微積分
極限、導関数、最適化、関数挙動。
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evaluate the function at the given value of the variable. $f(x)=4x^{2}-…
60
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graph the function. $p(x) = x^2 - 1$
To graph \( p(x)=x^2 - 1 \): 1. Recognize it's an upward - opening parabola (since the coefficient of \( x^2\) is positive) with vertex at \( (0,-1) \), x - intercepts at \( (-1,0…
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question 9 of 10 which sentence best describes the root of walters unha…
D. He wants to provide for his family but has limited options.
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what is one theme in a raisin in the sun? a. education can make people …
C. Racism limits a person's choices in life.
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which graph represents $y = \\sqrt3{x} + 2$?
The third graph (the one in the middle - lower position among the four graphs)
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a) $f(x) = x^2 + 4$ b) $f(x) = -x^2 - 2x$ 2 mieiscami zerowymi f
Assuming the problem is to find the zeros (roots) of the given quadratic functions. Let's solve each part: ### Part a) \( f(x) = x^2 + 4 \) # Explanation: ## Step 1: Set \( f(x) =…
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find the asymptotes and intercepts of the function, and graph the funct…
### For x - intercepts: A. The x - intercept(s) is/are \(1\) ### For y - intercepts: A. The y - intercept(s) is/are \(\frac{1}{24}\)
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question 8 of 10 what is one theme in a raisin in the sun? a. education…
C. Racism limits a person's choices in life.
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find the asymptotes and intercepts of the function, and graph the funct…
### Horizontal Asymptote: A. The function has one horizontal asymptote, \( \boldsymbol{y = 0} \). ### Vertical Asymptotes: A. The function has two vertical asymptotes. The leftmos…
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an air traffic controller is tracking two planes. to start, plane a is …
First box: 56 Second box: 7534
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evaluate the limit based on the graph of f shown. \\(\\lim\\limits_{x\\…
\(0\)
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question 3 of 10 what does the primary conflict over the insurance chec…
D. The conflict between the characters about their future as a family and as individuals
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find the domain of the function f. use limits to describe the behavior …
For the domain: A. The domain is the set of all real numbers except \( x eq - 6 \) For \( \lim_{x ightarrow - 6^{-}}f(x) \): \(-\infty\) For \( \lim_{x ightarrow - 6^{+}}f(x) \):…
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find the asymptotes and intercepts of the function, and graph the funct…
### For x - intercepts: A. The x - intercept(s) is/are \(1\). ### For y - intercepts: A. The y - intercept(s) is/are \(\frac{1}{30}\).
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find the asymptotes and intercepts of the function, and graph the funct…
For horizontal asymptote: B. The function has one horizontal asymptote, \( y = 0 \) For vertical asymptote (if we continue, but based on the first part): The function has two vert…
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find the domain of the function f. use limits to describe the behavior …
The domain option: A. The domain is the set of all real numbers except \( x=-6 \) \( \lim_{x ightarrow - 6^{-}}f(x)=-\infty \) \( \lim_{x ightarrow - 6^{+}}f(x)=+\infty \)
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a. the domain is the set of all real numbers except x≠ -6. (use a comma…
For \( \lim_{x ightarrow - 6^{-}}f(x) \), if \( f(x)=x \), the answer is \( - 6 \). For the second limit (if it's \( \lim_{x ightarrow - 6^{+}}f(x) \)) and \( f(x)=x \), the answe…
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a line passes through the point (-8, 5) and has a slope of \\(\\frac{5}…
\(y - 5=\frac{5}{4}(x + 8)\)
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a line passes through the point (4, 5) and has a slope of -2. write an …
$y - 5=-2(x - 4)$
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a line passes through the point (-8, -8) and has a slope of \\(\\frac{5…
$y + 8=\frac{5}{4}(x + 8)$
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graph the line. $y + 1 = 5(x - 4)$
To graph the line \( y + 1 = 5(x - 4) \): 1. Plot the point \( (4,-1) \) (from the point - slope form). 2. Use the slope \( m = 5 \) to find another point. For example, from \( (4…
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a line passes through the point (-5, 7) and has a slope of 1. write an …
\(y - 7=(x + 5)\)
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graph the line. $y - 4 = 3(x + 1)$
The line is graphed by first plotting the point \((-1,4)\) and then using the slope \(m = 3\) to find other points (such as \((0,7)\) and \((-2,1)\)) and drawing a straight line t…
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is the function k(x) even, odd, or neither?
