微積分
極限、導関数、最適化、関数挙動。
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use the drawing tool(s) to form the correct answer on the provided grap…
The composite function is $g(f(x)) = -x + 3$. To graph it: 1. Plot the y-intercept point $(0, 3)$ 2. Plot the x-intercept point $(3, 0)$ 3. Draw a straight line connecting these t…
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2. what is the result of limited culture contact? a. fewer marriages an…
C. Fewer ideas are shared, and people learn less
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n(x) = \\frac{1}{4}x^2 - 2x + 4 what is the value of n(m(4))? \\circ -4…
0
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the magna carta this passage includes selected clauses of the magna car…
B. Both passages are concerned with the rights all individuals have. (Assuming the option label; adjust if the original has different identifiers, but the reasoning confirms this …
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the function $y = f(x)$ is graphed below. what is the average rate of c…
2
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determine the appropriate key features for each function. for each func…
- $y=2\sqrt[3]{x+3}-2$: End behavior: as $x \to \infty, f(x) \to \infty$ and as $x \to -\infty, f(x) \to -\infty$ - $y=-4\sqrt[3]{x-1}$: Cube root with turning point at $(1,0)$ - …
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type the correct answer in the box. use numerals instead of words. cons…
The value of $m(n(2))$ is 1 The value of $n(m(1))$ is 2.25
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type the correct answer in the box. use numerals instead of words. cons…
1
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type the correct answer in the box. use numerals instead of words. cons…
The value of $m(n(2))$ is 2 The value of $n(m(1))$ is 1
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fill in the table using this function rule. y = 3x + 3 x | y 4 | 6 | 7 …
When x = 4, y = 15; when x = 6, y = 21; when x = 7, y = 24; when x = 8, y = 27. So the completed table is: | x | y | |---|---| | 4 | 15 | | 6 | 21 | | 7 | 24 | | 8 | 27 |
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x | f(x) -1 | \\(\\frac{1}{2}\\) 0 | 1 1 | 2 2 | 4 the value of \\((f \…
The value of $(f\circ g)(4)$ is $\boldsymbol{4}$. When $(g\circ f)(x)=1$, the value of $x$ is $\boldsymbol{0}$.
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evaluate the following. $2.1^{2} \\div 7 + 0.6 \\times 16.4$
10.47
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evaluate the following. $(16 - 14.6)^2 + 69.5 \\div 0.5$
140.96
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evaluate the following. 7.365 - 0.8 × 1.6²
5.317
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what is the domain and range of the function below? the domain is the r…
The domain is $\boldsymbol{\{x \mid x \in \mathbb{R}\}}$ The range is $\boldsymbol{\{y \mid y \geq -3\}}$
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the equation (-16x^2 + 10x + 15 = y) represents the height (y) in feet,…
a. 0.97 seconds b. 0 seconds, 0.63 seconds
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solve the equation by factoring, using tables, or by graphing $2x^2 + 3…
$x \approx 1.39, x \approx -2.89$
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your networking contact list should be limited to family members. pleas…
F
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solve the equation by graphing the related function $x^2 - 4 = 0$ selec…
A. The solution(s) is/are x = -2, 2
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use the graph of f(x) to find the x - intercepts of the graph and the z…
$(-1, 0)$, $(5, 0)$
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find the slope of the given line, if it is defined. the line through (0…
\( \frac{3}{2} \)
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sketch the graph of the equation. $y = \\sqrt{x + 4}$ choose the correc…
C
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8-44. match each rule below with its corresponding graph. can you do th…
a. $y = -x^2 - 2$ matches Graph 2 b. $y = x^2 - 2$ matches Graph 3 c. $y = -x^2 + 2$ matches Graph 1
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question move at least one of the 5 guide points below to complete the …
1. Shift the blue vertex point to $(0, 5)$ 2. Move the red point at $(1,1)$ to $(1,10)$ 3. Move the red point at $(-1,1)$ to $(-1,10)$ 4. Move the red point at $(2,4)$ to $(2,25)$…
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claims and arguments during the 20th century, widespread access to auto…
