Calcul
Limites, dérivées, optimisation et comportement des fonctions.
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attempt 1: 10 attempts remaining. if ( f(x) = \frac{x^3 - 7x}{7x^2 + 9}…
\( \boxed{\dfrac{7x^4 + 76x^2 - 63}{(7x^2 + 9)^2}} \)
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attempt 6: 5 attempts remaining. given ( y = \frac{x^5 - 1}{x^5 + 1} ),…
\( \frac{10x^4}{(x^5 + 1)^2} \)
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match each word with the phrase that best defines it. limitation priori…
- limitation → a reduction or a restriction on the amount of something - priority → a goal that receives special importance or emphasis - command economy → an economy that is mana…
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the area of the region bounded between the given graph of $f$ and the $…
\(64\)
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match each equation to the correct graph. the ^2 means to the second po…
To solve the problem of matching each quadratic function (in vertex form \( f(x) = a(x - h)^2 + k \), where \((h, k)\) is the vertex and \(a\) determines the vertical stretch/comp…
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writing the equation defining the function in the form $y = f(x)$ usual…
$y = 1 - 4x^2$
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using the graph of ( y = f(x) ) to the right, and given that the zero o…
(a) $20$ (b) $20$
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use them to evaluate each limit, if it exists. (a) $f(-1)g(-1)$ (b) $li…
To solve these problems, we analyze the graphs of \( y = f(x) \) and \( y = g(x) \) to determine the necessary function values and limits. ### Part (a): \( f(-1)g(-1) \) ## Step 1…
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which of the following provides an example of a limited government? the…
the United States
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in a limited government, leaders are subject to what? only their own au…
C. legal limits and punishments (assuming the options are labeled A, B, C as "only their own authority", "rites of public worship", "legal limits and punishments" respectively)
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many limited governments employ what as safeguards against corruption a…
C. bills of rights
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which of the following is an \unlimited\ style of government? democracy…
dictatorship
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write the equation of the line parallel to $f(x)=-\frac{3}{8}x + 7$ tha…
$y - 9 = -\frac{3}{8}(x - 5)$ --- ### Second Problem
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which of the following is a characteristic of unlimited governments? to…
A. total authority
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question 9 (4 points) what is the slope of the line shown in the follow…
undefined
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Question was provided via image upload.
$\boldsymbol{-\frac{2}{3}}$ (corresponding to the last option)
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the complex interaction between a person with an impairment or limitati…
The correct option is the first one: "The complex interaction between a person with an impairment or limitation and their environment" (the radio button next to this option is uns…
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question 5 (4 points) use desmos to find the turning point for the func…
Question 5: (0, 6) Question 6: 10 Question 7: $-3$
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what is the definition of disability the complex interaction between a …
The correct option is: The inability to perform significant tasks or functions that people in someone’s reference group (ex: adults) are ordinarily able to do
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question 2 (4 points) use the following graph to evaluate both $f(-2)$ …
$\boldsymbol{f(-2) = 5}$ and $\boldsymbol{f(4) = -1}$ (corresponding to the third option: $f(-2) = 5$ and $f(4) = -1$)
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exploring translations of square root functi each function and describe…
To determine the translations for the functions \( y = \sqrt{x - 3} + 2 \) and \( y = \sqrt{x + 3} - 2 \), we use the parent function \( y = \sqrt{x} \) and the transformation for…
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solve the expression. use pemdas 2.1+(9.2×3.3)×0.8= solve the following…
\(25.968\) ### Second Problem: Solve \(2.004 \times 10^{3}\)
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exploring translations of square root functions move the slider on the …
- \( y = \sqrt{x + 4} \): 4 units left - \( y = \sqrt{x - 4} \): 4 units right - \( y = \sqrt{x} - 2 \): 2 units down - \( y = \sqrt{x} + 2 \): 2 units up
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draw a model to represent the following problem. 2×7
A model for \(2 \times 7\) can be two rows (or groups) of 7 objects (e.g., circles) as shown: Row 1: ○ ○ ○ ○ ○ ○ ○ Row 2: ○ ○ ○ ○ ○ ○ ○ (Or seven columns of 2 objects each: Column…
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fill in the y values of the t–table for the function $y = sqrt3{x}$. th…
For \( x = -8 \), \( y = -2 \); for \( x = -1 \), \( y = -1 \); for \( x = 0 \), \( y = 0 \); for \( x = 1 \), \( y = 1 \); for \( x = 8 \), \( y = 2 \). So the filled t - table i…
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the range of $y = x^3$ is all real numbers, $y > 0$, $y \\geq 0$, done
all real numbers.
