微积分
极限、导数、最优化与函数性质。
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tenth. if $g(x) = -4.78x + 24$, then $g(18) = \\underline{\\quad\\quad}$
$-62.0$
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find the domain of f(x). $f(x) = \\frac{3x - 6}{6x + 6}$
The domain of \( f(x) \) is all real numbers \( x \) such that \( x eq -1 \), or in interval notation, \( (-\infty, -1) \cup (-1, \infty) \).
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14. use synthetic division and the remainder theorem to evaluate $f(5)$…
For the synthetic division table: - The first empty box (under -7) is \( 5 \) - The second empty box (under -2) is \( -10 \) - The bottom row boxes are \( 1 \), \( -2 \), \( -12 \…
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perform the operation and simplify the answer fully. \\(dfrac{\frac{7}{…
$-\frac{7}{81}$
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graph the given line. give the domain and range.\\(-x + 2 = 0\\)\\(\\)\…
The equation \(-x + 2 = 0\) simplifies to \(x = 2\), which is a vertical line. - Domain: \(\{2\}\) (or \([2, 2]\) in interval notation) - Range: \((-\infty, \infty)\) (all real nu…
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divide. $-4\\frac{2}{5} \\div -0.5 = \\square$ submit
\(8.8\) (or \(\frac{44}{5}\) or \(8\frac{4}{5}\))
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question 1 find the vertex of the following quadratic function: $f(x) =…
B. (0.5, -12.5)
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question 8 what is the vertex of the function, f(x) = 2x² - 3x + 1? (0.…
(0.75, -0.125)
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which of the functions represents a translation from the graph of a par…
D. $g(x) = (x^2 - 4) + 2$
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class examples: write the slope - intercept form of the equation of eac…
1) This vertical line cannot be written in slope-intercept ($y=mx+b$) form. Its equation is $x=2$. 2) $y=\frac{3}{2}x - 2$
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use the graphing tool to graph the equation. what is the domain? select…
A. The range in interval notation is \((-\infty, \infty)\)
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3. if $f(x)=\\begin{cases}\\ln x & \\text{for } 0 < x \\leq 2 \\\\ x^2 …
E. nonexistent
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multiply $-3\\frac{2}{5} \\times 0.5 = \\square$
\(-1.7\) (or \(-\frac{17}{10}\) or \(-1\frac{7}{10}\))
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one-a-day multi vitamins #18 5-4-3-2-1 5 multiple choice: do one-a-day!…
C. 2.40
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use technology to find points and then graph the function $y = 2sqrt3{x…
Points to plot: (4, -2), (5, 0), (6, 2), (13, 4) (and graph the cube - root function transformed by vertical stretch and horizontal shift)
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|-6.3 × 5| - 5²
$6.5$
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graph the linear function f(x)=3x. identify if it is a constant functio…
s: - Is the function a constant function? No - Domain (interval notation): \( (-\infty, \infty) \) - Range (interval notation): \( (-\infty, \infty) \)
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graph the linear function ( f(x)=\frac{1}{2}x - 7 ). identify if it is …
- The function \( f(x)=\frac{1}{2}x - 7 \) is not a constant function. - Domain: \( (-\infty,\infty) \) - Range: \( (-\infty,\infty) \)
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graph the following linear function. give the domain and range. identif…
- Domain: \((-\infty,\infty)\) - Range: \((-\infty,\infty)\) - It is not a constant function.
