Calcul
Limites, dérivées, optimisation et comportement des fonctions.
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find the domain of the function. h(x) = \\frac{7}{\\frac{2}{x} - 1} wha…
$(-\infty, 0) \cup (0, 2) \cup (2, \infty)$
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what is the slope of the line?
$\frac{1}{2}$
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find the slope of the line that passes through these two points. (2, 6)…
Slope: $\boldsymbol{\frac{-2}{5}}$ Slope sign: b) negative
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consider the function : g(x) = -(x - 3)^3 - 2 which ordered pair lies o…
\((-3,4)\) (assuming the option is \((-3,4)\))
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simplify $3^{log_{3}5x}$. the simplified expression is $\\square$.
$5x$
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complete to solve $63 + 7$. $63 + 7$ $= (60 + \\square) + 7$ $= 60 + (\…
First blank: \( 3 \), Second blank: \( 3 \), Third blank: \( 10 \)
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find g(a - 1) when g(x) = 3x - 3. a. 3a - 3 b. \\frac{1}{3}a - 3 c. 3a …
C. \( 3a - 6 \)
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find f(0) when f(x) = x² + 3x - 5. a. -5 b. 25 c. 0 d. 5
A. -5
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add: -93 + 96
3
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find f(4) when f(x)=x² - 5x - 7. a. 29 b. -11 c. 43 d. 3
B. -11
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evaluate 468·q when q = 57.
26676
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find f(-2) when f(x)=9x - 7. a. 2 b. -11 c. -25 d. -4
C. \( -25 \)
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evaluate $248 \\cdot r$ when $r = 91$.
22568
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give the domain and range of the relation. a. the domain is $(-infty,7)…
C. The domain is \((-\infty,\infty)\). The range is \(\{7\}\)
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does the relation shown below define a function? yes no
No
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does the relation shown below define a function? no yes
Yes
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does the relation shown below define a function? yes no
Yes
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does the relation shown below define a function? no yes
Yes
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does the relation shown below define a function? {(-3,8), (1,5), (4,-8)…
Yes
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the graph a function ( f ) is shown. find ( f(-2) ). ( f(-2) = square )
\( f(-2)=-4 \)
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the graph a function ( f ) is shown. for what value of ( x ) is ( f(x) …
\( 3 \)
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17. the graph of the function h is shown below. graph of h if f is the …
$-2$
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you might need: calculator what is the slope of the line?
$\frac{5}{2}$
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part of a linear function ( c ) is shown below. which inequality repres…
C. \(-3\leq x<1\)
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compare the most likely cause of death for an individual born in 1900 a…
- For an individual born in 1900: The most likely cause of death was an infectious disease (e.g., pneumonia, tuberculosis, or diarrheal disease), due to limited medical treatments…
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attempt 1: 10 attempts remaining. differentiate: $f(x) = (19x^3 - 15x^6…
\( \frac{5}{2}(57x^{2}-90x^{5})(19x^{3}-15x^{6})^{\frac{3}{2}} \) (or simplified forms like \( \frac{15}{2}(19x^{2}-30x^{5})(19x^{3}-15x^{6})^{\frac{3}{2}} \))
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what is the slope of the line?
$\frac{-3}{4}$
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attempt 1: 10 attempts remaining. differentiate $y = (x^2 - 5)ln x$ ans…
\( 2x\ln x + x-\frac{5}{x} \)
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the height of a punted football is approximated by the equation below. …
$\frac{3}{2}$ feet (or 1.5 feet)
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what is the rate of change of the following equation? y = -3
\( 0 \)
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graph the following equation: $y = \\frac{2}{3}x - 4$ first, fill in th…
The completed table is: | x | y | |---|---| | 0 | -4 | | 3 | -2 | To graph the line, plot the points \((0, -4)\) and \((3, -2)\) on the coordinate plane and draw a straight line t…
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4* the line $y = \\frac{1}{3}x + 7$ is graphed match each graph charact…
- domain: \(\boldsymbol{[-9, 3]}\) - range: \(\boldsymbol{[4, 8]}\) - x - intercept: \(\boldsymbol{-21}\) - y - intercept: \(\boldsymbol{7}\) - interval of increasing: \(\boldsymb…
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what is the slope of the line?
