微積分
極限、導數、最優化與函數性質。
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shilpa’s gym membership includes a one-time fee of $20. she then pays a…
\( 5 \)
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shilpa’s gym membership includes a one - time fee of $20. she then pays…
The statement " \(m = n\), so \(y=\frac{a_m}{b_n}\) is the horizontal asymptote." (the second option among the given choices)
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which graph models the piecewise functions shown below: $f(x) = \\begin…
To determine the correct graph, we check the key points and the behavior of each piece of the piecewise function. The correct graph should have: 1. A line segment with slope \(-\f…
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collision coverage: calculating insurance payout shia has a car insuran…
\$7,500
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which is the graph of $f(x) = \\frac{x - 1}{x^2 - x - 6}$?
The left - most graph (the first graph among the three)
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eddie asked his brother gerald to help him with his homework. eddies fi…
"I'm sorry, Eddie, but your answer is incorrect because your slope for your new equation in Step 3 was supposed to be \(-\frac{17}{13}\) and not \(\frac{13}{17}\)."
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write the equation of a line perpendicular to $y = -\frac{2}{3}x + 7$ a…
\( y=\frac{3}{2}x - 19 \) (the fourth option: \( y=\frac{3}{2}x - 19 \))
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identify the vertical asymptote(s) of the function. choose two correct …
The two correct answers are \(x=-1\) and \(x = 4\), so the options are: - \(x=-1\) - \(x = 4\)
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where is the hole for the following function located? $f(x) = \\frac{x …
\( x=-3 \)
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where is the removable discontinuity of $f(x) = \\frac{x + 5}{x^2 + 3x …
\(x=-5\)
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which statement is true about the discontinuities of the function $f(x)…
There are asymptotes at \(x = 7\) and \(x = -\frac{4}{3}\) (the second option).
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what are the removable discontinuities of the following function? $f(x)…
\(x=-6\) and \(x = 6\) (the option: \(x=-6\) and \(x = 6\))
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13) $6x^2 + 3x - 84$
\(3(2x - 7)(x + 4)\)
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seyed’s work: - vertical asymptote ( x^2 - 9 = 0 ) ( (x - 3)(x + 3) = 0…
Seyed's work is correct. For the vertical asymptotes, since the denominator \(x^{2}-9=(x - 3)(x + 3)\) has no common factors with the numerator \(x - 1\), setting the denominator …
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write the equation of a line parallel to $y = -3x + 9$ and passing thro…
\( y = - 3x+12 \) (the first option: \( y=-3x + 12 \))
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identify whether each value of x is a discontinuity of the function by …
- \(x = - 3\): asymptote - \(x=-2\): asymptote - \(x = 0\): hole - \(x = 2\): neither - \(x = 3\): neither - \(x = 5\): neither
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which functions have removable discontinuities (holes)? choose three co…
- \( f(x)=\frac{x + 7}{x^{2}+5x - 14} \) - \( f(x)=\frac{x^{2}-9}{x^{2}+7x + 12} \) - \( f(x)=\frac{x - 1}{x^{2}-1} \)
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use the equation $p = \\frac{8.31}{v}$, where $p = $ pressure and $v = …
The pressure approaches infinity.
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which of the following statements are true of this rational function? c…
- There is a removable discontinuity at \(x = -a\). - There is a vertical asymptote at \(x = 0\).