B. 76.6% of commuters drive alone to work, limiting their opportunities for spontaneous or planned social interactions.
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evaluate. 3 + 9 × 10 = \\square
93
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evaluate the expression. do not round your answer. \\(dfrac{17}{6^2} - …
\(\frac{1}{3}\)
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evaluate.\\( \\frac{12 + 6}{3} = \\square \\)
6
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evaluate the expression. do not round your answer. \\(\\frac{1}{5}(27 -…
\(4\)
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order of operations with fractions and expon ccss.math: 6.ee.a.1, 6.ee.…
\(85\)
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evaluate the expression. do not round your answer. \\(\\frac{1}{4}(3 + …
20
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the graph below is the function $f(x)$ find $limlimits_{x\\to -1^-} f(x…
s: $\lim_{x \to -1^-} f(x)=\boldsymbol{1}$ $\lim_{x \to -1^+} f(x)=\boldsymbol{-2}$ $\lim_{x \to -1} f(x)$: Does not exist $f(-1)=\boldsymbol{4}$
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the graph below is the function $f(x)$ find $limlimits_{x \\to -1^{-}} …
# Explanation: ## Step1: Analyze left - hand limit as \(x ightarrow - 1^{-}\) As \(x\) approaches \(-1\) from the left (values of \(x\) less than \(-1\)), we look at the part of t…
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solving systems of equations by graphing step 1. write the equations in…
s 1. The solution to \( y=-x + 3 \) and \( y=x - 5 \) is \( x = 4,y=-1 \) or the ordered pair \( (4,-1) \). 2. The solution to \( y = 2x+1 \) and \( y=x + 3 \) is \( x = 2,y=5 \) …
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4. $f(x) = 5sqrt4{x} + 1, g(x) = -3sqrt4{x} - 2; x = 1$
\( 1 \)
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4. $f(x) = 5sqrt4{x} + 1, g(x) = -3sqrt4{x} - 2; x = 1$
\(\boldsymbol{1}\)
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in exercises 1–4, find ((f + g)(x)) and ((f - g)(x)) then evaluate (f +…
1. $(f+g)(x) = 4\sqrt[3]{x}$, $(f-g)(x) = -5\sqrt[3]{x}$; $(f+g)(-1000) = -40$, $(f-g)(-1000) = 50$ 2. $(f+g)(x) = -4x^2+3x+8$, $(f-g)(x) = 2x^2-9x+8$; $(f+g)(-1) = 1$, $(f-g)(-1)…
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4. ( f(x) = 5sqrt4{x} + 1, g(x) = -3sqrt4{x} - 2; x = 1 )
If evaluating \( f(1)+g(1) \), the answer is \( \boldsymbol{1} \). (If the problem was different, adjust based on full context, but with given info, this is a common solution path…
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4. f(x) = 5\\sqrt4{x} + 1, g(x) = -3\\sqrt4{x} - 2; x = 1
If evaluating \( f(1) \): \( \boldsymbol{6} \) If evaluating \( g(1) \): \( \boldsymbol{-5} \) If evaluating \( f(1)+g(1) \): \( \boldsymbol{1} \) If evaluating \( f(1)-g(1) \): \…
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4. $f(x) = 5sqrt4{x} + 1$, $g(x) = -3sqrt4{x} - 2$; $x = 1$
If we assume the problem is to find \( f(1) + g(1) \), the answer is \( \boldsymbol{1} \). If it's to find \( f(1) \), it's \( 6 \); for \( g(1) \), it's \( -5 \). Based on common…
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find an equation of the line containing the given pair of points. (-4,0…
$y=\frac{3}{4}x+3$
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find the slope - intercept form for the line satisfying the conditions.…
$y = 4x + 5$
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6) \\overline{6\\big)5,556} \ 9) \\overline{\\frac{8}{4\\big)3,254}}
1. $926$ 2. $813.5$
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create your own examples and non - examples of functions for each repre…
### 1. Set of Ordered Pairs (Examples and Non - Examples) #### Examples (Function) A function is a relation where each input (first element of the ordered pair) has exactly one ou…
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if f(x) = 6x² − x³, find f’(1) and use it to find an equation of the ta…
The equation of the tangent line is \( y = 9x-4 \)
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a = b = equation:
\( a = 1 \) \( b = 2 \) Equation: \( y = 2^x \)
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exponential fun graphic organ y = 4(\\frac{2}{3})^x a = \\underline{\\q…
\( a = 4 \) \( b=\frac{2}{3} \) Growth or Decay? Decay
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write a slope - intercept equation for a line with the given characteri…
$y = -8.1x + \frac{2}{5}$ (or $y = -8.1x + 0.4$)
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fill out the table of values and select whether each function is odd, e…
(Tables and Odd/Even): - For \( f(x)=\tan x \): Table as above, Odd. - For \( f(x)=\sin x - 3 \): Table as above, Neither. - For \( f(x)=|x| - 4 \): Table as above, Even.
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for each equation. part a - identify the y-intercept part b - identify …
1a. The y-intercept is $-3$ 1b. The slope is $\frac{1}{2}$
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solve the system by graphing \\(\\begin{cases} 5x + 3y = 15 \\\\ 10x = …
B. There are infinitely many solutions. The solution set is \(\{(x,y)\mid5x + 3y=15\}\) or \(\{(x,y)\mid10x=-6y + 30\}\).
