微积分
极限、导数、最优化与函数性质。
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given $y = x^2 + 10x + 8$, determine the turning point. a. $(-5,17)$ b.…
d. (-5,-17)
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differentiate $6x^{\\frac{2}{3}}$. a. $4x^{-\\frac{2}{3}}$ b. $4x^{-\\f…
b. $4x^{-1/3}$
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the graph of $f(x) = x^2$ is reflected over the x-axis and compressed h…
The top-left (green) graph
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the graph of $f(x)=x^2$ was transformed to create $g(x)=(x + 3.5)^2 - 4…
B. A vertical shift down 4 units D. A horizontal shift to the left 3.5 units
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give the slope and y-intercept for the graph of the function $f(x) = \\…
The slope is \(\frac{1}{3}\) The \(y\) - intercept is \(-6\)
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look at this graph: what are the coordinates of the vertex? ( , ) submit
(0, 8) Wait, no, maybe the vertex is at (0, 8). Wait, perhaps the graph's vertex is at (0, 8). So the answer is (0, 8).
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suppose a ball thrown into the air has its height (in feet) given by th…
a. \(h(1)=159\); this is the height of the ball (159 feet) 1 second after it is thrown. b. \(h(5)=415\) feet c. The ball stops climbing at \(t=5\) seconds. Testing \(t=6\) gives \…
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the profit from the production and sale of music players is given by th…
a. $P(500)=395500$. This means the profit from producing and selling 500 music players is 395500 (in the relevant currency unit). b. $P(8000)=395500$
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find the domain of the function. $f(x) = \\frac{x + 3}{6 - x}$
All real numbers except $x=6$, or in interval notation: $(-\infty, 6) \cup (6, \infty)$
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evaluate the function graphically. find ( f(7) )
\(-8\)
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u5, l10: dividing decimals by decimals: algorithm homework 1. here is h…
The product equals 31.59, so Han's answer is correct. # 2. Step-by-Step Format: ## Step1: Rewrite division to eliminate decimals Multiply numerator and denominator by 10: $\frac{3…
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u5, l10: dividing decimals by decimals: algorithm exit ticket: the quot…
1. $368 \div 23$ (other equivalent expressions like $3680 \div 230$ are also valid) 2. $16$
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a car weighs 2321 pounds. if 375 pounds of old parts are removed and re…
2379
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find the value of the sum \\(\\sum\\limits_{j=1}^{32} (4j^2 - 8j + 2)\\…
$41600$
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write the following sum using sigma notation. $7 - \\frac{7}{2} + \\fra…
$\sum_{n=1}^{46} (-1)^{n+1}\frac{7}{n}$
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let $f(x) = \\begin{cases} 3x + 5 & \\text{if } x < -3 \\\\ x^2 + 1 & \…
\(x=-3\)
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attempt 1: 10 attempts remaining. find the limit of the function: \\(\\…
\(0\)
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attempt 1: 10 attempts remaining. determine the x-values where f(x) is …
\( 1,3 \)
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attempt 1: 10 attempts remaining. determine the x-values where f(x) is …
1, 3
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the function f(x) is graphed above. find the equations of the vertical …
First vertical asymptote: \( x = -10 \) Second vertical asymptote: \( x = 10 \) (Wait, but maybe the asymptotes are at \( x = -10 \) and \( x = 10 \). So the answers are \( x = -1…
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attempt 1: 10 attempts remaining. find the limit of the function: \\(\\…
\( 1 \)
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attempt 1: 10 attempts remaining. find the limit of the function at the…
\( 160 \)
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handwritten step-by-step work legibly and boxed your answer. please sho…
Remaining factors: $(x-5)(x+3)$ All zeros: $x=-3$, $x=5$, $x=6$ Fully factored polynomial: $g(x)=(x+3)(x-5)(x-6)$ ### Graph Notes: - The cubic polynomial has a positive leading co…
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3. if $f(x)=x^2 + 4x + 4$, then the domain of $y = \\frac{1}{f(x)}$ is …
B. $\{x|x eq -2, x \in \mathbb{R}\}$ --- ### Question 4
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sketch each the graph of each function. approximate each real zero, rel…
Real zeros: $x\approx-0.7$, $x\approx-1.8$ Relative maximum: $(0.3, 3.2)$ Relative minima: $(-1.7, -3.6)$, $(1.3, 1.7)$ (Graph: A quartic opening upwards, crossing the x-axis at t…
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mandy has a credit score of 450. which of the following judgments would…
