微積分
極限、導関数、最適化、関数挙動。
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the functions u and w are defined as follows.\\(u(x) = 2x - 2\\)\\(w(x)…
$-130$
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the graph of $y = -(x - 4)(x + 2)$ is shown in the $xy$-plane. which of…
A. \( x \)-intercept(s)
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at a gas station, the price of gas is 4 dollars per gallon. the graph b…
4
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8. the reciprocal of 1 is 1 and the reciprocal of -1 is -1. thus, the p…
The graph of \(g(x)=\frac{1}{x + 3}\) has a vertical asymptote at \(x=-3\), a horizontal asymptote at \(y = 0\), passes through \((-2,1)\) and \((-4,-1)\). The right - hand branch…
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read carefully and choose the name of the student who made the correct …
Alejandro ### For the justification part:
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7. sketch the graph of the function $f(x) = |x|$.
The graph of \(f(x)=\vert x\vert\) is a V - shaped graph with vertex at \((0,0)\), the right - hand branch (for \(x\geq0\)) is the line \(y = x\) and the left - hand branch (for \…
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diego is painting the walls of his house. he paints 8 square meters eve…
Horizontal distance (bottom box): 3 Vertical distance (top box): 24 Slope of the line: 8
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details lesson 7.2 - log vs exponent conversions completed notes (comin…
$\frac{1}{125}$
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7. target value: 29 $12\\times2^2 - 18.4\\div0.6$ 8. target value: 23 $…
1. For expression $12 \times 2^2 - 18.4 + 0.6$: $30.2$ (does not match target 29) 2. For expression $5^2 - 0.2 \times 8 + 12 \times \frac{1}{2}$: $29.4$ (does not match target 23)…
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details lesson 7.2 - log vs exponent conversions completed notes (comin…
s: a) \(\log_{2}\frac{1}{4}=-2\) b) \(\log420 = x\) (or \(\log_{10}420=x\)) c) \(\ln x = 5\)
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10. 4.67 ÷ 0.001 =
4670
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express each equation in logarithmic form. (a) $e^x = 7$ is equivalent …
(a) \(\ln(7)=x\) (or \(x = \ln(7)\)) (b) \(\ln(x)=8\) (or \(8=\ln(x)\))
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lesson 7.2 - log vs exponent conversions completed notes (coming soon) …
a) $4^{-2}=\frac{1}{16}$ b) $10^x = 338$ c) $e^4 = x$
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2) $y = -x + 2$
The line $y=-x+2$ is graphed by plotting the points $(0, 2)$, $(2, 0)$, and $(1, 1)$, then drawing a straight line passing through all three points.
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rewrite the following in exponential form: a) \\(\\log_{4}\\left(\\frac…
\(4^{-1}=\frac{1}{4}\) ### Part (b)
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7.1 hw - guess the exponent score: 5.67/12 answered: 6/12 question 7 ev…
\(\frac{1}{2}\)
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find the exact value of the following logarithmic expression. \\(\\log_…
11
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1. find the equation of the line that passes through the point (5, -2) …
The equation of the line is \( y=-\frac{1}{3}x-\frac{1}{3} \) (or \( x + 3y=-1 \))
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create a table of values to show that the exponential expression 3(2)^x…
The table of values is: | \( x \) | \( 3x^2 + 2x \) | \( 3(2)^x \) | |--------|----------------|-------------| | 0 | 0 | 3 | | 1 | 5 | 6 | | 2 | 16 | 12 | | 3 | 33 | 24 | | 4 | 56…
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2. an equation is shown. ( y = 3|x + 2| - 6 ) use the coordinate grid t…
The graph of \( y = 3|x + 2| - 6 \) is a V - shaped graph with vertex at \((-2, -6)\), right branch passing through points like \((-1, -3)\), \((0, 0)\) etc. (with slope \( 3 \)) …
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divide. write the quotient in simplified form. $-\frac{11}{12} \\div 22…
\(-\frac{1}{24}\) (and the correct choice is A)
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which of the functions shown is the graph of $y = -(x + 1)^3$?