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11 $y = 2x - 4$ (table with x and y values, graph) 6 $y = -x + 9$ (tabl…
For \( x = 1 \), \( y = 8 \); for \( x = 3 \), \( y = 6 \); for \( x = 5 \), \( y = 4 \); for \( x = 8 \), \( y = 1 \). ### Problem 8: \( y = -\frac{1}{4}x + 2 \)
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5 ( y = -3x + 5 ) | ( x ) | ( y ) | | --- | --- | | -1 | | | 1 | | | 3 …
### Problem 5: \( y = -3x + 5 \) #### Step 1: Calculate \( y \) when \( x = -1 \) Substitute \( x = -1 \) into the equation: \( y = -3(-1) + 5 = 3 + 5 = 8 \) #### Step 2: Calculat…
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3. write the quadratic equation that models the restaurants profit in v…
The standard form of the quadratic equation is \( y = -\frac{1}{2}x^2 + 30x \)
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3. $f(x) = 4x^3 + 12$, $g(x) = 2x^2 - 3x^3 + 9$; $x = 2$
(for \( f(2) \)): \( 44 \)
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problem. 4 : find the derivative of the function using the definition o…
\((0,\infty)\)
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2 ( y = -x ) x | y -5 | -2 | 0 | 3 | 4 ( y = 2x - 4 ) x | y -2 | 3 | 5 …
The completed table for \( y = -x \) is: | \( x \) | \( y \) | | ---- | ---- | | -5 | 5 | | -2 | 2 | | 0 | 0 | | 3 | -3 | ### Problem 4: \( y = 2x - 4 \)
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3 ( y = -4x ) | ( x ) | ( y ) | | --- | --- | | -2 | | | -1 | | | 0 | |…
For \( x = -2 \), \( y = 8 \); for \( x = -1 \), \( y = 4 \); for \( x = 0 \), \( y = 0 \); for \( x = 2 \), \( y = -8 \) Filling the table: | \( x \) | \( y \) | | ---- | ---- | …
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problem. 3 : find the derivative of the function using the definition o…
\((-\infty, \infty)\)
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problem. 3 : find the derivative of the function using the definition o…
\( (-\infty, \infty) \) ### Problem 4.1
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7. \\(y = 2x + 3\\)\\(y = -2x + 15\\)
$x=3$, $y=9$
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2. if $g(x)=2(5)^x$, which of the following is the value of $g(-3)$? (1…
(4) \(\frac{2}{125}\)
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plot the given parabola on the axes. plot the roots, the vertex and two…
- Roots: \( (-7, 0) \), \( (5, 0) \) - Vertex: \( (-1, 36) \) - Two other points: \( (0, 35) \), \( (1, 32) \) (or similar valid points) (Plot these on the coordinate axes with ap…
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write the point - slope form of the equation of the line satisfying eac…
The point - slope form of the equation is \(y + 6=-\frac{2}{3}(x - 9)\) The slope - intercept form of the equation written in function notation is \(f(x)=-\frac{2}{3}x\)
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name 5.5 notetaking with vocabulary (continued) extra practice in exerc…
Let's solve problem 3: \( f(x) = 4x^3 + 12 \), \( g(x) = 2x^2 - 3x^3 + 9 \); \( x = 2 \) ### Step 1: Find \( (f + g)(x) \) To find \( (f + g)(x) \), we add the two functions \( f(…
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7. \\( y = 2x + 3 \\)\\( y = -2x + 15 \\)
$x=3$, $y=9$
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question 15 of 20 what was the motivation behind the truman doctrine du…
D. To limit the spread of communism by supporting any country fighting for independence
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problem. 1 : find each interval over which $f(x) = \\frac{10}{(x + 8)^2…
\((-\infty, - 8)\cup(-8, \infty)\) ### Problem 2
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1. the graph on the coordinate plane represents the given system. verif…
The ordered pair \((-2,5)\) satisfies both equations \(y = - 2x+1\) and \(y=\frac{1}{2}x + 6\) because when \(x=-2\) and \(y = 5\) are substituted into each equation, the left - h…
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6 mark for review the functions ( f ) and ( g ) are given by ( f(x) = 2…
D. The graph of \(g\) is a horizontal translation of the graph of \(f\) by \(-a\) units
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5.6.2 test (cst): globalization and the world today number of deaths pe…
A. Developed areas have been better able to prevent the spread and limit the effects of the disease.
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the function ( f ) is given by ( f(x) = 3^x ). the function ( g ) is gi…
C. The graph of g is a combination of a vertical dilation of the graph of f and a reflection over the x - axis.
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1. the graph on the coordinate plane represents the given system. verif…
Since the ordered pair \((-2,6)\) satisfies both equations \(y=-2x + 2\) and \(y=\frac{1}{2}x+7\), it is a solution to the system of equations.