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7. \\((-84 \\times 0.6)^2 + 6\\)
2546.16
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graph the following linear function. give the domain and range. identif…
A. The domain in interval notation is \((-\infty, \infty)\)
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6 × |−3.4 × 5.2|
106.08
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5. \\(\\frac{(-14 \\times 0.5)^{3}}{14}\\)
$-\frac{49}{2}$ or $-24.5$
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(b) y = blue box × red cross
\(y = x-6\)
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use the graph of ( f(x) = |x| ) to write an equation for each function …
\( y = -|x + 2| \) ### Part (b)
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for the line $y = 5x + 2$, (a) find the slope, and (b) sketch the graph…
A. The slope of the line is \(5\)
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171. graph y = 3x + 1
To graph \( y = 3x+1 \): 1. Plot the y - intercept at \( (0,1) \). 2. Use the slope \( m = 3 \) to find another point (e.g., from \( (0,1) \), move 1 unit right and 3 units up to …
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45. sketch a graph ( f(x) ) such that ( f(x) = 0 ) has the indicated nu…
s (Graph Descriptions): a. A 5th - degree polynomial (e.g., \( f(x)=(x + 2)(x + 1)x(x - 1)(x - 2) \)) crossing the \( x \)-axis 5 times. b. A 5th - degree polynomial (e.g., \( f(x…
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question fill out the table of values and select whether each function …
### For $f(x)=7x^3 + 5x^5$: | $x$ | $y$ | |-----|-----| | $-2$ | $-176$ | | $-1$ | $-12$ | | $0$ | $0$ | | $1$ | $12$ | | $2$ | $176$ | Classification: Odd ### For $f(x)=2|x| - 1$…
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use technology to find points and then graph the function $y = 2sqrt3{x…
To graph \( y = 2\sqrt[3]{x + 4} + 4 \), plot points like \((-4, 4)\), \((-3, 6)\), \((4, 8)\), and \((-5, 2)\) (or others calculated) on the coordinate plane.
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question the function $f(x)$ is defined below. what is the end behavior…
as \( x \to \infty,y \to -\infty \) and as \( x \to -\infty,y \to -\infty \) (the first option in the given choices)
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use technology to find points and then graph the function $y = -2\\sqrt…
The points to plot are (-3, 3), (-2, 1), (5, -1), (-11, 7) (and then graph the function using these points).
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question the function $f(x)$ is defined below. what is the end behavior…
as \( x \to -\infty \), \( f(x) \to \infty \) and as \( x \to \infty \), \( f(x) \to \infty \) (the third option in the list, which is "as \( x \to -\infty \), \( f(x) \to \infty …
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use technology to find points and then graph the function $y = 2sqrt3{x…
The points to plot are (-8, 1), (-1, 3), (0, 5), (1, 7), (8, 9) (and you can plot them on the given graph and then click "done plotting points").
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question use technology to find points and then graph the function $y =…
The points to plot are \((-8,3)\), \((-1,1)\), \((0, - 1)\), \((1,-3)\), \((8,-5)\). After plotting these points, draw the curve of the function \(y = - 2\sqrt[3]{x}-1\) through t…
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how many five - letter permutations can be formed from the first eight …
6720 permutations
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find the slope of the line satisfying the following conditions. horizon…
A. The slope is \( 0 \)
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what is the value of c, if a = 5 and b = 8, for the formula? $c = \\sqr…
$\sqrt{89}$ (or approximately 9.43)
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fractions with denominators of 10 & 100 find the sum. \\(\\frac{3}{10} …
38
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match the description with the correct response. a function that is not…
D. \( f(x)=x^{3}+2 \)
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choose the correct function/equation for the following description. a l…
A. \( f(x) = 5x \)
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choose the correct function/equation for the following description. \ta…
C. \( f(x) = -8 \)
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which trigonometric ratios are correct for triangle def? select three o…
The correct options are: - \( \sin(D) = \frac{24}{25} \) - \( \tan(D) = \frac{24}{7} \) - \( \sin(E) = \frac{7}{25} \)
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fill in the boxes to complete the equation. your final answer should be…
$4\frac{5}{8} + 2\frac{6}{8} = 6\frac{\boldsymbol{11}}{\boldsymbol{8}} = \boldsymbol{7}\frac{\boldsymbol{3}}{\boldsymbol{8}}$
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find the value of each expression. explain or show your reasoning. 7.35…
4.75
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(int_{0}^{8}\frac{dx}{sqrt{1 + x}})
$4\sqrt{2}$
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38) write a linear function f with the given values: $f(0) = 2,$ $f(3) …
\( f(x)=-x + 2 \) ### Problem 39:
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the movement of the progress bar may be uneven because questions can be…
The world faces a calamitous food crisis if we do not stop overfishing.