Neither
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which of the functions below could have created this graph? a. $f(x)=x^…
C. \( F(x)=-x^{6}-5x^{4}-4x^{2}+5 \)
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rewrite the function to make it easy to graph using transformations of …
The graph \(\boldsymbol{\text{is stretched}}\) vertically by a factor of \(\boldsymbol{5}\) and is translated \(\boldsymbol{2}\) unit(s) to the \(\boldsymbol{\text{right}}\) and \…
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write the equation of the line in fully simplified slope - intercept fo…
\(y = 2x-2\)
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for the function below, find (a) the critical numbers; (b) the open int…
A. Decreasing on \((-1, 3)\)
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this is the graph of a linear inequality. write the inequality in slope…
$y > \frac{1}{2}x - 3$
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graph the equation. $y = 6|x - 7|$
The graph of \(y = 6|x - 7|\) is a V - shaped graph with vertex at \((7,0)\), opening upwards, passing through points such as \((6,6)\) and \((8,6)\) (and other points) and symmet…
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which integer is closest to \\(\\sqrt3{23}\\)?
\(3\)
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unit: functions progress: the movement of the progress bar may be uneve…
The correct option is the one with \( f(x + 2) = 3x + 1 \) (the second option among the given choices).
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plot all of the existing five features of the following rational functi…
- **Vertical Asymptote**: \( x = -4 \) (plot at \( x = -4 \)) - **Horizontal Asymptote**: \( y = 0 \) (plot along \( y = 0 \)) - **y-Intercept**: \( (0, \frac{3}{4}) \) (plot at \…
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two triangular pens are built against a barn. one hundred seventy meter…
The side perpendicular to the barn is about \(\boldsymbol{28.33}\) meters long and the side parallel to the barn is about \(\boldsymbol{85.00}\) meters long.
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unit d functions test review look at the relation. complete the stateme…
The relation \(\boldsymbol{\text{is not}}\) a function because for every \(\boldsymbol{\text{x - value}}\) there \(\boldsymbol{\text{is not}}\) exactly one \(\boldsymbol{\text{y -…
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slope and y-intercept quick check possible points: 50 anyah is driving …
$y = 85-\frac{3}{4}x$ (corresponding to the first option: $y = 85-\frac{3}{4}x$)
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unit d functions test review consider the data set shown on the graph n…
(0, 3) (Note: The answer may vary depending on the actual graph. Another possible answer could be any (x,y) pair where the x - value is repeated. For example, if there are two poi…
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evaluate. write your answer as a decimal or whole (0.2)² =
\(0.04\)
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three balloons and three exponential expressions are shown on the scree…
For the blue balloon's `driveDistance` code, change the exponent part from \(3^1\) to \(3^3\) (modify the last number in the exponent block from 1 to 3).
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5. write the equation of the line perpendicular to y = ½ x + 3 that pas…
\( y=\frac{1}{2}x-\frac{11}{2} \) (or \( y = 0.5x-5.5 \)) ### For the second sub - question (perpendicular line):
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unit: functions progress: the movement of the progress bar may be uneve…
All real numbers except 0 (corresponding to the option with text "All real numbers except 0")
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1 which statement best compares how absolute and constitutional monarch…
A. Constitutional monarchies limit the monarch’s power, while absolute monarchies give the monarch total control.
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example 4 15. weight the formula to convert weight in pounds to stones …
s: a. The inverse function is \( \boldsymbol{p^{-1}(x)=14x} \), and it converts weight in stones to weight in pounds. b. The weight of the dog in pounds is \( \boldsymbol{35} \).
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examples 2 and 3 find the inverse of each function. then graph th neces…
The inverse of \( f(x)=x + 2\) is \( f^{-1}(x)=x - 2\) ### Problem 7: \( f(x)=-2x + 1 \)
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which is the graph of the function f(x) = 2x³ - 7x² + 2x + 3?
