微积分
极限、导数、最优化与函数性质。
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estimate: 918 - 829 is about calculate: 918 - 829 = is your estimate re…
s: - Estimate: 90 - Calculate: 89 - Is the estimate reasonable: Yes
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5. use the graph of $f(x)$ below to calculate each limit. you do not ne…
s: (a) \(\lim_{x\to - 3^{-}}f(x)=\infty\) (or if we consider the context, maybe the graph is different, but based on the vertical asymptote, the left - hand limit as \(x\to - 3^{-…
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graph the following function on the axes provided. $f(x) = \\begin{case…
The function \(f(x)\) consists of two linear pieces: - For \(x < - 3\), the line \(y=2x + 12\) with an open circle at \((-3,6)\) and passing through points like \((-4,4)\). - For …
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graph the following function on the axes provided. $f(x) = \\begin{case…
To graph \( f(x) \): - Draw a horizontal line at \( y = 1 \) for all \( x < 1 \) (open circle at \( (1, 1) \)). - Draw a line with slope \( 1 \) (equation \( y = x - 3 \)) for all…
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multistep function inverses (level 1) score:0/3 penalty:none question f…
$f^{-1}(x) = (5x)^3$ (corresponding to the option $\boldsymbol{f^{-1}(x) = (5x)^3}$)
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graph the following function on the axes provided. $f(x) = \\begin{case…
To graph the piece - wise function: 1. For \( y=x + 4\) (\(-3\leq x\leq0\)): - Plot the points \((-3,1)\) (closed circle) and \((0,4)\) (closed circle) and draw a line segment con…
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graph the following function on the axes provided. $f(x) = \\begin{case…
The graph consists of a horizontal segment from \( (-4, 3) \) (open circle) to \( (-1, 3) \) (closed circle) and a linear segment from \( (-1, 2) \) (open circle) to \( (5, 8) \) …
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which table shows a function that is decreasing only over the interval …
The second table (with \(x\)-values \(-2, -1, 0, 1, 2\) and \(f(x)\)-values \(0, 3, 0, -3, 0\))
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solve the following system of equations graphically on the set of axes …
The solution to the system of equations is \( x = 2 \), \( y = 6 \) or the point \( (2,6) \)
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algebra 1 unit 3b quadratic functions putting it all together practice:…
### Part 1: Naming Vertex and Describing Transformations We use the vertex form of a quadratic function: \( y = a(x - h)^2 + k \), where \((h, k)\) is the vertex, \(a\) determines…
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2 a ladder leaning against a wall reaches a height of 16 feet. the ladd…
$\theta \approx 53.13^\circ$ (or $0.927$ radians)
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instructions use the graph to answer the questions. classify a graph 3 …
True
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in an attempt to calculate an integral, you perform a trigonometric sub…
A. \(\int\frac{2x^{3}}{(9 - 4x^{2})^{3/2}}dx\)
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#19-27, write the slope & y-intercept, then write the equation. 19. m=_…
| Problem | $m$ | $b$ | Equation | |---------|-----|-----|----------| | 19 | $-\frac{1}{2}$ | $3$ | $y=-\frac{1}{2}x+3$ | | 20 | $2$ | $2$ | $y=2x+2$ | | 21 | $-\frac{1}{4}$ | $1$…
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in an attempt to calculate an integral, you perform a trigonometric sub…
# Explanation: ## Step1: Recall trigonometric substitution For integrals involving $\sqrt{a^2 - b^2x^2}$, we use the substitution $x=\frac{a}{b}\sin\theta$ (or $x=\frac{a}{b}\cos\…
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for each of the indefinite integrals below, select which of the followi…
A. $x = 6\tan\theta$ ### Problem 2: $\int \frac{dx}{(36 - x^2)^{3/2}}$
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from x = 2 to x = 4, is the function increasing or decreasing?
Decreasing (the option with "Decreasing" text)
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from x = 0 to x = 2, is the function increasing or decreasing? decreasi…
Increasing (corresponding to the purple option labeled "Increasing")
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from x = -3 to x = 0, is the function increasing or decreasing? increas…
Increasing (assuming the graph shows that as \( x \) increases from -3 to 0, the function's value increases; the highlighted "Increasing" option also aligns with this analysis). S…
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is this function increasing, decreasing, or constant (neither)? constan…
Constant (Neither Increasing or Decreasing)
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is the graph of the equation increasing, decreasing, or constant? const…
B. Increasing (assuming the purple button is option B with text "Increasing")
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where could we say this graph is increasing? (look at the numbers on th…
B. It is increasing from -3 to 0, C. It is increasing from 2 to 4
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list the types of intervals that the graph demonstrates in order. incre…
increasing, constant, decreasing, constant
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why is this function nonlinear? this is a nonlinear function because it…
B. This is a nonlinear function because it is curved.
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why is this function linear? this is a linear function because the line…
