微積分
極限、導數、最優化與函數性質。
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a collector of rare books has a first - edition book worth $262, which …
$\$1059.94$
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solve on paper. then check your work on zearn. \\(\frac{3}{4}\\) of 5 i…
$3\frac{3}{4}$ (the whole number box gets 3, the numerator box gets 3, the denominator box gets 4)
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4. let ( f(x) = sqrt{2x + 1} ). find ( f(x) ) using the definition of t…
\( f'(x) = \frac{1}{2\sqrt{x + 1}} \) ### Problem 5: Let \( f(x) = \frac{1}{2x - 1} \). Find \( f'(x) \) using the definition of the derivative as a limit. (Do not use differentia…
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calculator which function is shown on the graph? $f(x) = -\frac{1}{2}si…
$f(x)=\frac{1}{2}\cos x$
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solve the inequality both algebraically and graphically. draw a number …
The solution as an inequality is $\boldsymbol{x < \frac{77}{5}}$ (or $x < 15.4$) The solution in interval notation is $\boldsymbol{(-\infty, \frac{77}{5})}$ The correct graph is *…
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the following function on the axes provided. $f(x) = \\begin{cases} -x …
To graph the piecewise function: - For $x < 0$, draw the line $y = -x - 6$ with an open circle at $(0, -6)$ and extending to the left (e.g., through $(-2, -4)$). - For $x > 5$, dr…
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f(x) = 2|x + 3| - 4
To determine the correct graph of \( f(x) = 2|x + 3| - 4 \), we analyze the key features of the absolute - value function: ### Step 1: Recall the vertex form of an absolute - valu…
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5\\frac{3}{8} + \\left(6\\frac{3}{4} - 4\\frac{1}{8}\ ight)
$8$
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for the given equation, list the intercepts and test for symmetry. $y =…
### Intercepts: A. The intercept(s) is/are $(0,0)$ ### Symmetry: The graph is symmetric about the origin, and has no symmetry about the y-axis or x-axis.
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question 13 (multiple choice worth 4 points) (01 obr mc) which of the f…
B. Investments usually limit access to the deposited funds.
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question 1-18 how did the chicano mural movement influence american cul…
A. Expressed cultural pride and heritage through public art
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4) if $f(x)=x^2 + 3x - 8$, then determine the equation of $g(x)$ if $g(…
\( g(x)=-x^2 - 5x + 7 \)
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he depicted figures that are stylized, with ideal beauty and proportion…
He depicted figures that are stylized, with ideal beauty and proportion.
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math 122 - activity 3 1. let ( f(x) = 3x^2 - x ). (a) find the equation…
The equation of the secant line is \( y = 8x-6 \) ### Problem 1(b)
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lesson 5 congress at work—organization and committees close reading con…
1. The rule repeal allowed experienced members to retain committee chairmanships, preserving institutional expertise and enabling longer-term legislative strategy. 2. This ensures…
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question 4 (4) intoxicated per se means that? a. a driver is drinking a…
Question 4: B. A driver is above or at the legal limit for blood alcohol concentration Question 5: D. All of the above
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optional: ch 6 review in 1851, the dakota exchanged 24 million acres of…
annuities for 50 years, cash and reservations
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the axis of symmetry for a function in the form $f(x)=x^2 + 4x - 5$ is …
\((-2, - 9)\)
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answer as ( x \to -infty, y \to infty ) and as ( x \to infty, y \to -in…
as \(x \to -\infty, y \to \infty\) and as \(x \to \infty, y \to -\infty\)
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given the function $f(x) = -5x^2 - x + 20$, find $f(3)$. -13 64 62 -28
\(-28\) (corresponding to the option with \(-28\))
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the graph of $y = f(x)$ is graphed below. what is the end behavior of $…
as $x \to \infty, f(x) \to -\infty$ and as $x \to -\infty, f(x) \to \infty$
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the graph of $y = f(x)$ is graphed below. what is the end behavior of $…
As \(x \to -\infty\), \(y \to \infty\) and as \(x \to \infty\), \(y \to \infty\)
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what is the vertex of the graph of the function $f(x)=x^{2}+8x - 27$ $(…
(-4, - 18)
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12 multiple choice 1 point the two basic types of tariffs are revenue a…