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the function ( f ) is given by ( f(x) = 2^x ), and the function ( g ) i…
B. A horizontal translation to the right 3 units
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let ( h(x) = f(x) cdot g(x) ), and ( k(x) = \frac{f(x)}{g(x)} ). use th…
A. $h'(-3)=4$ B. $k'(3)=\frac{1}{2}$
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the function ( f ) is given by ( f(x) = 2^x ), and the function ( g ) i…
B. A horizontal translation to the right 3 units
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write the quadratic function in standard form. $g(x) = x^2 - 8x$ $g(x) …
\(g(x)=(x - 4)^{2}-16\)
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evaluate the integral (int x^{7}(x^{8}-4)^{44}dx,) by making the approp…
$u = x^8 - 4$ $\frac{(x^8 - 4)^{45}}{360} + C$
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problem. 4 : the position function of a ball thrown into the air with a…
\(-105\)
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evaluate the integral \\(\\int \\frac{dx}{(6x + 10)^3}\\), by making th…
Appropriate substitution: $u = 6x + 10$ Integral result: $\boldsymbol{-\frac{1}{12(6x+10)^2} + C}$ (where $C$ is the constant of integration)
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7. 23×59.8 =
1375.4
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problem. 4 : the position function of a ball thrown into the air with a…
\( -16h - 105 \) ### Problem 5
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evaluate the indefinite integral.\\(\\int \\frac{2}{(t + 12)^8} dt\\)\\…
$-\frac{2}{7(t+12)^7}$
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problem. 1 : find the derivative of the function using the definition o…
\((-\infty, \infty)\)
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evaluate the indefinite integral.\\(\\int x^3 \\sqrt{5 + x^4} dx\\)\\(\…
$\frac{1}{6}(5 + x^4)^{\frac{3}{2}}$
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problem. 1 : find the derivative of the function using the definition o…
The domain of the function \( f(x)=-6x - 9 \) in interval notation is \( (-\infty, \infty) \). So the first box should be filled with \( -\infty \) and the second box should be fi…
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problem. 1 : find the derivative of the function using the definition o…
\( -6 \) ### Problem 2
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exercises 1.5 substitution score: 100/170 answered: 10/17 question 14 e…
$\frac{9}{4}\sin^4 x + C$
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find the slope of the line graphed below.
$\frac{-5}{4}$
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question 2 the graph of a function $f(x)$ is shown below. graph of a fu…
To determine the graph of \( f'(x) \) from the graph of \( f(x) \), we analyze the **slope** (derivative) of \( f(x) \) at different points: ### Step 1: Analyze Intervals of Incre…
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question 1 the graph of a function \\( f(x) \\) is shown below: for how…
4
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the graph of a function $f(x)$ is shown below. which of the following c…
The second option (the graph with the wave - like curve symmetric about the origin, the one in the middle of the four options)
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find the slope of the line graphed below.
$\frac{3}{7}$
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question 3 suppose a particle moves along the ( x )-axis and that its p…
3 (corresponding to the option with value 3)
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the graph of a function $f(x)$ is shown below: for how many values of $…
4
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integrate \\(\\int_{-2}^{2} 21(3x + 2)^{6} dx\\) answer =
2113536
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complete the table and then graph the function. $y = \\frac{1}{3}x$ | x…
The completed table is: | \( x \) | \( y \) | | ---- | ---- | | 0 | 0 | | 3 | 1 | | 6 | 2 | | 9 | 3 | (For graphing, plot the points \((0,0)\), \((3,1)\), \((6,2)\), \((9,3)\) and…
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homework 12 (6.10) graphical analysis the graph of ( h(x) ) is defined …
1. $(-5, 2)$ 2. $x=2$ 3. $-4$ 4. $x=-2, 2, 5$ 5. $(-2, 5) \cup (5, 7)$ 6. $x=-2, 5$ 7. $(-5, -2)$ 8. $(-2, 2)$ 9. $(2, 7)$
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y = \\frac{1}{2}x + 4\ click to select points on the graph.
The y - values in the table (6 for x = 4, 7 for x = 6, 9 for x = 10) are correct according to the equation \( y=\frac{1}{2}x + 4 \).
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i) complete the table and then graph the function. $y = \\frac{1}{2}x +…
For \( x = 4 \), \( y = 6 \); for \( x = 6 \), \( y = 7 \); for \( x = 10 \), \( y = 9 \) The completed table is: | \( x \) | \( y \) | | ---- | ---- | | 4 | 6 | | 6 | 7 | | 10 | …