B. This is a linear function because it is a straight line.
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which of the following is true of spearmans idea of expressing general …
C. Quickly accepted and widely used. (Assuming the options are labeled A, B, C, D with A being "Widely used, but found limited acceptance", B being "Used only by followers of Spea…
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which of the following graphs represents a function that is both non - …
C. A graph that forms a curved line going downwards from left to right
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the graph of ( y = f(x) ) is given. match each of the following equatio…
3. The graph labeled 3 (the curve shifted 4 units right from $f$)
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○ $y = f(x) - 5$ (e) reflect about the $x$-axis. ○ $y = f(x - 5)$ ○ $y …
(e) $y = -f(x)$ (f) $y = f(-x)$ (g) $y = 5f(x)$ (h) $y = \frac{1}{5}f(x)$
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the functions f and g are defined as follows. $f(x) = 3x - 3$ $g(x) = -…
$f(-3)=-12$ $g(-2)=22$
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suppose the graph of f is given. write an equation for each graph descr…
(a) $y = f(x) + 5$ (b) $y = f(x) - 5$ (c) $y = f(x - 5)$ (d) $y = f(x + 5)$
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the graph of $y = f(x)$ is given. match each of the following equations…
(a) 3 (b) 1
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graph the function by hand, not by plotting points, but by starting wit…
The correct graph is the top option (the parabola with vertex at $(-3, 0)$ opening upward).
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graph the function by hand, not by plotting points, but by starting wit…
The correct graph is the one with a starting point at $(-5,7)$, curving upward and to the right (the bottom-right option in the provided image, marked with the topmost radio butto…
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graph the function by hand, not by plotting points, but by starting wit…
The correct graph is the middle lower option (the one with x-axis extending to 10, y-axis starting at -2, and the curve beginning at $(-5,7)$ and increasing rightward).
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question shandra invested $140 in an account paying an interest rate of…
377 (rounded to the nearest dollar)
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5. governments role in a market economy is ______. options: pervasive, …
limited
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question given the definitions of f(x) and g(x) below, find the value o…
\(-14\)
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question given the definitions of f(x) and g(x) below, find the value o…
\( 5 \)
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question given the definitions of f(x) and g(x) below, find the value o…
18
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question given the definitions of f(x) and g(x) below, find the value o…
\(-11\)
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question given the definitions of f(x) and g(x) below, find the value o…
22
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question given the definitions of f(x) and g(x) below, find the value o…
2
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question given the definitions of f(x) and g(x) below, find the value o…
19
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question given f(x) = -3x + 2, solve for x when f(x) = -1. answer attem…
\( x = 1 \)
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question given f(x) = -x - 1, solve for x when f(x) = 6. answer attempt…
\( -7 \)
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question given ( g(x) = 3x - 4 ), solve for ( x ) when ( g(x) = 5 ). an…
\( x = 3 \)
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solve for input of function given output score: 4/20 penalty: 1 off que…
\( 3 \)
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question 1 micah was hired to work for an hourly wage which is shared w…
8.75
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a) linear function, of the form $f(x) = mx + b$ cubic function, of the …
Top question: cubic function, of the form $f(x) = ax^3 + bx^2 + cx + d$ Bottom question: exponential function, of the form $f(x) = a \cdot b^x + c$
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how many weeks can mr. wright wait until he you can use the model to he…
$3\frac{1}{4}$ (or $\frac{13}{4}$)
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find all horizontal asymptotes of the following function $f(x) = \\frac…
One Horizontal Asymptote, \( y = 3 \)
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question the graph of $f(x) = -2x^2$ is given below. write the equation…
\( g(x)=-2x^{2}-1 \)
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how many batches of muffins can ren make $2\\frac{1}{3} \\div \\frac{2}…
$3\frac{1}{2}$ (or $\frac{7}{2}$)
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question the graph of $f(x) = -2^x$ is given below. write the equation …
\( g(x) = -2^{x + 5} \)
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question the graph of $f(x) = \\sqrt{x}$ is given below. write the equa…
\( g(x)=\sqrt{x - 3} \)
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question the graph of $f(x) = \\frac{1}{x}$ is given below. write the e…
\( g(x)=\frac{1}{x}-2 \)
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which statement is true about $f(x)+2 = \\frac{1}{6}|x - 3|$?\ the grap…
The graph of $f(x)$ has a range of $f(x) \geq -2$.
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the graph of ( y = sqrt{x} ) is transformed as shown in the graph. whic…
$y = -\sqrt{x} + 2$
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functions and their inverses the tables for ( f(x) ) and ( g(x) ) are s…
16
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question the graph of ( f(x) = x^3 ) is given below. write the equation…
\( g(x)=x^3 - 5 \)
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question the graph of $f(x) = 2x^3$ is given below. write the equation …
\( g(x) = 2x^3 - 3 \)
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question the graph of $f(x) = 2\\sqrt{x}$ is given below. write the equ…
\( g(x) = 2\sqrt{x - 4} \)
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what is one downside for consumers to competition in a free - enterpris…