A. revenue and protective.
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(left( \frac{1}{3} + \frac{6}{15} ight) - \frac{4}{15})
$\frac{7}{15}$
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this exam is taken outside of class and close on its due date. the exam…
A. Free - market economies tend to result in unequal distribution of wealth. ### Question 2 (Note: The question seems to be cut off. Assuming it is about selling domestically prod…
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the distance a wave runner is from a dock on a shoreline is represented…
\((f\circ g)(t)=\sqrt{49 + 36t^{2}}\) represents the distance the wave runner is from the dock after \(t\) hours. The domain is \(t\geq0\) (the first option in the list of options…
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10) if the point ((a, b)) is on the graph (y = x^2), which of the follo…
d) \((a + 3,-b + 1)\)
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1 multiple choice 1 point which statement most accurately identifies a …
A. Free - market economies tend to result in unequal distribution of wealth.
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quadratic functions tables of values for two different functions are gi…
The second function grows approximately 21 times faster than the first function over the interval \(4 < x < 5\). (The option corresponding to this statement)
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the function $g(x) = 10x^2 - 100x + 213$ written in vertex form is $g(x…
- The vertex of the graph is (5, -37). - The parabola has a minimum. - The parabola opens up.
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mary throws a plastic disc to her friend. her friend catches the disc s…
\( A = 4, B = 3 \) (the option: \( A = 4, B = 3 \))
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use the functions below. - ( f(x) = 2x - 1 ) - ( g(x) = |x + 2| + 3 ) w…
\( (f \circ g)(x)=2|x + 2|+5 \) and the domain of \( (f \circ g)(x) \) is \( (-\infty, \infty) \), so the correct option is the one with \( (f \circ g)(x) = 2|x + 2|+5 \) and doma…
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write the fraction as a whole number. \\(\\frac{3}{4} \\times 16 = \\fr…
12
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the graph of y = f(x) is shown below. what are all of the real solution…
The real solutions of \( f(x)=0 \) are \( x=-4 \), \( x = 0 \), and \( x = 3 \). So we can write them as \( x=-4,0,3 \) (or list them separately as \( x=-4 \), \( x = 0 \), \( x =…
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what is the slope of this line? simplify your answer and write it as a …
\( 0 \)
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use technology to find points and then graph the function $y = 2^{x + 1…
The points with integer coordinates are \( (-1, -7) \), \( (0, -6) \), \( (1, -4) \), \( (2, 0) \), \( (3, 8) \) (and more can be calculated, e.g., \( x = 4 \) gives \( y = 2^{5}-…
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evaluate the following expression. $2^4 - 10 - 15 \\div 3 = \\square$
1
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give the slope and y-intercept of the line whose equation is given. the…
A. The slope is \(-5\). ### For the y - intercept:
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evaluate the function graphically. find $f(4)$
\( f(4)=-3 \) (Note: There might be a mis - calculation in the initial detailed analysis, but based on the graph's visual representation, the value at \( x = 4 \) is - 3)
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the formula for the volume of a cube is $v = x^3$, where $x$ is the edg…
64
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the function $y = f(x)$ is graphed below. what is the average rate of c…
\(0\)
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lets find \\(\\frac{2}{3} - \\frac{1}{4}\\). first write the subtractio…
$\frac{2}{3}-\frac{1}{4}=\frac{8}{12}-\frac{3}{12}=\frac{5}{12}$ (The boxes are filled with 8, 12, 3, 12, 5, 12 respectively)
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use the given conditions to write an equation for the line in point - s…
Point-slope form: $y-4=\frac{4}{3}(x-4)$ Slope-intercept form: $y=\frac{4}{3}x-\frac{4}{3}$
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graph the exponential function. \\( g(x) = -\frac{3}{2}(2)^x \\) plot f…
The five points are \( (-2, -\frac{3}{8}) \), \( (-1, -\frac{3}{4}) \), \( (0, -\frac{3}{2}) \), \( (1, -3) \), \( (2, -6) \). These points can be plotted on the graph to sketch \…
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find the value of $f(6)$. $y = f(x)$ answer attempt 1 out of 2
\( 4 \)
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evaluate the function graphically. find $f(1)$
\( f(1)=-1 \)
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multiply. 2 × 0.24
0.48
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solve the system of equations. y = -3x + 2 y = 2 - 3x y = mx + b m: slo…
### Part 1: Solve the system of equations The system of equations is: \[ \begin{cases} y = -3x + 2 \\ y = 2 - 3x \end{cases} \] #### Step 1: Analyze the equations Notice that both…
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of the function ( f(x) = 2x^2 + bx + c ) is shown. what are the values …
$b=-4$, $c=-6$
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solve the system of equations. $y = -3x + 2$ $y = 2 - 3x$ $y = mx + b$ …
- For the equation \( y=-3x + 2 \): - Slope (\( m \)): \(-3\) - y - intercept (\( b \)): \(2\) - To graph: Plot \( (0,2) \), use slope \( \frac{-3}{1} \) to find other points (e.g…
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the axis of symmetry for the function $f(x) = -2x^2 + 4x + 1$ is the li…
B. (1, 3)
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over what interval is the function shown in the table increasing? $f(x)…
B. $x<0$
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7. lesson quiz for which function is the average rate of change over th…
D. $k(x)=2x^2$
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calculate. (1) $\frac{5}{6} - \frac{3}{4} = $ (2) $\frac{2}{3} - \frac{…
$\frac{1}{12}$ ### (2)
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adam graphs ( f(x) = x^2 ) and ( g(x) = 3x^2 ). which of the following …
C. y-value when x = 5
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y = \\frac{1}{4}x + 3; y > -4x - 1
The shaded region in the graph correctly represents the solution set of the system of inequalities $\boldsymbol{y \geq \frac{1}{4}x + 5}$ and $\boldsymbol{y > -4x - 1}$.