$2$
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what is the slope of the line? show calculator
2
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the number of hats made by a manufacturer ( t ) days after the start of…
The total cost of the hats is changing at a rate of approximately \(\$5473.02\) per day on the 17th day.
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attempt 1: 10 attempts remaining. calculate the derivative of the funct…
\( r'(x) = 2.4(0.2x - 4.8)(0.1x^2 - 4.8x + 2.4)^{1.4} \) (or equivalent simplified forms like \( 0.48(x - 24)(0.1x^2 - 4.8x + 2.4)^{1.4} \))
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extra practice: given the function f(x) = x³ + 7 what is the value of f…
\( f(6)=223 \) ### Second Sub - Question (Finding \( k(1) \) for \( k(x)=2x^{2}-5x + 3 \))
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attempt 1: 10 attempts remaining. given ( f(x) = (5x^3 - 9x^2 + 6x - 4)…
\( 10(5x^3 - 9x^2 + 6x - 4)^9(15x^2 - 18x + 6) \) (or simplified as \( 30(5x^3 - 9x^2 + 6x - 4)^9(5x^2 - 6x + 2) \))
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multiply. write your answer in simplest form. \\(sqrt{3}(2 + sqrt{2})\\)
\(2\sqrt{3}+\sqrt{6}\)
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attempt 1: 10 attempts remaining. find \\( \\frac{dy}{dx} \\) if \\( y …
\( 3(-5x^3 + 7x^2 - x)^2(-15x^2 + 14x - 1) \)
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stretch, an adult giraffe, weighed 160 pounds when he was born. now, he…
2 tons
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(\frac{d}{dt}(ln(3 + 12t)) =)
\( \frac{12}{3 + 12t} \) (or simplified as \( \frac{4}{1 + 4t} \))
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what is the slope of the line?
$\frac{1}{2}$
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the functions f and g are defined as follows. $f(x) = \\frac{x + 6}{x^2…
Domain of $f$: $(-\infty, -6) \cup (-6, 5) \cup (5, \infty)$ Domain of $g$: $(-\infty, \infty)$
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sqrt{(-4)^{2}+(12)^{2}}
If the expression is $\sqrt{(-4)^2+(12)^2}$, the answer is $4\sqrt{10}\approx12.65$ (or $160$ without square - root, or $48$ if it's $\sqrt{(-4)^2\times(12)^2}$). The most probabl…
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attempt 1: 10 attempts remaining. find the derivative of $f(x) = \\sqrt…
\( \frac{21x^{3}+5x^{2}-6x - 5}{2\sqrt{x}} \) (or \( \frac{21}{2}x^{\frac{5}{2}}+\frac{5}{2}x^{\frac{3}{2}}-3\sqrt{x}-\frac{5}{2\sqrt{x}} \))
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use (-x^2 + 2x + 5) to answer the following questions. (x = -\frac{b}{2…
$(1, 6)$
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use $-x^2 + 2x + 5$ to answer the following questions. $x = -\frac{b}{2…
$x=1$
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use $2x^2 +8x + 13$ to answer the following questions. $x = -\frac{b}{2…
$(-2, 5)$
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use $2x^2 + 8x + 13$ to answer the following questions. $x = -\frac{b}{…
$x=-2$
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use $x^2 - 6x$ to answer the following questions. $x = -\frac{b}{2a}$ u…
$(3, -9)$
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use ( x^2 - 6x ) to answer the following questions. ( x = -\frac{b}{2a}…
$x=3$
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use $x^2 - 6x$ to answer the following questions. $x = -\frac{b}{2a}$ u…
$f(x)=(x-3)^2 -9$
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use ( x^2 - 8x + 16 ) to answer the following questions. ( x = -\frac{b…
$f(x)=(x-4)^2$
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use $2x^2 + 8x + 13$ to answer the following questions. $x = -\frac{b}{…
$2(x+2)^2+5$
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use (-x^2 + 2x + 5) to answer the following questions. (x = -\frac{b}{2…
$f(x)=-(x-1)^2 + 6$
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5. -/1 points find the vertical asymptotes (if any) of the graph of the…
$\theta=\frac{\pi}{8}+\frac{n\pi}{4}$, where $n$ is any integer