\( A(x) \) (the graph labeled \( A(x) \))
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which of the functions shown is the graph of y = x³ + 3?
The function \( A(x) \) (the pink - colored graph) is the graph of \( y = x^3+3 \).
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multiply. write the product in simplest form $-\frac{4}{7} cdot \frac{2…
\( -\frac{8}{77} \)
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the functions s and t are defined as follows. s(x)=2x+2 t(x)=-2x² -2 fi…
$-38$
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unit 7 review: cube & cube root which of the functions shown is the gra…
\( C(x) \)
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if you stretch your own canvases, you can get stretcher bars in just ab…
8. 16 9. First, you use your ruler to make a small mark at every inch at the top of the paper. Next, you place the ruler at the bottom and make a small mark at every inch. Followi…
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$-\frac{3}{11}+\frac{5}{7}=square$
\(\frac{34}{77}\)
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add. \\frac{2}{3}+\\left(-\\frac{5}{9}\ ight)
$\frac{1}{9}$
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which of the following radical functions has a domain of $x \\geq -2$ a…
C. \(h(x)=-\sqrt{x + 2}+3\)
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select the radical function with a domain of $x\\geq -2$. a. $a(x) = 3\…
C. \(C(x)=\sqrt[4]{x + 2}+10\)
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select all the radical functions with a range that includes all real nu…
A. \(A(x)=2\sqrt[3]{x + 4}\), D. \(D(x)=\sqrt[7]{2x}-8\)
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221÷13 =? \\square ÷13 = \\square
$221 \div 13 = 17$ $\boldsymbol{221} \div 13 = \boldsymbol{17}$
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5. find the inverse of $f(x) = -\frac{2x + 1}{3}$ rewrite as y = switch…
$f^{-1}(x) = \frac{-3x -1}{2}$
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a student says: we cannot subtract 1.97 from 20 because 20 does not hav…
No
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1. \\(\\begin{array}{r}5 \\\\ \\times 0.35\\end{array}\\) 2. \\(\\begin…
1. $1.75$ 2. $13$ 3. $0.07725$ 4. $102.9054$ 5. $0.00214$ 6. $0.72$ 7. $1.7$ 8. $5.72$
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write 9.6 as a mixed number and as an improper fraction. do not try to …
mixed number: $9\frac{6}{10}$ improper fraction: $\frac{96}{10}$
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104÷4=? type a helper equation to divide the problem into friend blank …
Helper equation: $100\div4 + 4\div4 = 25 + 1$ Final result: $26$
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write 8.56 as a mixed number and as an improper fraction. do not try to…
mixed number: $8\frac{56}{100}$ improper fraction: $\frac{856}{100}$
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504÷18=? □ ÷18=□
Helper equation: $504 \div 9 \div 2 = 28$ Final result: $28$
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type a helper equation to divide the problem into frie 247÷13=? \\squar…
Helper equation: $130 \div 13 = 10$ Final answer: $19$
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how does the graph of $y = 3^x$ compare to the graph of $y = 3^{-x}$? t…
The graphs are reflected across the \( y \)-axis.