A. She is a poor credit risk.
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3 multiple choice 5 points king kong wanted the people of skull island …
3. D. innovation 4. True
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7 multiple choice 10 points when a nation or individual concentrates it…
7. A. Specialization 8. B. False
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7 14 8 4 -16 ---- 68 2. 4 16 5 6 -18 ---- 38
Both subtraction problems are solved correctly. 1. $84 - 16 = 68$ 2. $56 - 18 = 38$
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activity 3 • distributed practice add. 1. \\begin{array}{r} 237 \\\\ + …
1. $1135$ 2. $1061$ 3. $1410$ 4. $1311$ 5. $1021$ 6. $751$
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select the correct answer. the function ( g(x) = x^2 ) is transformed t…
B. The graph of \( h \) is the graph of \( g \) horizontally shifted right 3 units.
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explain why the function is discontinuous at the given number a. (selec…
The correct option is: \( f(3) \) is defined and \( \lim_{x \to 3} f(x) \) is finite, but they are not equal.
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type the correct answer in each box. use numerals instead of words. wha…
\( h(x) = \boldsymbol{-2}(x + \boldsymbol{3})(x - \boldsymbol{1}) \)
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17 use the drawing tools to form the correct answer on the graph. draw …
- Axis of symmetry: Vertical line \( x = 2 \) - Vertex: \( (2, -9) \) - x - intercepts: \( (-1, 0) \), \( (5, 0) \) - y - intercept: \( (0, -5) \) (And draw the axis of symmetry \…
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d. they are not affiliated with a political party 18. which person is e…
18. A. A 40-year-old natural-born citizen who has lived in the U.S. for 14 years 19. C. 14 years 20. A. 8 years
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select the correct answer. what is the range of the function represente…
A. \( y \leq 1 \)
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explain why the function is discontinuous at the given number a. (selec…
- The correct option is: \( f(3) \) is defined and \( \lim_{x \to 3} f(x) \) is finite, but they are not equal.
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pretest: quadratic relationships options: a. x = 4 b. x = 3 c. x = 5 d.…
A. \(x = 4\)
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pretest: quadratic relationships which of the following statements is t…
B. The material’s temperature reaches a minimum at 15 hours.
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use the drawing tools to form the correct answer on the provided graph.…
The line is graphed by plotting the y - intercept \((0,1)\) and then using the slope \(-\frac{1}{3}\) to find another point (e.g., \((3,0)\)) and drawing a straight line through t…
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9) \\sec \\frac{\\pi}{2}
Undefined
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graph the line with the equation $y = 2x - 2$.
To graph \( y = 2x-2 \): 1. Plot the y - intercept \( (0,-2) \). 2. Use the slope \( m = 2 \) to find another point (e.g., from \( (0,-2) \), move up 2, right 1 to get \( (1,0) \)…
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what is the domain of this function? graph of a piece - wise linear fun…
All real numbers, or in interval notation \( (-\infty, \infty) \)
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graph the function. $y = 5(2)^x$ plot two points to graph the function.
Plot the points $(0, 5)$ and $(1, 10)$, then draw a smooth exponential curve through them.
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graph this function. $y = 0.5^x$ plot two points to graph the function.
Plot the points $(0, 1)$ and $(1, 0.5)$ (or $(-1, 2)$) on the grid, then draw a smooth decreasing curve that approaches the x-axis (y=0) as $x$ increases, and rises to infinity as…
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solve for x. \\(\\log_3 (4x - 19) = 4\\) \\(x = \\square\\)
$x = 25$
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select the correct answer. what is the domain of this function? $f(x) =…
C. \((-\infty, \infty)\)
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graph the function. y = 10(0.4)^x plot two points to graph the function.
Plot the points $(0, 10)$ and $(1, 4)$, then draw the exponential decay curve passing through them.
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graph the equation $y = 2x - 3$.
A straight line passing through the points $(0, -3)$ and $(1, -1)$ (and extended in both directions on the provided coordinate grid).
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graph the equation $y = -\frac{2}{3}x - 1$. next, identify the slope. s…
$-\frac{2}{3}$ --- For graphing context (additional clarification): The y-intercept is $-1$ (the point $(0, -1)$ already marked). To graph, from $(0, -1)$, move 2 units down and 3…
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graph the equation shown below by transforming the given graph of the p…
To graph \( y = 4x^2 \), we vertically stretch the parent function \( y = x^2 \) by a factor of 4. The vertex remains at \((0,0)\), and key points like \((-1,4)\), \((1,4)\), \((-…
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unit 7 mathspace 5. consider the following linear equations: equation 1…
| $x$ | $-3$ | $-2$ | $-1$ | $0$ | $1$ | $2$ | $3$ | |-----|------|------|------|-----|-----|-----|-----| | $y$ | $9$ | $7$ | $5$ | $3$ | $1$ | $-1$| $-3$|
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drag each label to the correct location on the table. match each econom…
- First scenario (Caribbean island): Hayek - Second scenario (bread price control): Keynes
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solution: 3. y = 2x + 4 2y = 2x + 4 (grid graph with x from -10 to 10, …
The solution to the system of equations is \(x = -2\), \(y = 0\) or the point \((-2, 0)\).
