Cálculo
Límites, derivadas, optimización y comportamiento de funciones.
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graph this line using the slope and y-intercept: y = 4x - 6 click to se…
To graph \(y = 4x-6\): 1. Plot the y - intercept \((0,-6)\) (since when \(x = 0\), \(y=-6\)). 2. Use the slope \(m = 4=\frac{4}{1}\): from \((0,-6)\), move 1 unit right and 4 unit…
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画图 \\(\\begin{cases} y = 2\\sqrt3{x^2} \\\\ y = x \\end{cases}\\)
1. 先求交点：联立方程得$x=2\sqrt[3]{x^2}$，解得$x=0$，$x=8$，对应交点为$(0,0)$，$(8,8)$。 2. $y=2\sqrt[3]{x^2}$即$y=2x^{\frac{2}{3}}$，定义域为$\mathbb{R}$，是偶函数，在$(-\infty,0)$单调递减，$(0,+\infty)$单调递增，过$(0,0)$，…
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using the slope and y-intercept: $y = 3x + 1$ click to select points on…
The line passes through points $(0, 1)$ and $(1, 4)$ (and other points following the slope, e.g., $(2,7)$, $(3,10)$), forming a straight line with slope 3 and y-intercept 1.
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画图 $y = 2sqrt3{x^2}$，$y = x$
交点为$(0,0)$和$(4,4)$ $y=2\sqrt[3]{x^2}$是过原点，在$\mathbb{R}$上单调递减于$(-\infty,0)$，单调递增于$(0,+\infty)$的偶函数曲线；$y=x$是过一、三象限的直线
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画图\\(\\begin{cases}y = 2\\sqrt3{x^2}\\\\y = x\\end{cases}\\)
1. 函数$y=2\sqrt[3]{x^2}$的图像：过原点，在$\mathbb{R}$上连续，是偶函数，在$(-\infty,0)$单调递减，在$(0,+\infty)$单调递增，呈“U”型且在原点处平缓。 2. 函数$y=x$的图像：过原点，斜率为1的直线，在$\mathbb{R}$上单调递增。
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画图 $y = 2sqrt3{x^2}$，$y = x$
1. 曲线$y=2\sqrt[3]{x^2}$：定义域为$\mathbb{R}$，过原点$(0,0)$和点$(1,2)$、$(-1,2)$，是偶函数，在$(-\infty,0)$单调递减，$(0,+\infty)$单调递增，呈“U”型且在原点处平缓。 2. 直线$y=x$：定义域为$\mathbb{R}$，过原点$(0,0)$和点$(1,1)$，斜率为1的…
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find the x- coordinates of the points where the graph crosses the x-axi…
For $y=4x^2+11x-3$: $x = -3$ and $x = \frac{1}{4}$ For $y=-3x^2+14x+5$: $x = -\frac{1}{3}$ and $x = 5$
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find the relative clause. if it is nonrestrictive, set it off with comm…
When we were kids, my eldest brother, whose imagination knew no limits, would entertain us for hours with his fanciful stories.
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6.1 slope intercept form after this section you should be able to: - id…
## Ex. 1 1. Slope: $\frac{1}{3}$, Y-intercept: $2$ 2. Slope: $-4$, Y-intercept: $-1$ ## Ex. 2 1. Slope: $-\frac{4}{3}$, Y-intercept: $3$ 2. Slope: $\frac{1}{2}$, Y-intercept: $2$
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31 carlos owns a $500,000 ul insurance policy and he wishes to withdraw…
b. With a policy loan, funds continue to earn tax - sheltered income within the policy's investment account.
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18. convert \\(\\frac{2}{5}\\) to a decimal. round to the hundredths pl…
0.4 (corresponding to the option: 0.4)
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17. subtract the mixed numbers $16 - 9\\frac{8}{9}$. $\\bigcirc\\ 7\\fr…
\( 6\frac{1}{9} \) (corresponding to the option \( 6\frac{1}{9} \))
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5 dolores, a 38 - year - old accountant, wishes to purchase a life insu…
d. A limited payment whole life policy
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how could the absolute monarchy of louis xvi best be described? democra…
D. unlimited government
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read the sentence. algebra is a precursor for calculus because it will …
preceding requirement
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test: question 9 when submitting a new work order ticket in incident iq…
B) You can include multiple devices on a single ticket, provided they are all experiencing the same issue.
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6. convert $1\\frac{4}{9}$ to a decimal. round to the hundredths place …
1.44 (the option C, assuming the options are labeled as A. 1.45, B. 1.49, C. 1.44, D. 1.99. But from the given options, the third option is 1.44, so the answer is 1.44 (the option…
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3. use the arrows to move each item into the correct order for subtract…
1. Write the subtraction problem for the scenario. 2. Check if the fractions have the same denominators. If they do not, find the least common multiple of the denominators, and re…
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1. subtract the mixed numbers $9\\frac{2}{5} - 7\\frac{5}{10}$.\ \\bigc…
\(1\frac{9}{10}\) (corresponding to the first option: \(1\frac{9}{10}\))
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look at the system of inequalities. $y \\geq 3x$ $y \\leq x + 6$ $y \\l…
(0, 0) (1, 7) (3, 9)
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find the slope of the line passing through the points (-4, -3) and (8, …
\(-\frac{1}{2}\)
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find the slope of the line passing through the points (-6, -5) and (4, …
\(\frac{9}{10}\)
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c. executive order 11111 (jfk) 4. checks and balances: write one way th…
### Question 4: a. Rule orders unconstitutional via judicial review. b. Pass legislation to limit or defund the order. c. Revoke/replace orders with new ones. ### Question 5: a. S…
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graph this function $y = x + 5$ click to select points on the graph.