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identifying domain and range of exponential fun identify the domain and…
The domain of this function is all real numbers (in interval notation, \( (-\infty, \infty) \)). The range of this function is all positive real numbers (in interval notation, \( …
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ying asymptotes of exponential functions identify the horizontal asympt…
\( y = -3 \) (corresponding to the option \( y=-3 \))
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in 4 - 6, evaluate each expression. 4. $5^2 - 9 \\div 3$ 5. $8 + 6 - 2 …
4. 22 5. 1 6. 2
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ying asymptotes of exponential functions identify the horizontal asympt…
\( y = 0 \)
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the function $f(x)$ is graphed below. write the domain and range using …
Domain: \(-\infty < x<\infty\) Range: \(y\leq8\) (or \(-\infty < y\leq8\))
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the function $f(x)$ is graphed below. write the domain and range using …
Domain: \( -\infty < x < \infty \) Range: \( -\infty < y \leq 5 \)
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om 5.1, 5.2, 5.3 score: 7/14 answered: 3/7 question 4 graph the followi…
\((-3, -1)\)
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given the function below, fill in at least 3 rows of the table of value…
| $x$ | $\frac{7}{4}x$ | $y=\frac{7}{4}x+2$ | |-----|----------------|---------------------| | $-4$ | $-7$ | $-5$ | | $0$ | $0$ | $2$ | | $4$ | $7$ | $9$ | *(Note: These 3 rows sa…
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erstanding graphs of exponential functions the graph of $y = b^x$ is sh…
\(\frac{1}{2}\)
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answers must be written as fractions in simplest form, but you only nee…
| $x$ | $\frac{1}{2}x$ | $y=\frac{1}{2}x-5$ | |-----|----------------|---------------------| | $-4$ | $-2$ | $-7$ | | $0$ | $0$ | $-5$ | | $2$ | $1$ | $-4$ |
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identifying domain and range of exponential functions identify the doma…
The domain of this function is all real numbers (or \(\mathbb{R}\) or \((-\infty,\infty)\)). The range of this function is \((3,\infty)\).
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divide. write your answer in sim\\(\\frac{6}{5} \\div \\frac{7}{6}\\)
$\frac{36}{35}$ or $1\frac{1}{35}$
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given the function below, fill in at least 3 rows of the table of value…
| $x$ | $-\frac{1}{4}x$ | $y = -\frac{1}{4}x - 5$ | |-----|------------------|---------------------------| | $-4$ | $1$ | $-4$ | | $0$ | $0$ | $-5$ | | $4$ | $-1$ | $-6$ |
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given the function below, fill in at least 3 rows of the table of value…
| $x$ | $-\frac{5}{4}x$ | $y = -\frac{5}{4}x - 4$ | |-----|-----------------|--------------------------| | $-4$ | $5$ | $1$ | | $0$ | $0$ | $-4$ | | $4$ | $-5$ | $-9$ |
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simplify the expression. select ot a real number\ if applicable. \\sqrt…
$-\frac{3}{4}$
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add: 89 + -1 = save answe
88
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add: -8 + -4 =
-12
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add: -15 + 99 = \\boxed{}
84
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add: 2 + -8 = save answe
-6
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add: -1 + 77 = save answer
76
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complete ordered pairs for the equation, and then graph the equation. 4…
4
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enter the correct answer that completes the sentence below. the y-inter…
\((0,3)\)
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compute the discriminant. then determine the number and type of solutio…
0 Additionally, since the discriminant is 0, the quadratic equation has **one real repeated rational solution**.
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multiply. \\(dfrac{3}{8} \\times 64\\)
24
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a line passes through the point (-2,-3) and is perpendicular to the lin…
y=-2x-7 (Option C)
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question 15 a line passes through the point (0,2) and is perpendicular …
C. $y=4x+2$
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question 13 what is the slope of a horizontal line? -1 0 undefined 1
0 (Option: 0)
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question 12 if the equation of a line is y = 7x - 5, what is its slope?…
B. 7
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question 11 a line has a slope of -3/4. which of the following could be…
Change in y = -3, change in x = 4 Change in y = 3, change in x = -4
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mrs. jacobs and mr. kanavins buy food for an school party. the cost of …
$\$15$
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2. evaluate: 2 × (4^2 - 2) 3. evaluate: 12 ÷ (3^2 - 1) + 2 4. evaluate:…
Problem 2: 28 Problem 3: 3.5 Problem 4: 33 Problem 5: 6 Challenge Problem: 29
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set 3 decimal place value and rounding decimals fill in the blanks. 1 i…
0.7 2.
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¿qué ecuación tiene ceros reales correspondientes a la $x$-¿interseccio…
$y = \log_{3}(x) - 1$
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¿cómo explicarías la relación entre el cero real de la función y x-¿int…
Dado que el gráfico nunca cruza el $x$-eje, la función no tiene ceros reales.