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identify the vertical asymptotes of the function. choose two correct an…
B. \( x = 4 \), D. \( x=-4 \) (assuming the options are labeled as: A. \( x = 16i \), B. \( x = 4 \), C. \( x=-16 \), D. \( x=-4 \), E. \( x = 0 \))
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nancy deposited $5,000 into a savings account with a 3% simple interest…
\( 750 \)
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identify the vertical asymptotes of the function. choose two correct an…
B. \(x = 1\), E. \(x = 2\) (assuming the options are labeled as: A. \(x=-2\), B. \(x = 1\), C. \(x=-8\), D. \(x = 8\), E. \(x = 2\), F. \(x=-1\))
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question simplify the expression below using order of operations. (6 + …
141
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where is the vertical asymptote(s) for the simplified function $f(x) = …
\( x = -1 \) (the last option: \( x = -1 \))
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question simplify the expression below using order of operations. 4 - 4…
\(0\)
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b) $g(x) = \\frac{1}{2} \\cdot 4^x$ left: $\\lim\\limits_{x \\to -\\inf…
- Left Limit: $\boldsymbol{0}$ - Right Limit: $\boldsymbol{\infty}$ - Increasing or Decreasing: $\boldsymbol{\text{Increasing}}$ - Concave Up or Concave Down: $\boldsymbol{\text{C…
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finding discontinuities of a rational function find the discontinuities…
The removable discontinuity is at \(x = - 3\) (or the point \((-3, \frac{(-3)+9}{(-3)+1})=(-3, - 3)\))
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question simplify the expression below using order of operations. $7 \\…
\(58\)
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question simplify the expression below using order of operations. $4^2 …
113
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true or false? when graphing a line in point-slope form, i am supposed …
False
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question simplify the expression below using order of operations. $6 \\…
\(58\)
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ifying multiple vertical asymptotes what are the vertical asymptotes of…
A. \(x=-1\), B. \(x = 1\)
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a function is represented by the values in the table. | x | y | |----|-…
is not
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describe the end behavior of each function. 1) $f(x) = -2x^2 - 8x - 7$ …
1. As \( x\to\pm\infty \), \( f(x)\to-\infty \) 2. As \( x\to\pm\infty \), \( f(x)\to-\infty \) 3. As \( x\to+\infty \), \( f(x)\to+\infty \); as \( x\to-\infty \), \( f(x)\to-\in…
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identifying the vertical asymptote identify the vertical asymptote of t…
\( 8 \)
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a. $4\\cdot10^{3} + 7\\cdot10^{2} + 8\\cdot10 + 2 + 9\\cdot10^{-1} + 6\…
$\frac{1101}{100000}$
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ating a rational function x | f(x) -1 | -1 -0.1 | -10 -0.01 | -100 -0.0…
s: 1. As \( x \) approaches zero from the positive direction, \( f(x) \) approaches \( +\infty \) (increases without bound). 2. As \( x \) approaches zero from the negative direct…
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complete the table of values for the function f(x) = 1/x. first table (…
\( g = 10 \) \( h = 1 \)
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complete the table of values for the function \\( f(x) = \\frac{1}{x} \…
\( a = -1 \) \( b = -10 \) \( c = -100 \) \( d = -1000 \) \( e = 1000 \) \( f = 100 \)
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which of the following is not an equation that can model the graph belo…
None of the answers
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is the function in a graph a linear function or a nonlinear function? s…
The function in the graph is a straight line, so it is a linear function. (First drop - down: "is a straight line" (or similar indicating straight - line graph); Second drop - dow…
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does the table of values represent a function that is linear or nonline…
For each pair of points, the rate of change is 3. Since the rate of change is constant, the function is linear.
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which graph shows a system of equations that solves $-\\frac{1}{x - 1} …
The Middle Graph (the second graph among the three shown)
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a. what are the other three members of this fact family? select all tha…