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the domain of $y = x^3$ is all real numbers. $x > 0$. $x \\geq 0$. done
all real numbers.
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a ball is thrown upward and outward from a height of 8 feet. the height…
The maximum height is \( 10.5 \) feet, which occurs \( 3.5 \) feet from the point of release.
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look at the graph: what is the equation of the horizontal asymptote? su…
\( y = 3\)
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look at the graph: what is the equation of the vertical asymptote? subm…
\( x = 0 \)
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fill in the table using this function rule. y=3x-4 x | y -6 | -3 | 0 | …
For x = -6, y = -22; for x = -3, y = -13; for x = 0, y = -4; for x = 3, y = 5.
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unit 1 test study guide 1. label the points where underutilizing, effic…
1. - Underutilizing: Point A - Efficient: Points B, D, C - Unattainable: Point E 2. Unlimited wants + limited resources cause scarcity. 3. An independent coffee shop owner. 4. - L…
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37.7 - 3·6
19.7
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41. why are the northern and eastern coasts of the islands greener and …
41. These coasts receive more consistent rainfall from trade winds, which fuels greener, lusher plant growth. 42. Many islands have limited natural freshwater sources, and periodi…
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use the graph to identify zeros and multiplicity. order your zeros from…
Zero at $\boldsymbol{-4}$ with multiplicity $\boldsymbol{1}$ Zero at $\boldsymbol{0}$ with multiplicity $\boldsymbol{2}$ Zero at $\boldsymbol{3}$ with multiplicity $\boldsymbol{1}…
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per ______ graph the quadratic function in intercept form ( y = a(x - p…
### 1) \( f(x) = (x - 2)(x + 4) \) #### a) Eje de simetría ## Paso 1: Encontrar las intersecciones con el eje x Las raíces son \( x = 2 \) y \( x = -4 \). ## Paso 2: Calcular el e…
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find the value of \\( \\theta \\) in the interval \\( 0 \\leq \\theta \…
\(\theta=\boxed{1.265}\)
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find the value of \\( \\theta \\) in the interval \\( 0 \\leq \\theta \…
\( \theta\approx\boxed{1.267} \) (in radians)
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select all the intervals where h is increasing. y 40 30 20 10 -4 -3 -2 …
B. $-2 < x < 0$
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select all the intervals where ( g ) is decreasing. ( y = g(x) ) is gra…
B. $1 < x < 2$, C. $3 < x < 4$
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rewrite each equation in logarithmic form: (a) $e^x = 47$ (b) $e^{90} =…
(a) $\ln(47) = x$ (b) $\ln(x) = 90$
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y = \\square x + \\square
$y = 5x + 4$
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find the slope of the line that passes through (6, 2) and (9, 7). simpl…
\(\frac{5}{3}\)
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graph the equation $y = x^2 + 2x - 8$ on the accompanying set of axes. …
The five points to plot are \((-4, 0)\), \((2, 0)\), \((-1, -9)\), \((0, -8)\), and \((1, -5)\). The parabola opens upward (since \( a = 1 > 0 \)) and passes through these points.
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what is the slope of this line? simplify your answer and write it as a …
3
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find the zeros for the polynomial function and give the multiplicity fo…
The zeros are $-7, 4, -4$; Multiplicities: each zero has multiplicity 1; Graph crosses the x-axis at each zero.
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determine whether the following graph represents a function. answer att…
The graph does not represent a function because at least one input value is mapped to more than one output value.
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q(x) = \\sqrt3{x - h} f(x) = \\sqrt3{x} find the value of h. h = \\squa…
\( h = -8 \) (Note: There might be a discrepancy with the shift options, but based on the graph, this is the calculation.) For the shift: The graph of \( q \) is a translation 8 u…
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f(x) = \\sqrt3{x}\ g(x) = \\sqrt3{x} + k\ find the value of k .\ k = \\…
For the value of \( k \): \( k = 4 \) For the transformation: translation 4 units up
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draw a line representing the ise\ and a line representing the un\ of th…
The slope of the line is $\frac{-1}{3}$ (For the rise/run lines: Draw a vertical segment from $(0,1)$ down to $(0,0)$ to represent the rise of $-1$, and a horizontal segment from …
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graph the following features: • y-intercept = 2 • slope = $-\frac{2}{3}$
A straight line passing through the points $(0, 2)$ and $(3, 0)$ (and extending infinitely in both directions) is the required graph.
