Analysis
Grenzwerte, Ableitungen, Optimierung und Funktionsverhalten.
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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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what is the slope of the line?
$\frac{1}{2}$
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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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find the derivative of the function y = e^{\\sqrt{x^2 + 4}} using the c…
\( \frac{x e^{\sqrt{x^2 + 4}}}{\sqrt{x^2 + 4}} \)
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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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write an equation for a line passing through the point (2,5) that is pa…
- Equation of the line parallel to \( y=\frac{2}{3}x + 2 \) and passing through \( (2,5) \): \( y=\frac{2}{3}x+\frac{11}{3} \) - Equation of the line perpendicular to \( y=\frac{2…
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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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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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write an expression in factored form for the polynomial of least possib…
\(y(x)=-\frac{1}{36}(x + 2)^2(x - 1)(x - 3)^2\) (or we can also write it as \(y(x)=\frac{-1}{36}(x + 2)^2(x - 1)(x - 3)^2\)) Wait, but maybe I made a mistake in the leading coeffi…
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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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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…
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homework assignment 3.3: power functions and polyno score: 9/10 answere…
2
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5. the graph of a function is a line that passes through the points (0,…
$y=3x+1$
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homework assignment 3.3: power functions and polyno score: 7/10 answere…
5
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consider the polynomial function $f(x) = -9x - 6x^2 + x^7 + 5x^9$. as $…
s: As \( x\to -\infty \), \( f(x)\to\boldsymbol{-\infty} \) As \( x\to\infty \), \( f(x)\to\boldsymbol{\infty} \)
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consider the polynomial function $f(p) = -p^8 - 2p^7 + 4p^6 - 5$. as $p…
As \( p \to -\infty \), \( f(p) \to \boldsymbol{-\infty} \) As \( p \to \infty \), \( f(p) \to \boldsymbol{-\infty} \)
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3. lacey and richens each have a personal function machine. lacey’s mac…
a. $L(x) = x^2 - 1$, $R(x) = 3(x + 2)$ b. 30 c. Yes, it changes the output. The composite functions $R(L(x)) = 3x^2 + 3$ and $L(R(x)) = 9x^2 + 36x + 35$ are not equivalent, and te…
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question the table below represents a linear function. identify the slo…
\(\frac{7}{4}\)
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describe the long run behavior of $f(n) = 5n^9 - n^5 - 5n^3 + 4$ as $n …
As \( n ightarrow-\infty \), \( f(n) ightarrow-\infty \); As \( n ightarrow\infty \), \( f(n) ightarrow\infty \)
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describe the long run behavior of $f(x) = -x^7$ as $x \\to -\\infty$, $…
As \(x \to -\infty\), \(f(x) \to \infty\) As \(x \to \infty\), \(f(x) \to -\infty\)
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describe the end behavior (long run behavior) of $f(x)=x^2$ as $x\\to -…
As \( x \to -\infty \), \( f(x) \to \infty \) As \( x \to \infty \), \( f(x) \to \infty \)
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2-variable linear inequality a $y > \\frac{3}{2}x + 3$ b $y \\geq \\fra…
### First, determine the inequality from the graph: ## Step1: Analyze the line The line has a slope of $\frac{3}{2}$ (rise over run: from $(0,3)$ to $(2,6)$? Wait, no, from $(0,3)…
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#1-9 count the slope using the two points on the line. *all answers in …
1) $\frac{7}{5}$ 2) $-\frac{1}{4}$ 3) $-\frac{3}{5}$ 4) $-\frac{4}{3}$ 5) $2$ 6) $-\frac{1}{4}$ 7) $\frac{1}{2}$ 8) $-1$ 9) $-1$
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question 4 of 10 what constitutes a disability? impairment activity lim…
All of the Above
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2-variable linear inequality which linear inequality graphs the solutio…
B. \(y\geq\frac{3}{2}x + 3\)
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graph the function. $y = 4\\sqrt3{x}$
To graph \( y = 4\sqrt[3]{x} \), we can analyze key points and the shape of the cube - root function: ### Step 1: Recall the parent function The parent function of a cube - root f…
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graph the function. $y = \\sqrt3{x} + 1$
To graph \( y=\sqrt[3]{x + 1} \), follow these steps: 1. **Identify Transformation**: The function is a horizontal shift of \( y = \sqrt[3]{x} \) 1 unit to the left. 2. **Find Key…
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graph the function. $y = \\frac{3}{2}\\sqrt3{x}$
To graph \( y = \frac{3}{2}\sqrt[3]{x} \), we: 1. Recognize it's a vertical stretch (\( \frac{3}{2} \) factor) of \( y=\sqrt[3]{x} \). 2. Find key points using the function: - Whe…
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the height ( y ) (in feet) of a ball thrown by a child is ( y = -\frac{…
5 ### Part (b)
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suppose that the functions p and q are defined as follows. p(x)=x+1 q(x…
$(q\circ p)(4)=49$ $(p\circ q)(4)=32$
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suppose that the functions p and q are defined as follows. p(x)=2x+3 q(…
$(p \circ q)(-3) = -33$ $(q \circ p)(-3) = -18$
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$\\sqrt{-15}$ $\\sqrt{-15}=\\square$ (simplify your answer. type your a…
$0+\sqrt{15}i$
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consider the function $g(x)=x^2 + 8x + 18$ graph $g(x)$ what is the ver…
s: - Vertex of \( g \): \((-4, 2)\) - Equation of the line of symmetry of \( g \): \( x=-4 \) - \( g \) has a minimum of \( 2 \) - The \( x \)-intercept(s) of \( g \): DNE - The \…
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graph $g(x) = -3x^2 - 12x - 14$.