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find the value of $f(-5)$. $y = f(x)$
\(f(-5)=8\)
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y = -1/4 x + 2; y > -4x - 1
The system of inequalities for the shaded region is: $y\geq\frac{1}{4}x+3$ $y>-4x-1$
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find the value of $f(-7)$. $y = f(x)$
\( 7 \)
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find the value of $f(-2)$. $y = f(x)$
\( 0 \)
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find the value of $f(7)$. $y = f(x)$
\( 7 \)
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period y = -x + 2 y > -4x - 1
The solution to the system of inequalities is the region that is above the solid line $y=-x+2$ and above the dashed line $y=-4x-1$, with the intersection point of the two lines at…
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3 $f(x) = \\frac{\\cdots}{\\cdots}$ hole: no hole vertical asymptote(s)…
- Hole: No hole - Vertical Asymptote: $x=3$ - Slant Asymptote: $y=x+4$ - Domain: $(-\infty,3)\cup(3,\infty)$
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which function has the following end behavior? - as ( x \to 2 ), ( y \t…
A. \( y=\sqrt{x - 2}-1 \)
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which function has the following end behavior? - as ( x \to 2 ), ( y \t…
A. \(y=\sqrt{x - 2}-1\)
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find the value of $f(6)$. $y = f(x)$
-5
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question 2 a increasing and positive b decreasing and positive c increa…
D. decreasing and negative
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8. multimedia : communicate * a) airplane : travel b) cook : stove c) m…
a) airplane : travel ### Question 9
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graph the piecewise function given below. $f(x) = \\begin{cases} -4 & \…
The graph consists of a horizontal line \( y = - 4 \) for \( x\leq4 \) (with a closed dot at \( (4,-4) \)) and an upward - opening parabolic segment \( y=(x - 5)^2 \) for \( 4<x\l…
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a town has a population of 2000 and grows at 4.5% every year. what will…
3544
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a part of an exponential function is graphed on the grid. which stateme…
To solve this, we analyze the domain and range from the graphed exponential function: ### Step 1: Identify the domain The domain of a function is the set of all \( x \)-values it …
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question 1. which statement about $p(x) = -7(4)^x$ is true? a. the doma…