The graph of the function \( f(x)=2x^{3}-7x^{2}+2x + 3 \) is the one that crosses the x - axis at \( x =-\frac{1}{2}\), \( x = 1 \) and \( x = 3 \), with the left - end going down…
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the graph of f(x) = x³ - 3x² + 4 is shown. based on the graph, how many…
two real number solutions (the option with "two real number solutions")
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question 9 of 10 jayden received a $600 signing bonus when he accepted …
C. \( y = 26x + 600 \)
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Question was provided via image upload.
(The graph with x - intercepts at \( x=-3,-2,-1 \), falling as \( x ightarrow-\infty \) and rising as \( x ightarrow+\infty \), and with the correct sign changes between the roots…
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question 8 of 10 the equation $y = \\begin{cases} 25x & 0 \\leq x \\leq…
B. 38
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question 6 of 10 when modeling hourly pay, which part of the equation i…
D. \( y \)-intercept
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write the equation in exponential form. \\(\\log_{2} 85 = x\\) \\(\\log…
$2^x = 85$
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explain how the domain and range of a one - to - one function and its i…
domain
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explain how the domain and range of a one-to-one function and its inver…
range
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write an equation of the inverse for the one-to-one function as defined…
\( x + 3 \)
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explain how the domain and range of a one-to-one function and its inver…
domain
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explain how the domain and range of a one-to-one function and its inver…
range
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write an equation of the inverse for the one-to-one function as defined…
\( x - 9 \)
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this is the graph of a linear inequality. write the inequality in slope…
\( y > -4x + 1 \)
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-93² + 4 × 5 - 20²
\(-729\)
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\\(\\frac{2^3(4^2 - 4)}{2 \\times 3}\\)
16
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solve the equation. \\ln y = 11 the solution set is \\square .
$\{e^{11}\}$
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under continuous compounding, the amount of time t in years required fo…
23.2
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under continuous compounding, the amount of time t in years required fo…
11.6
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under continuous compounding, the amount of time t in years required fo…
20.4
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use the change-of-base formula to approximate the logarithms to four de…
\(1.3181\)
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simplify the expression. \\ln e^{15} = \\square
15
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graph the equation by completing the table and plotting points. identif…
To graph \( y = \ln x-6 \): - **Vertical Asymptote**: Draw the vertical line \( x = 0 \) (dashed line, since it's an asymptote, not part of the graph). - **Plot Points**: Plot the…
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graph the equation by completing the table and plotting points. identif…
The domain of the function \( y = \ln x - 6 \) is \( (0, \infty) \) (or all positive real numbers).
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graph the equation by completing the table and plotting points. identif…
The domain of the function \( y = e^x+3 \) is all real numbers, or in interval notation \( (-\infty, \infty) \)
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graph the equation by completing the table and plotting points. identif…
For \( x=-4 \), \( y\approx3.02 \); for \( x = -3 \), \( y\approx3.05 \); for \( x=-2 \), \( y\approx3.14 \); for \( x=-1 \), \( y\approx3.37 \); for \( x = 0 \), \( y = 4.00 \); …
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graph the equation by completing the table and plotting points. identif…
To graph \( y = e^x + 5 \): 1. Plot the horizontal asymptote \( y = 5 \) (dashed line). 2. Plot the points from the table: \((-3, 5.05)\), \((-2, 5.14)\), \((-1, 5.37)\), \((0, 6)…
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graph the equation by completing the table and plotting points. identif…
For \( x = -3 \), \( y\approx5.05 \); for \( x = -2 \), \( y\approx5.14 \); for \( x = -1 \), \( y\approx5.37 \); for \( x = 0 \), \( y = 6 \); for \( x = 1 \), \( y\approx7.72 \)…
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expand into a sum and/or difference of logarithms of z, or as a single …
\(\frac{1}{6}\log_{8}z\)
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find the domain of the function and express the domain in interval nota…
\((-\infty, 7)\)
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find the vertex of the following quadratic y = 2x² -12x +11 a) (3, -7) …
A. (3, -7)
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graph the logarithmic function by writing the function in exponential f…
\( x = 4^{y} \)
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evaluate the common logarithm without the use of a calculator. log0.000…
\(- 4\)
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evaluate the common logarithm without the use of a calculator. log 1000…
3
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module 4 - practice quiz (ch 7) quadratic equations and functions quest…
The graph labeled D (the bottom - right graph)
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graph the function on a graphing calculator. use the max or min feature…
\((0.5,4)\)
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write the function in the form f(x)=a(x - h)^2 + k by completing the sq…
\(3(x - 3)^2 - 16\)
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graph the function. $k(x) = (x - 1)^2$
The graph is a parabola opening upwards with vertex at \((1, 0)\), passing through points like \((0, 1)\), \((2, 1)\), \((3, 4)\), \((-1, 4)\) (plotted on the given coordinate gri…
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graph the function. $r(x) = (x + 1)^2$
The graph is a parabola opening upwards with vertex at \((-1, 0)\), passing through points like \((0, 1)\), \((-2, 1)\), \((1, 4)\), \((-3, 4)\) (plotted and connected smoothly).
