Cálculo
Límites, derivadas, optimización y comportamiento de funciones.
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question 5 of 24 step 1 of 3 consider the following rational function. …
\( x = 4 \)
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question 2 1 pts given the line $y = \\frac{2}{7}x + 1$ find the equati…
\( y=\frac{2}{7}x+\frac{29}{7} \)
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question 4 of 24 step 1 of 1 use synthetic division to determine if the…
Yes
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which function represents y = -tan x ?
The bottom - left (green) graph
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read the excerpt from \the storyteller.\ \she did all that she was told…
A. It indicates that the aunt's portrayal of right and wrong is inauthentic and unconvincing.
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where are the vertical asymptotes of y = tan x between $-pi$ and $pi$? …
The vertical asymptotes of $y = \tan x$ between $-\pi$ and $\pi$ are at $x = -\frac{\pi}{2}$ and $x = \frac{\pi}{2}$. So the missing denominator in both cases is $2$.
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question 2 of 24 step 1 of 1 02:25:31 use the properties of logarithms …
$2 + 2\log_{9}(x)$
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question 1 of 24 step 1 of 1 construct a polynomial function with the s…
\(p(x)=\frac{7}{12}x^{3}-\frac{91}{12}x - 7\)
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3/8 + 2/3 make like units.
\(\frac{25}{24}\) (or \(1\frac{1}{24}\))
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warm up dive in wrap up \\(\\frac{4}{5} + \\frac{1}{2}\\) make like uni…
\( \frac{13}{10} \) (or \( 1\frac{3}{10} \))
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solving quadratics by factoring score: 3/15 penalty: 1 off question sol…
\(x = 3\) or \(x = -3\) (or in boxed form, if needed, but as per instructions, we present the solutions clearly. If we were to box each, it would be \(\boxed{3}\) and \(\boxed{-3}…
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use the graph of y = f(x) to graph the function g(x) = f(x - 4) - 3. ch…
(Assuming the correct graph is, for example, Option D after analyzing shifts; but since the exact graph details are from the image, the correct graph would be the one where each p…
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use the given conditions to write an equation for the line in point - s…
- Point - slope form: \( y + 2=-4(x - 4) \) - Slope - intercept form: \( y=-4x + 14 \)
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divide and simplify to the form a + bi. \\(\\frac{20i}{3 + i}\\) \\(\\f…
\(2 + 6i\)
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water is steadily pumped out of a flooded basement. let v be the volume…
6
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water is steadily pumped out of a flooded basement. let v be the volume…
24
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9 mark for review a submersible device is used for ocean research. the …
35
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7 f(x) = (x + 6)(x + 5)(x - 4) the function f is given. which table of …
B. | x | y | |---|---| | -6 | -3 | | -5 | -3 | | 4 | -3 |
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the graph shows the relationship between the number of shares of stock …
B. \(8x + 12y = 480\)
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4 mark for review the function f is defined by $f(x) = \\frac{1}{10}x -…
B. \((0, - 2)\)
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water is steadily pumped out of a flooded basement. let v be the volume…
14
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22 mark for review $f(x) = 4x^2 + 64x + 202$ the function $g$ is define…
A. -13
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21 mark for review for the exponential function f, the value of f(1) is…
C. \( f(x) = 128(1.6)^{x-1} \)
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solve the following equation. $3^{x^2} = 47$ the solution set is (type …
\(\pm\sqrt{\frac{\ln(47)}{\ln(3)}}\) (or equivalent forms like \(\pm\frac{\sqrt{\ln(47)}}{\sqrt{\ln(3)}}\))
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14 mark for review each year, the value of an investment increases by 0…
C. Increasing exponential
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solve the logarithmic equation. be sure to reject any value of x that i…
\(\frac{19}{4}\)
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sketch the solution to this system of inequalities: $y < 1$ $y > x - 2$…
C
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graph the equation. $y = 3|x + 5| + 4$
To graph \( y = 3|x + 5| + 4 \): 1. Plot the vertex at \((-5, 4)\). 2. Since \( a = 3>0 \), the graph opens upward and is vertically stretched by a factor of 3. 3. Plot additional…
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solve the logarithmic equation. be sure to reject any value of x that i…