D. The range is all real numbers less than 0.
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graph this line using the slope and y-intercept: $y = -8x - 1$ click to…
The line is graphed by first plotting the y - intercept \((0,-1)\) and then using the slope \(-8\) to find another point (e.g., \((1,-9)\) or \((-1,7)\)) and drawing a straight li…
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57. logistic growth the logistic growth model $p(t) = \\frac{0.8}{1 + 1…
Approximately \( 0.30 \) (or \( 30\% \)) of new cars in 2006 had a GPS. ### Part (b)
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15 find the maximum or minimum value of the function f(x) = -x² + 24x -…
The maximum value of the function is \( -2 \) (occurring at \( x = 12 \)). ### Problem (next, e.g., finding max/min of \( f(x) = (x + 3)^2 + 6 \))
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1. $f(x)=x^{3}+2x^{2}-x - 2$ rel. max: ______ rel. min: ______ abs. max…
- Rel. Max: \((-1.54, 0.65)\) - Rel. Min: \((0.21, -2.11)\) - Abs. Max: None (or \(\infty\)) - Abs. Min: None (or \(-\infty\)) - Inc: \((-\infty, -1.54) \cup (0.21, \infty)\) - De…
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graph the piecewise function given below. $f(x)=\\begin{cases} |x + 5| …
The graph consists of two parts: 1. A V - shaped graph (for \( y = |x + 5|,x\leq0 \)) with vertex at \((-5,0)\) and passing through \((0,5)\). 2. A line segment (for \( y=-x + 3,0…
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topic 3 rational functions skills practice continued describe the verti…
(for a typical graph like "9"): Vertical asymptote: \( x = 0 \) (y - axis); Horizontal asymptote: \( y = 0 \) (x - axis)
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watch the video and then solve the problem given below. click here to w…
$f(x) = \sqrt[7]{x}$ $g(x) = x^4 - 8$
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express the given function h as a composition of two functions f and g …
$g(x)=6x-9$
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type the correct answer in the box. use numerals instead of words. a li…
-18
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graph the following function on the axes provided. $f(x)=\\begin{cases}…
The graph consists of two rays: 1. A horizontal ray starting with an open circle at $(2, -3)$ and extending to the left along the line $y = -3$. 2. A ray starting with an open cir…
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questions solve the following system of inequalities graphically on the…
The point \((0,0)\) is in the solution set. (Other valid points could also be chosen, for example, \((- 5,0)\) : For \(y < -x + 1\), \(0 < -(-5)+1=6\) (true); for \(y < \frac{1}{5…
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pregunta 16 (5 puntos) jon acuff says you should do all of these things…
oubt voices focuses on engaging with them through sharing, truth, and writing, not arguing. Pregunta 17: Dave Ramsey's goal-setting guidelines include specificity, personal owners…
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look at these graphs. southern colonies exports by value tobacco rice b…
B. The colonies had different growing seasons.
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ex. 4: given $f(x) = -x + 2$, find $x$ if $f(x) = 6$
$x = -4$
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which type of sentence is this? bhutan, an isolated country in the east…
simple
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name hines 5-5 lesson quiz function operations 1. let ( f(x) = 3x^2 - 2…
C. \( 3x^2 + 5x + 2 \) ### Problem 2 (Part A):
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use the graphs of f and g to evaluate the composite function, (g ∘ f)(6…
$-6$
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1. $f(x) = 2^x$ | $x$ | $f(x)$ | | --- | --- | | $-2$ | | | $-1$ | | | …
The filled table is as above with \( f(-2)=\frac{1}{4} \), \( f(-1)=\frac{1}{2} \), \( f(0) = 1 \), \( f(1)=2 \), \( f(2)=4 \).
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1. $f(x) = 2^x$ | $x$ | $f(x)$ | | ---- | ---- | | $-2$ | | | $-1$ | | …
| \( x \) | \( f(x) \) | | ---- | ---- | | \( -2 \) | \( \frac{1}{4} \) | | \( -1 \) | \( \frac{1}{2} \) | | \( 0 \) | \( 1 \) | | \( 1 \) | \( 2 \) | | \( 2 \) | \( 4 \) |
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a point of the form 25 +bi is 37 units from 13 - 31i. what is the value…
4
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ex. 3: given $h(x) = 5x - 1$, find $x$ if $h(x) = 9$
$x = 2$
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evaluating functions ex. 1: given $f(x) = 7x - 1$, find $f(-2)$. ex. 2
$-15$
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for f(x)=4−x and g(x)=3x²+x+9, find the following functions. a. (f∘g)(x…
a. $\boldsymbol{-3x^2 - x - 5}$ b. $\boldsymbol{3x^2 -25x +61}$ c. $\boldsymbol{-19}$ d. $\boldsymbol{23}$
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which function represents exponential growth? a) $y = 8x$ b) $y = 0.5x^…
C) \( y = 3(1.5)^x \)
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graph the exponential function. \\( g(x) = -\frac{3}{2}(2)^x \\) plot f…
The five points to plot are \((-2,-\frac{3}{8})\), \((-1,-\frac{3}{4})\), \((0,-\frac{3}{2})\), \((1, - 3)\), \((2,-6)\) (or in decimal form \((-2,-0.375)\), \((-1,-0.75)\), \((0,…
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determine whether the function represents exponential growth or exponen…
exponential growth
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multiply and divide fractions (positive) l1 score: 0/3 penalty: none qu…
$\frac{4}{15}$