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4. -/1 points details my notes ask your teacher practice another find t…
$t=-3$
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exercises 1.4 integration formulas and the net change theorem score: 80…
$C(p) = 0.02p + 6.37$
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consider the following function. $f(x) = \\frac{1}{x^2 - 16}$ complete …
### Completed Table: | $x$ | $f(x)$ | |-------|--------| | -4.5 | 0.24 | | -4.1 | 1.23 | | -4.01 | 12.48 | | -4.001| 124.98 | | -3.999| -125.02| | -3.99 | -12.52 | | -3.9 | -1.27 …
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for the pair of functions ( f(x) = x^2 + 1 ) and ( g(x) = x^2 - 9 ), fi…
### Part a: \( f(g(x)) \) and its domain #### Step 1: Substitute \( g(x) \) into \( f(x) \) We know \( f(x) = x^2 + 1 \) and \( g(x) = x^2 - 9 \). To find \( f(g(x)) \), we replac…
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f(x) = \\frac{1}{x - 3} determine whether f(x) approaches \\infty or -\…
(a) $-\infty$ (b) $+\infty$
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exercises 1.4 integration formulas and the net change theorem score: 70…
4880 cars
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attempt 1: 10 attempts remaining. evaluate \\(\\frac{d}{dt}\\ln(6t^2 + …
$\frac{12t + 11}{6t^2 + 11t + 8}$
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write the equation of the graph shown below in factored form. options: …
A. \(f(x)=(x + 1)(x - 2)(x - 3)\)
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a company’s marginal cost function is $c(x)=\frac{20}{sqrt{x}}$ where $…
$\$320$
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attempt 1: 10 attempts remaining. let ( f(x) = -6ln(4x^3) ). find ( f(x…
$f'(x)=\boldsymbol{-\frac{18}{x}}$, $f'(-2)=\boldsymbol{9}$
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water leaks from a tank at a rate r( t ) where r( t ) = 2 + 0.144 t gal…
Between 10 and 14 hours, the tank lost 10.88 gallons.
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which of the following describes the function ( x^4 - 3 )? the degree o…
The degree of the function is even, so the ends of the graph continue in the same direction. Because the leading coefficient is positive, the left side of the graph continues up t…
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find \\(\\int (x + 5)(x - 4) dx\\) + c
$\frac{x^3}{3} + \frac{x^2}{2} - 20x$
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find \\( \\int \\left(6x^4 + 5x^6\ ight) dx \\) \\( + c \\)
$\frac{6}{5}x^5 + \frac{5}{7}x^7$
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12.4 submarines 1. a submarine is descending to examine the seafloor 2,…
1. $y = -1050x$ (where $y$ is the submarine's elevation in feet, $x$ is time in hours) 2. 8.75 hours
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18) base your answer to the following question on the poem excerpt belo…
A) People from all nations should be welcomed.
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solve the system by graphing.\\begin{cases}x - y = 1\\\\y = 3\\end{case…
The solution to the system of equations is \( x = 4,y = 3 \), or the ordered pair \( (4,3) \).
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select the equation that describes the graph shown.\ \ \\(\\circ\\ y = …
$\boldsymbol{y=(x - 5)^2}$ (Option B)
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solve. simplify your answer(s). if there are multiple answers, separate…
2, -1
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the graph of the velocity ( v(t) ), in ft/sec, of a car traveling on a …
Positive acceleration on \( \boldsymbol{[0, 35]} \) (or \( (0, 35) \)) because velocity \( v(t) \) is increasing (so \( v'(t) = a(t) > 0 \)); negative acceleration on \( \boldsymb…
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divide \\(25\\enclose{longdiv}{1658}\\). to find the quotient, start by…
The first box should be filled with 25, and the second box should be filled with 165. So the answer is 25 and 165 (in the order of dividing 25 into 165).