C. There is no solution.
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y = -4|x - 3| + 2
The graph of \( y = -4|x - 3| + 2 \) has a vertex at \((3, 2)\), opens downward, is vertically stretched by a factor of 4, and passes through points like \((2, -2)\), \((4, -2)\),…
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solve the logarithmic equation. be sure to reject any value of x that i…
The solution set is \(\{1\}\)
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2 mark for review the function f is defined by f(x) = -3x + 60. what is…
D. 84
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solve the following logarithmic equation. be sure to reject any value o…
The solution set is $\boxed{-\dfrac{80}{27}}$
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solve the following logarithmic equation. be sure to reject any value o…
The solution set is $\boxed{20}$ (corresponding to option A: The solution set is 20 (type an integer or a simplified fraction))
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solve the following exponential equation. express the solution set in t…
In terms of natural logarithms, \(x = \frac{\ln(889)}{2\ln(7)}\); the decimal approximation is \(x\approx1.743\)
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the cost of mailing a first-class letter is $0.46 for the first ounce a…
step function
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solve the exponential equation. express the solution in terms of natura…
In terms of logarithms, \( x = \log(311) \) (or \( x=\frac{\ln(311)}{\ln(10)} \)) and the decimal approximation is approximately \( 2.49 \) (or more precisely \( 2.4928 \)).
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what is the minimum value of the function $g(x) = x^2 - 6x - 12$? $3 - …
-21
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solve the exponential equation. express the solution in terms of natura…
In terms of common logarithms, \(x = \log(3.58)\approx0.55\) (or in terms of natural logarithms \(x=\frac{\ln(3.58)}{\ln(10)}\approx0.55\))
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solve the following exponential equation by expressing each side as a p…
The solution set is \(\{-9\}\)
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given $f(x) = x + 1$ and $g(x) = x^2$, what is $(g \\circ f)(x)$? $(g \…
\((g \circ f)(x)=(x + 1)^{2}\) (the third option)
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a students savings account has a balance of $4200 on september 1. each …
\( -350t + 4200 \)
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is the function $f(x) = x^4 + x$ even? use the drop-down menus to compl…
To determine if \( f(x) \) is even, find \( f(-x) = \boldsymbol{x^4 - x} \). Because \( f(-x) \) is \(\boldsymbol{\text{not}}\) equal to \( f(x) \), the function is \(\boldsymbol{…
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what is the inverse function of $f(x) = \\frac{x}{x - 2}$? $f^{-1}(x) =…
\( f^{-1}(x)=\frac{2x}{x - 1} \) (the option with this expression)
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the function f(x) is shown in the table. x | -4 | -2 | 0 | 2 | 4 f(x) |…
The y - intercept of \( f(x) \) is \( -6 \) and the y - intercept of \( g(x) \) is \( 8 \). The y - intercept of \( f(x) \) is less than the y - intercept of \( g(x) \).
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solve the following exponential equation. express the solution set in t…
In terms of logarithms: \( x = \frac{\ln(6)}{\ln(7)} \) (or \( x = \log_7(6) \) using change of base formula). Decimal approximation: \( x \approx 0.92 \)
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use a graphing utility and the change - of - base property to graph the…
(Assuming the correct graph is, for example, Option B is incorrect (decreasing), Option D is incorrect (decreasing), Option C may have wrong asymptote, so the correct one is the g…
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use a graphing utility and the change-of-base property to graph the fun…
(Assuming the correct graph is the one that is increasing, has vertical asymptote at \( x = 0 \), passes through \( (1,0) \), so for the given options, if we assume the labels, bu…
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use properties of logarithms to expand the logarithmic expression as mu…
$3 + \log(x)$
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evaluate the expression without using a calculator. \\(\\log_{7} 1\\) \…
\( 0 \)
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22 mark for review the speed of a vehicle is increasing at a rate of 7.…
B. 16.3
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is the inverse of g(x) a function? use the drop - down menus to explain…
1. The graph of the inverse of \( g(x) \) is the reflection of the graph of \( g(x) \) across the \(\boldsymbol{\text{line } y = x}\). 2. The inverse of \( g(x) \) \(\boldsymbol{\…
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21 mark for review the cost of renting a carpet cleaner is $52 for the …
A. \(C(d)=26d + 26\)
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question 1 economics is the study of how people ○ make money. ○ run a b…
make choices using limited resources.