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match the function with its graph. $g(x)=(x + 4)^2$
B
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for the following expression, $2f(x + 3) + 7$, write this as a square r…
Function: \( \boldsymbol{g(x)=2\sqrt{x + 3}+7} \) Transformations: Vertical Stretch by 2, Horizontal translation left 3, vertical translation up 7
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(u5) the graph of the function f, defined by $f(x) = \\frac{1}{3}(x + 2…
\( x = -5 \) & \( x = -2 \)
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question 3 (1 point) what is the slope of the line pictured in the stan…
D. \(\frac{1}{2}\)
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precalculus unit 3 test 2025 name date per multiple choice: circle the …
The polynomial of least degree is \( x^3-5x^2 - 3x + 15 \) ### Question 8: Describe the end behavior of the function \( f(x)=-2x^3+6x^2 - 5x + 4 \) and find \( \text{As }x ightarr…
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a student showed the steps below while solving the equation 14 = \\log_…
The error is in Step 2. The function \( y_1 \) should be \( y_1 = 14 \) (a horizontal line with \( y = 14 \)), not \( y_1=\log 14 \). The student misapplied the change of base for…
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the exponential function ( f ) is defined by ( f(x) = ab^x ), where ( a…
D. \(f\) demonstrates exponential growth because \(a>0\) and \(b > 1\)
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1 which of the following statements is true about the exponential funct…
D. \( h \) is always decreasing, and the graph of \( h \) is always concave down.
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what is the message of this poster? young men should join the navy. opp…
A. Young men should join the navy.
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quiz, marcar para revisar, 1 de 10, gua y s (image of coordinate grid w…
La gráfica superior (la primera gráfica mostrada) es la que representa una función con asintota horizontal en \( y = 0 \) y comportamiento de decrecimiento a medida que \( x \) au…
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¿qué conjunto de pares ordenados podría generarse mediante una función …
\( (0, 1), (1, 3), (2, 9), (3, 27) \)
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available: dec 10, 2025 12:00am until dec 17, 2025 5:00pm details no ad…
6 (assuming the slope is 2, which is a common case for such problems when the table is missing but the logic is that linear function's output difference is slope * input differenc…
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¿qué función tiene un rango de? $y < 3$? $y = (2)^x - 3$ $y = 3(2)^x$ $…
\( y = -(2)^x + 3 \) (la última opción)
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300 multiples of 100 one of these numbers is a multiple of 100. which o…
3
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¿qué gráfica representa una función exponencial?
La gráfica que **no** es simétrica en el eje \( y \) (aunque en la imagen dada, la primera gráfica es simétrica en \( y \) y no es exponencial, así que la otra gráfica, si existe,…
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¿qué gráfica representa una función exponencial?
La gráfica que representa la función exponencial es la que no tiene asíntota vertical, es decir, la que tiene una curva suave, sin saltos, y con una asíntota horizontal. En la ima…
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10. suppose you invest $2000 at an annual interest rate of 5.1% compoun…
\$2324 (assuming the correct option is the last one, but let's calculate properly) Wait, let's do the calculation. The formula for continuous compounding is \( A = Pe^{rt} \), whe…