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find the inverse of $y = \\log_{2}x$. $y = \\square$
$y=2^x$
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find the inverse of $y = 0.3^x$. $y = \\square$
$\log_{0.3}(x)$ (or equivalently $\frac{\log(x)}{\log(0.3)}$)
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what number makes this equation true? hint: use the place value blocks …
67
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evaluate \\(\\log_{5} \\frac{1}{625}\\). \\(\\log_{5} \\frac{1}{625} = …
$-4$
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find the domain of the function. $f(x) = \\frac{1}{\\sqrt{x - 5}}$ the …
$(5, \infty)$
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find the domain of the function. f(x)=x² - 2x + 10 the domain of f(x) i…
$(-\infty, \infty)$
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4. the line ( y = \frac{2}{3}x + 7 ) is graphed. match each graph chara…
- Domain: \(\boldsymbol{(-\infty,\infty)}\) - Range: \(\boldsymbol{(-\infty,\infty)}\) - \(x\) - intercept: \(\boldsymbol{x =-\frac{21}{2}}\) (or \(x=-10.5\)) - \(y\) - intercept:…
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describe how you could use a graphing calculator to estimate the value …
A. Enter the function \( f(x) = 8(1.25)^x \) on the \( Y = \) screen, display the corresponding table, and find the value of \( x \) where \( y = 15 \)
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the line $y = \\frac{7}{3}x + 7$ is graphed match each graph characteri…
- Y - intercept: \(7\) - Slope: \(\frac{7}{3}\) - X - intercept: \(-3\)
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you know the speed limit is 55 mph on all back country roads. you know …
knowledge
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compare the two logarithmic functions $f(x) = \\log_{3} x$ and $g(x) = …
C. Functions \(f(x)\) and \(g(x)\) will have similar shapes but will increase at different rates.
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describe the end behavior of the function $y = \\log x$. (1 point) \\bi…
D. As \( x \to 0^{+} \), \( y \to -\infty \), and as \( x \to \infty \), \( y \to \infty \) (assuming the options are labeled A, B, C, D in order as given in the problem)
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identify a possible base ( b ) of this logarithmic function. (1 point) …
\( b=\frac{1}{4} \) (corresponding to the option \( b=\frac{1}{4} \))
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which inequality does the given graph represent? a ( y > x - 3 ) b ( y …
D. \(y > -x - 3\)
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graphing logarithmic functions quick check where does the logarithmic f…
A. \( x = 0 \)
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4x which inequality does the given graph represent? a ( y leq 5x + 2 ) …
C. \( y \geq 5x - 2 \)
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graph the following logarithmic functions. which has a graph that decre…
\( \boldsymbol{\log_{0.5} x} \) (corresponding to the option with \( \log_{0.5} x \))
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write an expression in factored form for the polynomial of least possib…
\((x + 1)^{2}(x - 2)^{2}\)
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determine an equation for the pictured graph. write your answer in fact…
\( y=-x^{2}(x + 2)(x - 1) \)
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determine an equation for the pictured graph. write your answer in fact…
\( y = -x^2(x + 2)(x - 1) \)
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given the function $g(n)=2n^4 + 6n^3 - 36n^2$: its $g$-intercept is its…
s: - The \( g \)-intercept is \( \boldsymbol{0} \) (the point is \( (0,0) \), and the \( g \)-intercept value is \( 0 \)). - The \( n \)-intercepts are \( \boldsymbol{n = 0} \) (w…
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given the function $c(x) = -(x - 5)(x + 1)(x - 3)$: the coordinates of …
s: - The coordinates of its \( C \) - intercept are \( \boldsymbol{(0,-15)} \). - The coordinates of its \( x \) - intercepts are \( \boldsymbol{(5,0)}, \boldsymbol{(-1,0)}, \bold…