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here is a graph of a segment of $f(x) = x$. $g(x) = f(x - 5)$ graph $g$…
To graph \( g(x)=f(x - 5) \), we shift the graph of \( f(x)=x \) 5 units to the right. The endpoints of the segment of \( f(x) \) (e.g., \((-2, -2)\) and \((3, 3)\)) are shifted t…
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question 3 (1 point) which statement about opportunity cost is not true…
A. Opportunity cost is the financial value of the forgone opportunity ### Question 4
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equations learning target: i can solve systems of equations using the g…
The solution to the system is \( x = -3 \), \( y = 2 \) (or the ordered pair \((-3, 2)\))
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section 2.6 homework for quiz 2 question 11 of 11 (1 point) | question …
Undefined
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the graph of $y = g(x)$ is given. (a) find $g(4)$. (b) find $g(-3)$. (c…
\( 5 \)
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what division number sentence is represented by the model shown? option…
C. \(\boldsymbol{\frac{13}{4} \div \frac{3}{4}}\) (assuming the third option is labeled C; if the options are A, B, C, D with A: \(\frac{13}{4} \times \frac{3}{4}\), B: \(4 \div \…
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rebecca tries to find 436 - 271. rebecca breaks apart the numbers by pl…
Step 1
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find 897 - 635. 897 - 635 = 7
$262$
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find 967 - 713. 967 = 900 + 60 + 7 -713 = 700 + 10 + 3 200 + 50 + 4 967…
\(254\)
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what is 7/8 of 6? options: 5 1/4, 5 2/8, 4 10/8
5 1/4
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use the graph of the function to complete the table. | input | output |…
| input | output | |-------|--------| | 4 | 3 | | 5 | 6 | | 6 | 7 |
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read the story summary below, and think about author’s purpose. one of …
3. to express the idea that solutions to problems may come from a unexpected places
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read the story summary below, and think about author’s purpose. one of …
1. The photos and the flea market experience help resolve the conflict between Heather and her mother, so the story shows a novel solution to a common problem.
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here is a system of equations. \\begin{cases} y = 3x - 6 \\\\ y = x - 4…
The solution is $(1, -3)$ To graph: 1. For $y=3x-6$: plot the y-intercept $(0, -6)$, then use slope $3$ (rise 3, run 1) to plot a second point, then draw the line. 2. For $y=x-4$:…
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the following text is adapted from charles dickenss 1854 novel hard tim…
A. To emphasize the uniformity of both the town and the people who live there
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on painter william h. johnson’s return to the united states in 1938 aft…
A. It elaborates on the previous sentence's statement about a transitional moment in Johnson's artistic career.
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use inductive reasoning to predict the next three numbers in the patter…
768, -3072, 12288
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determine features of polynomial graph question the polynomial function…
The degree of \(f(x)\) is \(\boldsymbol{4}\) (even) and the leading coefficient is \(\boldsymbol{\text{negative}}\). There are \(\boldsymbol{2}\) different real zeros and \(\bolds…
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graph $f(x) = \\frac{3}{4}x + 2$. use the line tool and select two poin…
To graph \(f(x)=\frac{3}{4}x + 2\), use the points \((0,2)\) (y - intercept) and \((4,5)\) (found using slope \(\frac{3}{4}\)) and draw a line through them with the line tool.