C. \(9 + 2 = 11\), F. \(2 + 9 = 11\), G. \(11 - 9 = 2\)
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the graph of the function h(x) is shown. find the function values h(5),…
\( h(5)=\boxed{0} \) \( h(7)=\boxed{6} \) \( h(8)=\boxed{6} \)
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write a function in any form that would match the graph shown below. an…
\(f(x)=-\frac{3}{2}(x + 1)(x - 4)\) (or \(f(x)=-\frac{3}{2}x^{2}+\frac{9}{2}x + 6\))
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21/41 graph $y = (x - 3)^2 - 4$
The graph is a parabola with vertex at \((3, - 4)\), opening upward, axis of symmetry \(x = 3\), and passing through points like \((2,-3)\), \((4,-3)\), \((1,0)\), \((5,0)\) (plot…
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24. find the exact value of the logarithm without using a calculator. \…
\( 4 \)
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sketching rational functions ( t(x) = \frac{2x - 3}{x - 2} ) find the f…
- **X - intercepts**: \(\boldsymbol{(\frac{3}{2},0)}\) - **Y - intercepts**: \(\boldsymbol{(0,\frac{3}{2})}\) - **Vertical asymptotes**: \(\boldsymbol{x = 2}\) - **Horizontal asym…
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e a function in any form that would match the graph shown below. answer…
\(f(x)=-\frac{3}{4}(x - 2)^{2}(x - 6)\) (or expanded form)
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the graph of the function below, including correct signs, x-intercepts …
The x - intercepts (roots) are at \( x=-6 \), \( x=-4 \), and \( x = 0 \) (the point \( (0,0) \) is both an x - intercept and a y - intercept). To plot the points: - For \( x=-6 \…
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question what is the equation of the line that passes through the point…
The equation of the line is $y=-x + 4$ (or $x + y=4$ or $y - 3=-1(x - 1)$)
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which of the following equations represents the graph pictured? f(x) = …
\(f(x)=-|x + 1|\) (the fourth option)
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write the equation of the line in fully simplified slope - intercept fo…
\(y =-\frac{7}{6}x + 7\)
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1. for the graph of a function shown to the right, find (a) the domain …
B. The equation of the line in slope - intercept form is \( y = \frac{7}{3}x+\frac{28}{3} \) ### Problem 20: Solve the system using elimination \(\begin{cases}4x + 16y=4\\4x-16y =…
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here is the graph that represents a function which equation represents …
\(f(x)=|x|-5\)
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what is the equation of the absolute value function? f(x)= |x+4| f(x)= …
B. \(f(x)=|x| + 4\)
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(18) (6 - 2)·0 + 8 6÷2=3,3·9=27+ 16=43
8
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a. \\(\\int \\frac{tan^{-1}(x)}{1 + x^2} dx\\)
\( \frac{(\tan^{-1}(x))^2}{2} + C \)
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the function $f(x)=x^2$ was transformed to create the function $g(x)=f(…
(4, -1)
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13. every man being presumed innocent until he has been pronounced guil…
Law (under Social Science)
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h(t) = -16t² + 27t + 12 what is the velocity? what is the starting heig…
Velocity: \( 27 \) Starting height: \( 12 \)
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c. $12 = 3e^{-x + 5}$
\(x = 5-\ln(4)\) (or \(x = 5 - 2\ln(2)\) or the approximate decimal value \(x\approx3.614\))
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name date 2. y = x + 3 y = 2x + 4
The solution is \( x = -1 \), \( y = 2 \)
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find all the zeros of the function. (enter your answers as a comma-sepa…
(Zeros): \(\frac{3}{4}, 5i, -5i\)
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instructions: elves like to represent their toy - making with number pr…
s: 1. \( 3\times(10\times2)\div5 = 12 \) 2. \( 8 + 3 + 3\times6 = 29 \) 3. \( 5\times10-(6 - 3) = 47 \) 4. \( 12\div(6 + 4 - 8) = 6 \) 5. \( 4+(3 - 3)^{3} = 4 \) 6. \( (15 - 9)\di…
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for the graph of a function shown to the right, find (a) the domain and…
To solve this problem, we analyze the graph of the function: ### Part (a): Domain and Range - **Domain**: The domain of a function is the set of all possible \( x \)-values. From …
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2/10 what impact did greco-roman civilization have on western civilizat…