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a student divided $f(x) = 3x^3 + 8x^2 + 5x - 4$ by $x + 2$ and found th…
The point \((-2, -6)\) lies on the graph of \( f(x) \).
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use common logarithms or natural logarithms and a calculator to evaluat…
-2.8054
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17 mark for review the function f is defined by f(x) = ½(x + 6). what i…
D. 5
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find the slope of the line passing through the given points. state whet…
A. The slope of the line is \(\frac{1}{3}\). The line is increasing.
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the image shows a coordinate grid with a graph. points marked are (0, -…
The horizontal asymptote is \(y = 0\) (the x - axis)
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11 mark for review $f(x) = (x - 44)(x - 46)$ the function $f$ is define…
B. 45
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10 mark for review in the xy-plane, line s passes through the point (0,…
C. 72
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the graph of f(x) is shown. which graph represents g(x) = f(2x)?
The Left - most Graph (the first graph among the four options)
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determine the inverse of h(x), including any restrictions that should b…
- If the domain of the original function \( h(x) \) is restricted to \( \boldsymbol{x\geq0} \) (or \( x\leq0 \)), then the inverse of \( h(x) \) is the function represented by the…
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use common logarithms or natural logarithms and a calculator to evaluat…
For the first blank (rewrite using change - of - base property): \(\frac{\ln41}{\ln\pi}\) (or \(\frac{\log41}{\log\pi}\)) For the second blank (evaluate the expression): \(3.2440\)
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the function f(x) is shown below. is the inverse of f(x) also a functio…
The function \( f(x)\) maps every range value to exactly one domain value. The domain of \( f(x)\) is all real numbers and the range of \( f(x)\) is \((-3,\infty)\). Therefore, th…
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the functions f and g are shown. are the functions inverses? use the dr…
The function \( f(g(x)) \) is equal to \( x \). The function \( g(f(x)) \) is equal to \( x \). The functions \( f(x) \) and \( g(x) \) are inverses.
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the horsepower, h(s), required for a racecar to overcome wind resistanc…
\(0.61\)
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use transformations of the graph of f(x)=3^x to graph the given functio…
The equation of the asymptote for \( g(x) = 3^x + 5 \) is \( y = 5 \). The domain of \( g(x) = 3^x + 5 \) is \( (-\infty, \infty) \). The range of \( g(x) = 3^x + 5 \) is \( (5, \…
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use properties of logarithms to condense the logarithmic expression. wr…
$\ln(19x)$
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use properties of logarithms to expand the logarithmic expression as mu…
$2 + \frac{1}{2}\log(z)$ (or equivalent forms, assuming base 10 logarithm; if natural logarithm, it would be $2+\frac{1}{2}\ln(z)$ but the problem likely uses base 10 as 10000 is …
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at sunshine citrus co., workers take oranges from a large bin and pack …
The slope of - 10 tells us that for each box of oranges packed, the weight of the bin decreases by 10 pounds.