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question the polynomial function $f(x)$ is graphed below. fill in the f…
The degree of \( f(x) \) is \(\boldsymbol{\text{even}}\) and the leading coefficient is \(\boldsymbol{\text{positive}}\). There are \(\boldsymbol{3}\) different real zeros and \(\…
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the polynomial function f(x) is graphed below. fill in the form below r…
The degree of $f(x)$ is $\boldsymbol{4}$ and the leading coefficient is $\boldsymbol{positive}$. There are $\boldsymbol{1}$ different real zeros and $\boldsymbol{2}$ relative mini…
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question the polynomial function $f(x)$ is graphed below. fill in the f…
The degree of \(f(x)\) is \(\text{odd}\) and the leading coefficient is \(\text{negative}\). There are \(\boldsymbol{3}\) different real zeros and \(\boldsymbol{2}\) relative maxi…
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given the function below, fill in the table of values, use the table of…
### Completed Table: | $x$ | $x+2$ | $y=2^{x+2}$ | |-----|-------|-------------| | $-4$ | $-2$ | $\frac{1}{4}$ | | $-3$ | $-1$ | $\frac{1}{2}$ | | $-2$ | $0$ | $1$ | | $-1$ | $1$ …
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given the function below, fill in the table of values, use the table of…
### Completed Table: | $x$ | $2^x$ | $y=2^x+4$ | |-----|-------|-----------| | $-2$ | $\frac{1}{4}$ | $\frac{17}{4}$ | | $-1$ | $\frac{1}{2}$ | $\frac{9}{2}$ | | $0$ | $1$ | $5$ |…
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use the calculator below to approximate \\(\\sqrt{32}\\) as a decimal t…
$\sqrt{32} \approx 5.66$
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the given figure shows a transformation of the graph of f(x)=|x|. write…
\( y = |x + 3| - 6 \) (Note: This is an example based on assumed vertex; the actual answer depends on the exact transformation shown in the figure.)
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question the polynomial function $f(x)$ is graphed below. fill in the f…
- The degree of \( f(x) \) is \( 5 \) (impar, pero el análisis del comportamiento final y extremos indica grado 5). - The leading coefficient is \( \text{positive} \). - There are…
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graph this function: y = |x| - 9 click to plot the vertex first.
The vertex of the function \( y = |x| - 9 \) is at \((0, -9)\). To graph the function, plot the vertex \((0, -9)\) first, then plot other points like \((1, -8)\), \((-1, -8)\), \(…
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function g can be thought of as a translated (shifted) version of $f(x)…
B. $g(x) = |x| + 5$
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solve the following system of equations graphically on the set of axes …
The solution is \((3,1)\) (the point of intersection of the two lines \(y = 3x - 8\) and \(y=-\frac{1}{3}x + 2\)).
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what is the range of the function $y = 4e^x$? all real numbers less tha…
all real numbers greater than 0
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if $f(x)=3x^2 + 12x + 9$, what are the coordinates of the vertex? a. $(…
c. (-2, -3)
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for the quadratic function $f(x)=x^2 - 10x + 25$, what is the $y$-coord…
b. 0
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given the quadratic function $f(x) = -4x^2 + 8x - 1$, what is the maxim…
c. 3
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the maximum value of the function $f(x) = -2x^2 + 4x + 5$ occurs at wha…
b. 7
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lessons 2.1-2.2 review & refresh complete the equation. identify the pr…
1. $8$, Propiedad conmutativa de la suma 2. $2$, Propiedad asociativa de la multiplicación 3. $1$, Elemento identidad de la multiplicación 4. $0$, Elemento identidad de la suma 5.…
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for what value of x is \\(\\cos(x) = \\sin(14^\\circ)\\), where \\(0^\\…
A. 76°
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lesson 8.6 extra practice subtract. 1. $5\\frac{1}{2} - 2\\frac{1}{4} =…
1. $3\frac{1}{4}$ 2. $2\frac{1}{6}$ 3. $3\frac{3}{4}$ 4. $\frac{7}{10}$ 5. $3\frac{1}{4}$ 6. $3\frac{7}{8}$ 7. $7\frac{17}{24}$ 8. $7\frac{1}{9}$ 9. $7\frac{13}{24}$ 10. $4\frac{1…
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lesson 8.5 extra practice add. 1. $3\\frac{1}{2} + 2\\frac{1}{4} = \\un…
1. $5\frac{3}{4}$ 2. $11\frac{1}{2}$ 3. $9\frac{1}{10}$ 4. $6\frac{7}{12}$ 5. $6\frac{5}{8}$ 6. $10\frac{3}{4}$ 7. $8\frac{5}{9}$ 8. $9\frac{5}{24}$ 9. $2\frac{17}{20}$ 10. $4\fra…
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write an equation of the line below. try again
\(y = -3x\)
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write an equation of the line below. your answer
\(y = 4x - 1\)
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what is the absolute value of 2? 0 2 -2 rewatch submit
$\boldsymbol{2}$ (the option with the value 2)
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what is the effect of replacing the graph of the function $f(x)=2x^2 + …
The graph of $f(x)$ shifts to the left by 5 units.
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practice: 9. identify the slope and y-intercept of $y = -3x + 7$.
Slope: $-3$ y-intercept: $7$ (or the point $(0, 7)$)
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what is the effect of replacing the graph of the function $f(x)=x^3 - 2…
The graph of $f(x)$ shifts down by 3 units.
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what does the transformation $f(x) \\mapsto 4f(x)$ do to the graph of $…
stretches it vertically