To graph \( g(x) = -3x^2 - 12x - 14 \): 1. **Vertex**: \((-2, -2)\) (from vertex form \( g(x) = -3(x + 2)^2 - 2 \)). 2. **Direction**: Opens downward (since the coefficient of \( …
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graph $g(x) = 4(x + 4)^2 - 2$.
To graph \( g(x) = 4(x + 4)^2 - 2 \): 1. Plot the vertex at \( (-4, -2) \). 2. Since \( a = 4 > 0 \), the parabola opens upward. 3. Use the narrow width (due to \( |a| = 4 > 1 \))…
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homework assignment 3.2: quadratic functions score: 2/10 answered: 3/10…
Vertex: \( (3.5, -20.25) \) Largest x-intercept: \( x = 8 \) Y-intercept: \( (0, -8) \)
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le for finding the domain and range of a function graphically ______ → …
1. Domain → Inputs; Found along the \( \boldsymbol{x} \) axis (left to right) 2. Range → Outputs; Found along the \( \boldsymbol{y} \) axis (bottom to top)
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write 9.5 × 10² in standard form. enter your answer as an integer or de…
950
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homework assignment 3.2: quadratic functions score: 0/10 answered: 0/10…
\(y=\frac{8}{9}(x - 3)^2-2\) (or other equivalent forms like standard form \(y=\frac{8}{9}x^2-\frac{16}{3}x + 6\))
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finding slope #1 (graphing method) graph the points and find slope usin…
\(\frac{1}{4}\) ### Problem 2:
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unit 1.2 functions and graphs day 2 notes date:__________ domain and ra…
- First blank: input - Second blank: \(x\) - Third blank: input values (or \(x\)-values) - Fourth blank: output values (or \(y\)-values)
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what is the y - value of this function when x = -9?
\(-0.7\) (or \(-\frac{7}{10}\))
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what is the y - value of this function when x = 2?
-6
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question determine if the function below has a horizontal or a slant as…
The slant asymptote is \(y = 3x - 5\), so as \(x\) approaches infinity (positive or negative), \(y\) approaches \(3x - 5\). If we consider the linear part (the slant asymptote), t…
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i was born in a little town called hope, arkansas... i remember that ol…
B. He talked about hope and the American dream. C. He talked about growing up in a family that didn't have much money.
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find all vertical asymptotes of the following function. $f(x) = \\dfrac…
The vertical asymptotes are \(x = 0\) and \(x=-2\)
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directions: read each problem and answer carefully. explain your work. …
1. (Graph: $f(x)=(x-1)^3-2$ plotted with key points $(-1,-10), (0,-3), (1,-2), (2,-1)$; inverse $y=\sqrt[3]{x+2}+1$ plotted with reflected points $(-10,-1), (-3,0), (-2,1), (-1,2)…
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find all vertical asymptotes of the following function. $f(x) = \\dfrac…
There are no vertical asymptotes.
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find all vertical asymptotes of the following function. $f(x) = \\dfrac…
The function \( f(x)=\frac{x^{2}-2x - 15}{3x - 15} \) has no vertical asymptotes (it has a hole at \( x = 5 \)).
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25. 6 + 3²(5 - √4)
33
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*23. 0.014 ÷ 0.5 answer:
0.028
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no calculators 11.) sketch the following below each equation, then desc…
s (Descriptions of Transformations): - \( y = x^2 \): Parent parabola, vertex \((0,0)\), no transformations. - \( y = x^2 + 2 \): Vertical shift up 2 units, vertex \((0,2)\). - \(…