin{cases} 5 - \\dfrac{1}{3}x, & -9 \\leq x < -3 \\\\ \\dfra…
A. <The graph with the first segment from (-9, 8) (closed dot) to (-3, 6) (open dot), and the second segment from (-3, -2) (closed dot) to (8, ~5.33) (closed dot)>
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f(x) = |x| g(x) = |x + 9| - 5 we can think of g as a translated (shifte…
To get the function $g$, shift $f$ **down** by $\boldsymbol{5}$ units and to the **left** by $\boldsymbol{9}$ units.
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match each expression with its value. -6 -5 7 undefined $f(4.999)$ $cir…
- $f(4.999)$: $\boldsymbol{-6}$ - $f(5)$: $\boldsymbol{7}$ - $f(5.0001)$: $\boldsymbol{-5}$ - $f(9)$: $\boldsymbol{7}$
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you might need: calculator\\(f(t) = \\begin{cases} t^2 - 5t &, \\ t \\l…
150
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f(x) = \\begin{cases} \\dfrac{1}{2}x + 6 &, -4 \\leq x < 0 \\\\ -5 &, 0…
A. [Graph with upper segment from closed dot (-4,4) to open dot (0,6), lower horizontal segment from closed dot (0,-5) to closed dot (7,-5)]
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g(x) = \\begin{cases} 3x + 4, & -4 \\leq x < 0 \\\\ -4, & 0 \\leq x \\l…
B. <The graph with left line segment having closed dot at (-4,-8) and open dot at (0,4), and horizontal line segment from (0,-4) (closed dot) to (6,-4) (closed dot)>
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you might need: calculator\\(f(x) = \\begin{cases}-x - 4 &, \\ x < 3 \\…
9
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match each expression with its value. 2 -9 -1 undefined $g(-0.0001)$ $g…
- $g(-0.0001)$: $-9$ - $g(0)$: $-1$ - $g(0.0001)$: $-1$ - $g(9)$: Undefined
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g(x) = \\begin{cases} -8, & -9 \\leq x < 3 \\\\ 4, & 3 \\leq x \\leq 9 …
A. The graph with a horizontal line at $y=-8$ (closed dot at $x=-9$, open dot at $x=3$) and a horizontal line at $y=4$ (closed dots at $x=3$ and $x=9$)
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question 16 4 pts amdm.par.8.1 (mc) given this recursive rule, identify…
B. $Y_{n+1} = Y_n \times 2.65$
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solve the exponential equation for x. 64^{7x - 8} = 1 x = show calculat…
$\frac{8}{7}$
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question 19 4 pts amdm.par.8.1 (mc) given this exponential function rul…
$Y_n = 15 \times 47^n$
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19 find the slope of the line that passes through all of the points on …
slope \(=-\frac{1}{2}\) y - intercept \(=-8\)
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which best describes the graph of the function $f(x) = 4(1.5)^x$? the g…
The graph passes through the point (0, 4), and for each increase of 1 in the x-values, the y-values increase by a factor of 1.5.
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read the excerpt from the code book. just as whit diffie predicted in t…
The evidence shows how much we use digital information today.
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function a and function b are linear functions. function a function b c…
The slope of Function A is less than the slope of Function B. The y - intercept of Function A is greater than the y - intercept of Function B. So first blank: less than; second bl…
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a limited - edition poster increases in value each year with an initial…
$y = 18(1.15)^x$
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which is the graph of $f(x) = 0.5(4)^x$?
The correct graph is the bottom (third) one, which passes through the points $(0, 0.5)$, $(1, 2)$, $(2, 8)$, and $(3, 32)$.
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8.31+2.5-4+0.9
7.71
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4. simplify the expression. \\sqrt{9e^{6x}} = \\square
\(3e^{3x}\)
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41.) given the graph with the points (-2, 0) and (0, 4), find the rate …
2 ### 42) #### a) Graph of \(y = 3x-2\)
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ramon is graphing the function $f(x) = 3(4)^x$. he begins by plotting t…
The middle graph with the plotted point $(0, 3)$
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6. $3 - 1\frac{1}{2} + \frac{1}{2} + 1$
4
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which is the graph of $f(x) = 5(2)^x$?
The bottom graph (with y-intercept $(0,5)$ and increasing exponential curve) is the graph of $f(x)=5(2)^x$.
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3. simplify the expression. $(4e^{-2x})^3 = \\square$
\(64e^{-6x}\)
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(\frac{7}{3}+\frac{4}{5}-\frac{1}{15})
$\frac{46}{15}$ or $3\frac{1}{15}$
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fill in the blanks below. (a) find the slope of the line passing throug…
\( 0 \) ### Part (b)