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a line passes through the points in this table, (table with x and y val…
\(\frac{8}{5}\)
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a line passes through the points in this table. x | y 30 | 45 33 | 33 3…
\(-4\)
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a line passes through the points in this table. x | y 13 | 22 14 | 16 1…
\(-6\)
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find the slope of the line that passes through (10, 8) and (2, 11). sim…
\(-\frac{3}{8}\)
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find the slope of the line that passes through (8, 11) and (10, 10). si…
\( -\frac{1}{2} \)
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find the slope of the line that passes through (7, 4) and (4, 6). simpl…
\(-\frac{2}{3}\)
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find the slope of the line that passes through (2, 1) and (9, 10). simp…
\(\frac{9}{7}\)
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find the slope of the line that passes through (2, 1) and (9, 10). simp…
\( \frac{9}{7} \)
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determine whether the following graph represents a function. the graph …
The graph **does not** represent a function because **at least one input** is mapped to **more than one output**. For example, the input $x = 0$ is mapped to two outputs: $y = 3$ …
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select all the intervals where ( h ) is decreasing. ( y = h(x) ) choose…
A. \(-4.5 < x < -4\), B. \(-3.5 < x < -2.5\), C. \(4 < x < 4.5\)
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the plot below represents the function $f(x)$ evaluate $f(-3)$ $f(-3) =…
\( \boldsymbol{2} \)
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which of these is an advantage of checking accounts? checking accounts …
B. Checking accounts allow convenient ways to deposit or withdraw funds.
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graph the equation $y = -x^2 - 12x - 32$ on the accompanying set of axe…
Points to plot: \((-8, 0)\), \((-6, 4)\), \((-4, 0)\), \((-5, 3)\), \((-7, 3)\) (plot these on the axes).
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write a piecewise function for the given graph. the piecewise function …
$$f(x)=\begin{cases} \boldsymbol{-\dfrac{3}{10}x+\dfrac{7}{2}} & \boldsymbol{\text{if } x\geq -2} \\ \boldsymbol{x-3} & \boldsymbol{\text{if } x < -2} \end{cases}$$
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a piecewise - defined function is shown below. $f(x)=\begin{cases}x - 1…
a. $f(x) < 4$ b. Yes, changing the value of $n$ changes the range. When $n$ changes, the upper bound of the function's output changes: for $n<\frac{5}{2}$, the range is $f(x)<-n+4…
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a piecewise - defined function is shown below. $f(x)=\begin{cases}x - 1…
a. $f(x) < 4$ b. Yes, changing $n$ changes the range. The upper bound of the function's output depends on $n$: the maximum value of the function is $\max(n-1, -n+4)$, which shifts…
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find the y - intercept, the axis of symmetry, and the vertex of the gra…
- y - intercept: \((0,-4)\) - Axis of symmetry: \(x=-1\) - Vertex: \((-1,-2)\)
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find the y - intercept, the axis of symmetry, and the vertex of the gra…
- y - intercept: \((0,-7)\) - Axis of symmetry: \(x = 1\) - Vertex: \((1,-5)\) (Note: The original answer for the axis of symmetry was incorrect. The correct axis of symmetry for …
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what is the y - intercept of the function? f(x) = - 0.5x² + 0.4x - 0.8 …
\((0,-0.8)\)
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what is the y - intercept of the function? $f(x)=3x^2 - 4x - 9$ the y -…
\((0, - 9)\)
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estimate the coordinates of the vertex of the graph of ( f(x) = 1.25x^2…
The formula for the x - coordinate of the vertex is \( \boldsymbol{-\frac{b}{2a}} \), and the exact vertex is \( \boldsymbol{(0.8, - 1.8)} \) (or \( \boldsymbol{(\frac{4}{5},-\fra…
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estimate the coordinates of the vertex of the graph of $f(x) = 1.25x^2 …
The x - coordinate of the vertex is approximately \( 1 \), and the y - coordinate of the vertex is approximately \( - 2 \)
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attempt 1: 10 attempts remaining. find a pair of functions ( f(x) ) and…
\( f(x)=\frac{6}{x^3} \), \( g(x)=x + 2 \) (Note: There are other possible pairs, but this is a valid one.)