The graph is a straight line passing through points $(0, 5)$ and $(1, 6)$, extending infinitely in both directions along the slope of 1.
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how would you limit the domain to make this function one to one and sti…
\( 2 \)
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how would you limit the domain to make this function one to one and sti…
\(-3\)
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find the inverse function. $f(x) = -12\\frac{1}{x}$ $f^{-1}(x) = ?\\fra…
The first box is \(-12\) and the second box is \(x\), so \( f^{-1}(x)=-12\frac{1}{x} \) (or in the filled - in form: the first green box is \(-12\) and the white box is \(x\)).
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72 + 23; 53 + 26; 64 + 24; 68 + 21; 79; 88; 89; 95
$72 + 23 ightarrow 95$ $53 + 26 ightarrow 79$ $64 + 24 ightarrow 88$ $68 + 21 ightarrow 89$
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mix and match 45 + 13 45 + 23 45 + 3 48 58 68
$45 + 13 ightarrow 58$ $45 + 23 ightarrow 68$ $45 + 3 ightarrow 48$
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graph the following features: - slope = -\\frac{2}{3} - y-intercept = -2
The line $y = -\frac{2}{3}x - 2$ is graphed by plotting the y-intercept $(0, -2)$, a second point such as $(3, -4)$ or $(-3, 0)$, and drawing a straight line through these points.
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75 + 14 75 + 4 75 + 24 79 99 89
$75 + 14 ightarrow 89$ $75 + 4 ightarrow 79$ $75 + 24 ightarrow 99$
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which of the following is the graph for this piecewise defined function…
The first graph (the one with the upward - opening parabola for \( x\leq2 \) and the line with an open dot at \( x = 2 \) for \( x>2 \))
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52 + 15 52 + 25 52 + 5 67 77 97
$52 + 15 ightarrow 67$ $52 + 25 ightarrow 77$ $52 + 5 ightarrow 57$
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find the horizontal and vertical asymptotes for the function. f(x) = (7…
Vertical asymptote: \(x = -2\) Horizontal asymptote: \(y = 7\)
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¿cuál es el valor de? x en la expresión $\\log_{2}(3x + 8) = 5$?
$x = 8$
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resolver una ecuación logarítmica resolver: \\(\\log_{2}(3x + 8) = 5\\)…
$2^5 = 3x + 8$
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20) $(-6)+(-1)+4$
$-3$
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evaluación de logaritmos evaluar: \\(\\log_{16}64\\) options: \\(\\frac…
$\boldsymbol{\frac{3}{2}}$
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evaluación de logaritmos evaluar: \\(\\log_{125} 5\\) \\(\\frac{2}{3}\\…
$\boldsymbol{\frac{1}{3}}$
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4 pavan receives $50,000 as a gift from his father. he calls his adviso…
b. The management expense includes operating expenses and taxes.
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evaluación de logaritmos evalúa cada expresión. \\(\\log_3 27 = \\squar…
$\log_{3}27 = 3$ $\log_{12}1 = 0$ $\log_{5}\frac{1}{25} = -2$ $\log_{2}128 = 7$
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3. divide using partial quotients. then, check your work with multiplic…
The quotient is 255, and verification confirms $255\times7=1785$.
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graph these equations: -2y = -x + 6 2y = x - 6 click to select points o…
The two equations graph as the same line. The system has infinitely many solutions. Key points to plot for the line: $(0, -3)$ and $(6, 0)$ (all points along this line satisfy bot…
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26 lee is a single dad who is 41 years old. he wishes to purchase a lif…
c. A limited payment whole life policy
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enter the function of the form $f(x)=a(2)^x$ that is represented by the…
\( f(x)=4(2)^x \)
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find each sum, difference, or product. 8. $\frac{2}{5}+\frac{1}{4}$ 9. …
$\frac{13}{20}$ ### Problem 9: $\boldsymbol{\frac{5}{6} - \frac{1}{4}}$ ## Step1: Find a common denominator (12) $\frac{5}{6} = \frac{5\times2}{6\times2} = \frac{10}{12}$, $\frac{…
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4.2 solve exponential equations 1. $3^{2x - 1} = 3^{x + 2}$ 2. $2^{3x} …
\( x = 3 \) ### Problem 2: \( 2^{3x} = 4^{x + 2} \)
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decide whether each expression is less than 4,000 or greater than 4,000…
Less than 4,000: $9\div0.01$ Greater than 4,000: $60\div0.01$
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match values that are equal. 5 × 100 5,000 500 ÷ 0.01 answer bank 5 ÷ 0…
- $5 \times 100$ matches $5 \div 0.01$ - $5,000$ matches $50 \div 0.01$ - $500 \div 0.01$ matches $50,000$
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parent graph\ y = b^x\ transformations\ y = a b^(x - h) + k\ f(x) = 2^x…
Vertical shift up by 1 unit. 2. **\( f(x)=2^{(x - 3)} \)**:
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parent function $f(x)=2^x$ $f(x)=2^{x+5}$ transformation: graph it!