C. It had a profound impact on its development.
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9/41 which equation represents an absolute value function shifted down …
D. \( y = |x| - 3 \) (assuming the options are labeled A, B, C, D in order as shown: A. \( y = |x| + 3 \), B. \( y = |x - 3| \), C. \( y = |x + 3| \), D. \( y = |x| - 3 \))
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what is the effect of the transformation $y = \\sqrt{x} + 4$ compared t…
B. Shift up by 4 units
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simplify the expression. (1) $9^2 + 3 \\cdot 5$ (2) $4^3 - 30 \\div 2$ …
\( 96 \) ### (2) \( 4^3 - 30 \div 2 \) ## Step1: Calculate the exponent and division \( 4^3 = 64 \), \( 30 \div 2 = 15 \) ## Step2: Subtract the results \( 64 - 15 = 49 \)
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andrea made a mistake when trying to find \\(\\frac{3}{4}\\) of 24. and…
First box: 4, Second box: 3
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how can i find \\(\\frac{2}{3}\\) of 12? first, find \\(\\frac{1}{3}\\)…
4
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functions and lines identifying linear functions given ordered pairs fo…
Function 1: Not linear Function 2: Not linear Function 3: Not linear Function 4: Linear (For each function, the correct option is: Function 1: Not linear Function 2: Not linear Fu…
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functions and lines identifying linear functions given ordered pairs fo…
Function 1: Linear Function 2: Linear Function 3: Linear Function 4: Not linear
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question for the function $f(x) = x^7 - 1$, find $f^{-1}(x)$. answer - …
\( f^{-1}(x) = \sqrt[7]{x + 1} \) (the third option)
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for the function $f(x) = sqrt3{x + 9}$, find $f^{-1}(x)$. answer - $f^{…
\( f^{-1}(x) = x^{3}-9 \) (the fourth option: \( f^{-1}(x) = x^{3}-9 \))
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for the function $f(x) = sqrt3{x} - 10$, find $f^{-1}(x)$. answer $f^{-…
D. \( f^{-1}(x) = (x + 10)^3 \)
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homework: hw 7 in each of the following problems, write an addition or …
For part a, the expression is \( 121 - (-65) \) and the difference is 186. For part b: ## Step1: Identify the operation The initial temperature is -2, and it rose by 17, so we use…
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for the function $f(x) = x^{\frac{1}{3}} - 7$, find $f^{-1}(x)$. answer…
\( f^{-1}(x) = (x + 7)^3 \) (the second option)
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use the chip model to show the following. a. (4)(2) b. 4(-2) c. -14 ÷ 7…
B (the bottom right figure, labeled B)
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1 yard = 36 inches how many inches are in \\(\\frac{1}{4}\\) yard? \\(\…
9
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juanita is testing her new model airplane. she starts its descent at an…
-500
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a new homeowner is painting the walls of a room. the walls have a total…
5.5
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divide. -82.5 ÷ 1000 -82.5 ÷ 1000 = \\square (type an integer or a deci…
\(-0.0825\)
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divide. \\(\\frac{19.57}{10}\\) the quotient is \\(\\square\\). (type a…
1.957
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one painter can paint a house in 10 days, yet a more experienced painte…
\( 2.308 \) (or \(\frac{30}{13}\approx2.308\))
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divide 0.846 ÷ 0.039. round the quotient to the nearest hundredth. the …
\(21.69\)
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divide. \\(\\frac{1.215}{0.027}\\) the quotient is \\(\\square\\). (typ…
45
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samara is going on a hike on a nature trail. she starts at the trail he…
\( d = 0 + 150t \) (or simplified \( d = 150t \)) Filling the boxes: First box \( d \), second box \( 0 \), third box \( 150t \)
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divide. also, estimate to see if the answer is reasonable. $5.2\\overli…
\(8\)
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24/25 choose the graph for y = -2x² + 4x - 6 (show your work on paper)
A (assuming A is the graph that opens downward, has vertex at (1, - 4) and y - intercept at (0, - 6))
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what is the vertical intercept for this line? this is the distance sama…
0
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divide -2.1 by -0.3. the quotient is \\(\\square\\). (type an integer o…
7
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divide. 27 ÷ (-0.03) 27 ÷ (-0.03) = \\square (type an integer or decima…
\(-900\)
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divide. then estimate to see whether the proposed answer is reasonable.…
\(5.8\)
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0.07\\overline{)35} the quotient is \\square. (type an integer or a dec…
\(500\)
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evaluate the expression using a calculator. round your answer to two de…
$\approx\boxed{27.86}$ (or approximately 27.81 if we use a different method, but the more accurate calculation with the calculator gives approximately 27.86) Wait, let's use a cal…
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question move at least one of the 5 guide points below to complete the …
To graph \( y = 2(x + 2)^2 \): 1. Move the blue vertex point (originally at \((0,0)\)) 2 units to the left to \((-2, 0)\). 2. For the red guide points: - Take the points that are …
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evaluate the expression using a calculator. round your answer to two de…
3.72