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for the given polynomial p(x) and c = -3, use the remainder theore p(x)…
384
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use synthetic division and the remainder theorem to find p(a). p(x)=x³+…
$9$
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(\frac{1}{3} + \frac{2}{9})
$\frac{5}{9}$
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the function ( f(x) = 2x - 8 ) is shifted 3 units up. which equation co…
D. \( g(x) = 2x - 5 \)
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o $f(x) = -sqrt{x + 2} + 2$ o $f(x) = sqrt{x + 2} - 2$ o $f(x) = -sqrt{…
$f(x)=\sqrt{x+2}$
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c) \\( f(x) = \\sqrt{x + 2} - 2 \\) \\( f(x) = \\sqrt{x + 2} \\) \\( f(…
$\boldsymbol{f(x) = \sqrt{x+2} - 2}$
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in public discussions about automation, the conversation often swings b…
B. even-handed
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b) \\(\\boldsymbol{f(x) = \\sqrt{x + 2}}\\) \\(\\boldsymbol{f(x) = -\\s…
$\boldsymbol{f(x) = -\sqrt{x+2} + 2}$ (Option 4)
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6. a. $f(-3) =$ b. $f(4) =$ c. $f(1) =$ d. $f(-1) =$ e. $f(0) =$
a. $f(-3) = -2$ b. $f(4) = 4$ c. $f(1) = 1$ d. $f(-1) = 1$ e. $f(0) = 1$
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which point is on the line that passes through (0, 6) and is parallel t…
(-12, 8)
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let $f(x) = 6x + 2$. which of the following is the inverse of $f(x)$? -…
$\boldsymbol{f^{-1}(x)=\frac{x-2}{6}}$ (the second option)
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5. a. $f(-1) =$ b. $f(2) =$ c. $f(1) =$ d. $f(-2) =$ e. $f(0) =$
a. $-1$ b. $1$ c. $1$ d. $0$ e. $1$
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suppose $f(x)=x^3 + 1$. a) find the inverse function $f^{-1}(x)$.
$f^{-1}(x) = \sqrt[3]{x - 1}$
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there are many situations that have a minimum or maximum value and many…
1. Word Problem: A part-time job pays $12 per hour, plus a $50 weekly bonus for showing up on time every day. You need to earn at least $230 this week to pay your phone bill. How …
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how many zeros does this polynomial have? options: 3, 2, 0, 5
5
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4. $f(x) = \\begin{cases} |2x + 7|, & x \\leq -4 \\\\ 1 + x^2, & -4 < x…
a. $\frac{29}{3}$ b. $2$ c. $1$ d. $6$
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use synthetic substitution to evaluate the given value and determine th…
The remainder when \( f(x)=-4x^{4}+9x^{3}+8x^{2}+9x - 13 \) is evaluated at \( x = 3 \) using synthetic substitution is \( 5 \).
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2. $f(x)=\\begin{cases}x^3 - 7x, & x\\leq - 3\\\\8, & - 3 < x\\leq 3\\\…
a. $f(-5) = -90$ b. $f(11) = 5$ c. $f(0) = 8$ d. $f(3) = 8$
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use synthetic substitution to evaluate the given value and determine th…
The remainder is \(5\), so the value of \(f(3)\) is \(5\).
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3. $f(x)=\\begin{cases}\\ \\dfrac{3}{x + 4},&x < -5\\\\x^2 - 3x,&-5 < x…
a. $4$ b. $249$ c. $-\frac{1}{2}$ d. $0$
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obergefell v. hodges by justice anthony m. kennedy applying these estab…
The changing social climate may reverse earlier Court assumptions.
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use the passage to answer the question. which word has a connotation th…
The word with a connotation suggesting disapproval is related to the negative context of unhealthy diets. Among the options, "exposure" (in the context of exposure to unhealthy di…
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© bridgeman art library / universal images group/ image quest 2015 whic…
Low prices made automobiles available to many Americans.
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k5 learning mixed addition and subtraction (2 - digits) math practice w…
s (row-wise): 14, 19, 141, 1, 126 115, 28, 12, 71, 35 28, 50, 7, 65, 45 110, 40, 140, 67, 170 80, 115, 45, 169, 71