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at noon, to begin a study, a petri dish had 3000 bacteria cells. each h…
\( y = 3000(1.11)^t \)
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evaluate the following expression without using a calculator. \\(\\log_…
$\frac{1}{2}$
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partially correct your answer is incorrect. - (b): your answer is incor…
(b) The minimum value occurs at \( x=-4 \) (c) The minimum value of the function is \( - 1 \)
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solve the logarithmic equation. be sure to reject any value of x that i…
The exact solution is \(x = e^4 - 7\), and the decimal approximation is \(47.60\). The solution set is a single value, so for the first part (exact solution) the answer is \(e^4 -…
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the functions q and r are defined as follows. q(x) = 2x + 2 r(x) = -x² …
\( -14 \)
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use properties of logarithms to expand each logarithmic expression as m…
$-2\log(p)$
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how much should be invested now at an interest rate of 5.5% per year, c…
\(\$17917.43\)
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approximate the number using a calculator. $e^{-0.48}$ $e^{-0.48} \\app…
$0.619$
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find the domain of the logarithmic function. f(x) = log (12 - x) the do…
\((-\infty, 12)\)
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a) determine the equations of the asymptotes for the equation b) graph …
B. \(y=\frac{1}{5}x,y =-\frac{1}{5}x\) ### Part (b)
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for the real - valued functions ( g(x)=\frac{x + 6}{x+3} ) and ( h(x)=4…
\( (g \circ h)(x) = \frac{4x + 7}{4x + 4} \) Domain of \( g \circ h \): \( (-\infty, -1) \cup (-1, \infty) \)
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graph the following function. what are the domain and range of the func…
- **Domain**: A. The domain is \(\{x|x\text{ is a real number}\}\) - **Range**: The range is \(\{y|y\leq0\}\) - **Positive interval**: The function \(p(x)=-5|x|\) is never positiv…
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use properties of logarithms to expand the logarithmic expression as mu…
$6 + \log(x)$
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sketch a graph of y = f(x). f(x) = \\frac{1}{4}x + 8 use the graphing t…
Plot the points \((0,8)\) and \((4,9)\) and draw a straight line through them to graph \(y=\frac{1}{4}x + 8\).
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the function f(x) = 4x + 10 models the amount of money francis makes wh…
D. 18
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subtract the mixed numbers. enter your answers. \\(\\begin{align}2\\fra…
First? : 5, Middle? : 1, Last? : 4 (So filling the boxes: \(2\frac{1}{2}=2\frac{\boldsymbol{5}}{10}\), \(-1\frac{1}{10}=-1\frac{\boldsymbol{1}}{10}\), result is \(1\frac{\boldsymb…
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simplify the expression without using a calculator. $10^{log sqrt3{6x}}…
\(\sqrt[3]{6x}\)
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evaluate or simplify the expression without using a calculator. $e^{\\l…
\( 3x^{5} \)
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evaluate or simplify the expression without using a calculator. $e^{ln …
133
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evaluate. \\(\\ln \\frac{1}{e^{6}}\\) \\(\\ln \\frac{1}{e^{6}} = \\squa…
-6
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evaluate the expression without using a calculator. \\(\\ln e^{9}\\) \\…
9
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evaluate the expression without using a calculator. $10^{log 10}$ $10^{…
\( 10 \)
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find the domain of the logarithmic function. f(x) = log (6 - x) the dom…
\((-\infty, 6)\)
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find the slope and the y-intercept of the line. y = 9x - 5 slope: y-int…
Slope: $9$; $y$-intercept: $- 5$
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find the domain of the function. g(x) = \\log_{9}(x - 7) the domain of …
\((7, \infty)\)
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fill in the missing values to make the equations true. \\(\\log_{5} 8 -…
First equation: $\frac{8}{11}$; Second equation: $5$; Third equation: $2$
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complete the sentences about resizing the number 4. 4 × 4 > 4 the produ…
4 times as big as
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complete the sentences about resizing the number 4. 4 × 4 > 4 the pl ? …
\(4\times4\ >\ 4\)
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the function $f(x) = 25(0.965)^x$ models the percentage of surface sunl…
The depth is 213 feet, and the point on the graph is \((213, 1)\)