A. Consumers must be knowledgeable.
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find a formula for the quadratic function whose graph is shown. f(x) = …
$f(x)=2(x-4)^2$ or $f(x)=2x^2-16x+32$
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question the graph of ( f(x) = |x| ) is given below. write the equation…
\( g(x) = |x| - 2 \)
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(a) $y = 5x$ $\\bigcirc$ $f$ $\\bigcirc$ $f$ $\\bigcirc$ $g$ $\\bigcirc…
(a) G (b) f (c) F (d) g
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question the graph of $f(x) = x^2$ is given below. write the equation o…
\( g(x)=(x + 1)^2 \)
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match each equation with its graph. (do not use technology.) (a) $y = 5…
(a) $\boldsymbol{G}$ (b) $\boldsymbol{f}$ (c) $\boldsymbol{F}$
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match each equation with its graph. (do not use technology.) (a) $y = x…
(a) h (b) f (c) g
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question\ the graph of $f(x) = 2x^2$ is given below. write the equation…
$g(x)=2(x+6)^2$
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(e) $y = \\frac{\\sqrt{x}}{x^2 + 8}$ \\bigcirc power function \\bigcirc…
(e) algebraic function (f) logarithmic function
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classify each function as a power function, root function, polynomial (…
(a) polynomial function of degree 3 (b) trigonometric function (c) power function (d) exponential function
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question the graph of ( f(x) = -2x^3 ) is given below. write the equati…
$g(x) = -2(x-4)^3$
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use what you have learned to identify reasons that governments create r…
A. to protect the health and safety of consumers C. to ensure that competition is fair E. to educate consumers about specific products
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find the intercepts and graph the equation by plotting points. y = x² -…
A. The intercept(s) is/are $(-3, 0), (3, 0), (0, -9)$
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understanding free enterprise introduction: sort the tiles to show the …
## Possible Benefits: - better quality - freedom of choice - lower prices ## Possible Limitations: - need for consumer knowledge - lack of fair competition - potential for higher …
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7) $w(x) = 3x^2 + 1 + 2x$; find $w(-5)$
$66$
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which best explains the benefits of the free enterprise system in the u…
D. The system encourages innovation through property protection and incentives.
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write a linear function that relates y to x. (see examples 1 and 2.) 1.…
$y=3$ --- ### Problem 2
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5 multiple choice 1 point what is the value of x if \\(\\log_{3} x = 5\…
243
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how can the government reduce the wealth gap in a mixed market economy?…
C. The government can improve education to provide new opportunities for workers in the lower class.
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18. 3 ÷ 0.6
5
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ivan works for an automobile factory that exports cars around the world…
C. a command economy with heavy government regulation.
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simplify: |3 + 7 - 4| -6 6 19 22 cant simplify there are two points con…
1. 6 2. 10
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over what interval is the graph of $f(x) = -(x + 8)^2 - 1$ decreasing?\…
$(-8, \infty)$
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what is one way a command economy affects the lives of private citizens…
A. Citizens cannot make most economic decisions.
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find the point(s) on the graph below in which the tangent line to the p…
A. A B. B
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another look! draw a model to add $1\\frac{7}{8}+2\\frac{1}{4}$. rememb…
\( 5 \) ### Problem 2: \( 2\frac{5}{12} + 4\frac{1}{4} \)
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4. $y = -2|x + 2|$
The graph is a downward-opening V with vertex at $(-2, 0)$, passing through $(0, -4)$ and $(-4, -4)$. When plotted on the grid, these points connect to form the absolute value fun…
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6) g(x) = 4x + 5 f(x) = 3x find (g · f)(x)
$12x^2 + 15x$
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graph the following function on the axes provided. $f(x) = \\begin{case…
The graph consists of two lines: 1. A line with slope - 1 for \( x < 0 \), passing through \( (-6,0) \) and having an open circle at \( (0, - 6) \). 2. A line with slope 3 for \( …
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the graphs of two linear functions f and g are shown in the following f…
(a) $x=2$ (b) $x \geq 2$
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4. matching: given the graphs of 4 rational functions, a b c & d, find …
s: a) \(\boldsymbol{B}\) b) \(\boldsymbol{A}\) c) \(\boldsymbol{D}\) d) \(\boldsymbol{C}\)
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solve the exponential equation. express the solution in terms of natura…
In terms of logarithms: $\log(4.23)$ Decimal approximation: $0.6263$
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3. using the graph of ( y = f(x) ) provided, answer the following quest…
\( f(x)=\frac{x - 1}{x - 2} \) (or \( f(x)=1+\frac{1}{x - 2} \)) ### Part (b)
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8. what is the difference? $4\\frac{2}{6}-2\\frac{10}{12}=$? a. $\\frac…
B. $1\frac{6}{12}$
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what type of employer - sponsored retirement plans limit the investment…
B. defined contribution plans
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exponential and logarithmic equations question 9, 4.4.23 part 1 of 2 hw…
Solution in logarithms: $\log(3.21)$ Decimal approximation: $0.507$ (rounded to three decimal places)
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what is the frequency of the sinusoidal graph? enter your answer in the…
$\frac{1}{\pi}$