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attempt 1: 10 attempts remaining. for the pair of functions ( f(x) = -3…
### Part a: Find \( f(g(x)) \) and its domain #### Step 1: Substitute \( g(x) \) into \( f(x) \) We know that \( f(x) = -3x - 3 \) and \( g(x) = x^2 - 9 \). To find \( f(g(x)) \),…
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attempt 1: 10 attempts remaining. suppose that $f(x) = \\frac{9}{\\ln(x…
\( -\frac{108}{11(\ln 11)^2} \) (or approximately \( -1.71 \))
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attempt 1: 10 attempts remaining. the profit, in dollars, from selling …
The rate of change of profit when 200 magazines are sold is approximately \( \$2 \) per magazine.
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attempt 1: 10 attempts remaining. the total ticket sales ( s(x) ), in d…
a) \( S'(600)\approx\boxed{2400} \) b) The ticket sales is increasing by approximately 2400 dollars.
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attempt 1: 10 attempts remaining. the resale value ( v(t) ) of a car, i…
\(-10.35\)
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f(x)=\\begin{cases}x^3 - 6x, & x \\leq -3\\\\-4, & -3 < x \\leq 3\\\\\\…
\( 3 \)
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$$log_{4}3 + log_{4}(x - 2) = 2$$ $$log_{4}(3x - 6) = 2$$ $$log_{4}2 = …
\(x = \frac{22}{3}\)（若按照正确步骤，原书写的第三行\(\log_{4}2 = 3x - 6\)是错误的，正确求解得\(x=\frac{22}{3}\)）
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f(x)=\\begin{cases}x^3 - 6x, & x \\leq -3 \\\\ -4, & -3 < x \\leq 3 \\\…
\( 3 \)
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f(x)=\\begin{cases} 3x^3 - 1, & x < 1 \\\\ 3, & 1 \\leq x < 4 \\\\ |x -…
\(-25\)
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f(x)=\\begin{cases}3x + 1, & x \\leq 0 \\\\ \\dfrac{1}{2}x - 2, & x > 0…
\( 1 \)
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f(x)=\\begin{cases}\\frac{2}{x + 4},&x < -4\\\\x,&-4 \\leq x \\leq 0\\\…
\(-4\)
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f(x)=\\begin{cases}|2x + 6|, & x \\leq -3 \\\\ 2x^2, & -3 < x \\leq 0 \…
2
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derivative of hyperbolic functions (v) $10^{\\cosh \\sqrt{x}}$ (vi) $e^…
We have shown that if \( y = a \sinh \omega \theta + b \cosh \omega \theta \), then \( \frac{d^2 y}{d \theta^2} = \omega^2 y \), as required.
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f(x)=\\begin{cases}-\\dfrac{1}{4}x - 2, & x \\leq 2 \\\\ 2x + 1, & x > …
\(-\frac{7}{4}\)
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f(x)=\\begin{cases}-2x + 1, & x < 1 \\\\ \\dfrac{2}{3}x - 3, & x \\geq …
\( 1 \)
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f(x)=\\begin{cases}-2x^2 + 1, & x \\leq 2 \\\\ \\dfrac{3}{4}x - 3, & x …
\(-1\)
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f(x)=\\begin{cases}5, & x \\leq 3 \\\\ 2x - 2, & x > 3\\end{cases} eval…
6
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f(x)=\\begin{cases}-2x + 1, & x < 1 \\\\ \\frac{2}{3}x - 3, & x \\geq 1…
\(5\)
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problem. 7 : consider the rational function $f(x) = \\frac{x^2 - 7x + 1…
# Explanation: ## Step1: Factor numerator and denominator First, factor the numerator \(x^2 - 7x + 12\). We find two numbers that multiply to 12 and add to -7, which are -3 and -4…
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problem. 6 : consider the rational function $f(x) = \\frac{x^2 - 9x + 2…
\( y = 1 \)
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problem. 4 : determine the limit. \\(\\lim\\limits_{x \\to 7^+} \\frac{…
\( 1 \)
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problem. 5 : consider the rational function $f(x) = \\frac{x^2 + 2x}{x^…
\((-2, \frac{1}{2})\) ### Problem 6.1
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problem. 5 : consider the rational function $f(x)=\\frac{x^2 + 2x}{x^2 …
\( x = 2 \) ### Problem 6
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question 1 0.5 pts let ( f(x) ) be a function and let ( f(a) ) be the d…
I and II (the option with "I and II" text, as per the multiple - choice options in the question)
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question 3 let ( f(x) = sqrt{x} ). it can be seen using the definition …
5.02
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question 2 0.5 pts which of the following limits gives the slope of the…
\(\boldsymbol{\lim\limits_{h\to0} \frac{[(2 + h)^{3}-1]-7}{h}}\) (the first option)