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the movement of the progress bar may be uneven because questions can be…
D. A hook (Note: Assuming the options are labeled A - D as per typical multiple - choice, with the last option being "A hook". If original options had "A hook" as an option, the c…
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government question 5 what term matches the definition below. an organi…
b. Political Party ### Question 6
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division – area model use the area model to answer the division questio…
s: - \( 258\div4 = 64 \) r\( 2 \) - \( 428\div2 = 214 \) - \( 372\div6 = 62 \) - \( 612\div6 = 102 \) - \( 735\div5 = 147 \)
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etermine the vertex form and the maximum or minimum value of the functi…
D. \( f(x) = 2(x + 2)^2 - 5 \), the minimum value of \( f \) is \( -5 \)
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graph the systems of equations below, then place a point indicating the…
The solution to the system of equations is the point \( (4, - 3) \)
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2. find the first 3 iterates of the function $f(x) = -2x + 3$ when $x_0…
3, -3, 9
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⑤ 41.6 ÷ 6.5 = 6.45 × 2.7 =
$41.6 \div 6.5 = 6.4$ $6.45 \times 2.7 = 17.415$
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notes: pour écrire l’équation d’une fonction linéaire, nous devons conn…
L'équation de la fonction linéaire est $y=-3x + 17$
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notes: pour écrire l’équation d’une fonction linéaire, nous devons conn…
The equation of the line in slope - intercept form is \(y = 3x+5\)
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divide. 4.67 ÷ 100
0.0467
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try again one of the digits in your answer is wrong. check your work ca…
0.0786
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divide: 76.6 ÷ 1000
\(0.0766\)
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√(5x) + 2y when x = 5 and y = -2
$1$
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graph the equation $y = \\frac{1}{2}x + 3$
The graph is a straight line passing through points $(0, 3)$ and $(2, 4)$, with a slope of $\frac{1}{2}$ and y-intercept at $(0, 3)$.
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graph the equation $y = \\frac{1}{3}x - 2$. next, identify the slope. s…
$\frac{1}{3}$
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graph the equation $y = \\frac{1}{3}x - 2$. first, identify the $y$-int…
$-2$
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felipe and trevon used the equation $y = 2 \\cdot 1.5^x$, but it didnt …
Trevon
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find f+g, f−g, fg, and \\(\\frac{f}{g}\\). determine the domain for eac…
1. $f+g = 5x^2+x+6$, Domain: $(-\infty, \infty)$ 2. $f-g = -5x^2+x+6$, Domain: $(-\infty, \infty)$ 3. $fg = 5x^3+30x^2$, Domain: $(-\infty, \infty)$ 4. $\frac{f}{g} = \frac{x+6}{5…
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Question was provided via image upload.
B. The domain of $\frac{f}{g}$ is $(-\infty,-7) \cup (-7,6) \cup (6,\infty)$.
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solve the system by graphing: \\(\\begin{cases} x + y = 4 \\\\ -x + y =…
The solution of the system is \(x=\frac{3}{2},y=\frac{5}{2}\) (or \((\frac{3}{2},\frac{5}{2})\))
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graph the equation using the slope and the y - intercept. ( y = \frac{6…
D. <The graph with a positive slope rising from left to right, crossing the y-axis at (0,5)>
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write an equation in slope-intercept form of the line passing through t…
$x=8$
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which best describes the economies in newly independent countries? ○ ad…
C. limited industrialization (assuming the options are labeled A to D with C being "limited industrialization")
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valuate the expression. 0.4 ÷ 2 - 0.6 + 0.7 write your answer as an int
\(0.3\)
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peyton steers a remote - control car. the equation $y = 3x + 4$ can be …
Plot the point at the coordinates $(0, 4)$ (on the vertical axis, 4 units above the origin).
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5 solve the system of linear equations by graphing. (3 pts) ( x + 3y = …
The solution to the system of linear equations is \(x = 3,y = 1\) or the ordered pair \((3,1)\).
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x + 3y = 0\ 4x - 6y = 0
The solution of the system of equations is \(x = 0,y = 0\) (the solution is the point \((0,0)\)).
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evaluate the expression. -0.7 + 0.9 + -0.4 × 0.5 write your answer as a…
\(0\)
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4 directions - solve the system by graphing. \\(\\begin{cases}\\text{li…
The solution to the system is $(3, -2)$ (the point where the two lines intersect when graphed).
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subtract: \\frac{7}{8} - \\frac{5}{12} write your answer as a fraction …
$\frac{11}{24}$
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12. graph: $y = \\frac{3}{2}x$
To graph \( y=\frac{3}{2}x \): 1. Recognize it is a linear function with \( y \)-intercept \( (0,0) \) and slope \( \frac{3}{2} \). 2. Plot the point \( (0,0) \). 3. Use the slope…
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evaluate the expression, -0.13 + (-0.4 - -1.2)² write your answer as an…
\(0.51\)
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evaluate the expression. \\(\frac{3}{4} + \frac{2}{5} div \frac{2}{3} \…
$\frac{21}{20}$
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practice mixed number addition and subtraction match the equivalent sub…
To solve this, we need to find a common denominator for each pair of mixed numbers and rewrite them, then match with the equivalent expression. ### For \( 3\frac{5}{6} - 1\frac{3}…
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u4:05: unit 4 test what is a linear equation? 0 / 10000 word limit
A linear equation is an algebraic equation where the variables are raised to the first power (degree 1) and, when graphed (for equations with two or more variables), represents a …
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Question was provided via image upload.
1. factoring 2. volumes (or 3D measurements) 3. perfect cubes 4. algebra (or calculus/advanced math topics) 5. product
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what is the range of f? choose 1 answer: a $-3 leq f(x) leq 7$ b the $f…
A. \(-3\leq f(x)\leq7\)
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evaluate functions google classroom microsoft teams k(t) = 13t - 2 k(3)…
\( 37 \)
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evaluate the expression. 0.6 - 0.4 ÷ 2 write your answer as an integer …
0.4
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solve the system of equations graphed on the coordinate axes below. $y …
$(0, -1)$
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fill in the table using this function rul\\(y = -10x + 2\\)\\(\\begin{a…
当\(x = -5\)时，\(y = 52\)；当\(x = -1\)时，\(y = 12\)；当\(x = 0\)时，\(y = 2\)；当\(x = 1\)时，\(y = -8\)。 表格填写如下： | \(x\) | \(y\) | | ---- | ---- | | \(-5\) | \(52\) | | \(-1\) | \(12\) | | \…
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5-3 graphing radical functions (lms graded) write the function that des…
$\boldsymbol{\sqrt{x+4}-3}$
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describe the behavior of the graph at the x-intercepts for the function…
The x - intercepts of the function \(f(x)=(2x - 7)^{7}(x + 3)^{4}\) are \(x=\frac{7}{2}\) and \(x = - 3\). - At \(x=\frac{7}{2}\), since the exponent of the factor \((2x - 7)\) is…
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what is the value of \\(\\log_{7} 343\\)? \\(-\\frac{1}{3}\\)\\(-3\\)\\…
3
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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 tables display two functions: ( f(x) ) and ( g(x) ). function ( g(x…
The transforming function \( g(x)=-0.5x \) (or in the form \( y = A\times f(x)+D \), \( A=-0.5 \), \( D = 0 \))
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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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on a piece of paper, graph $y < -\frac{2}{5}x + 1$. then determine whic…
C. Graph C
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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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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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find the value of \\(\\sqrt3{-1000}\\).
\(-10\)
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what is the y - value of this function when x = 2?
-6