# Explanation: ## Step1: Identify Transformation Type The parent function is \( f(x) = 2^x \), and the transformed function is \( f(x) = 2^{x + 5} \). For exponential functions of…
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equation by filling in the missing number. 9.) 2.9 - ______ = 1.4 10.) …
\( 1.5 \) ### Problem 10:
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subtracting decimals (\ directions: complete each equation \ 1) \\( 7.7…
\( 0.7 \) ### Problem 2: \( \underline{\quad} - 3.2 = 0 \)
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simplify the radical expression. 16. $sqrt{44} + 2sqrt{11}$
$4\sqrt{11}$
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which expression shows how to find $6 \\div 0.01$? $6 \\div 100$ $6 \\d…
$6 \times 100$
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equation by filling in the missing number. 9.) 0.9 + ______ = 2.6 10.) …
\( 1.7 \) ### Problem 10:
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read the excerpt from herbert hoover’s “rugged individualism” speech, d…
1. "It would impair the very basis of liberty and freedom not only for those left outside the fold of expanded bureaucracy but for those embraced within it" 2. "When the Federal G…
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parent ( f(x) = 2^x ) for each question, identify and describe the tran…
Vertical shift up by 3 units ### 2. $f(x) = 2^x - 4$
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3.) 0.0 + \\underline{quadquad} = 4.9
\( 4.9 \)
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1) 3.2 + = 5
The unknown number is \( 1.8 \)
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pre - algebra assignment name date use simple interest to find the endi…
The ending balance is $\$9296$. You can follow the same steps for each of the other problems: 1. Convert the percentage rate to a decimal (e.g., 5% becomes 0.05, 15% becomes 0.15,…
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you looked at some division expressions and found quotients. the table …
100
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sketch the graph of the quadratic function $f(x) = x^2 - 4x + 3$, label…
- **Vertex**: \( (2, -1) \) - **Axis of Symmetry**: \( x = 2 \) - **x-intercepts**: \( (1, 0) \) and \( (3, 0) \) - **y-intercept**: \( (0, 3) \) - The graph is a parabola opening…
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question given $f(x) = -x^2 + 2x$, find $f(-3)$
-15
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question given ( h(x) = -3x + 2 ), find ( h(1) ). answer attempt 1 out …
-1
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question given $f(x) = -x - 5$, find $f(0)$. answer attempt 1 out of 2
-5
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question given $g(x) = -2x - 1$, find $g(-1)$. watch video
1
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write s if states held the specific power under the articles of confede…
S #### 3.017) to coin money The National Government (Congress) had the power to coin money.
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yumi has a pet hedgehog named spike. every day, spike eats a serving of…
$1 \div 0.01$
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y = type your answer... x + -2
\(-2\)
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decide whether each expression is less than 100 or greater than 100. le…
### Less than 100: $9\div0.1$ ### Greater than 100: $18\div0.1$, $11\div0.1$
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decide whether each expression is less than 100 or greater than 100. le…
- Less than 100: $9\div0.1$ - Greater than 100: $18\div0.1$
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answer $y = -f(x + 4)$ $y = -f(x - 4)$ $y = f(-x) - 4$ $y = f(-x) + 4$
# Explanation: ## Step1: Analyze the original function The original function (black curve) seems to be an exponential - like function with a horizontal asymptote at \(y = 0\) (the…
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y - 3 = \\frac{0}{0}(x + 8)
The equation (after correcting the undefined \(\frac{0}{0}\) to a slope of 0, assuming a typo) represents the horizontal line \( y = 3 \). If we strictly consider \(\frac{0}{0}\),…
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which expression shows how to find 23 ÷ 0.1? 1 ÷ 23, 23 × 10, 23 ÷ 10, …
$23 \times 10$
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evaluate the expression $4 \\cdot 3 - (9 - 7)^2 + 6$. next, evaluate th…
The first blank (multiplication result) is 12, the second blank (exponent result) is 4. So the filled line is \(12 - 4 + 6\). So the first box is 12 (for \(4 \cdot 3\)) and the se…
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calculate. (1) $1\\frac{13}{72} \\div 1\\frac{7}{10} - \\frac{1}{4} =$ …
$\frac{4}{9}$ ### (2)
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g19b (5) (left(1\frac{3}{7} - 1\frac{1}{5} ight) div left(2\frac{2}{5} …
\(\frac{3}{14}\) ### (6)
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the end of a hose was resting on the ground, pointing up an angle. sal …
3.2 feet
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find the sum of the infinite geometric series $500 + 100 + 20 + \\dots$…
A. 625
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question 16 of 20 which description matches the transformations $y = \\…
C. Vertical stretch by factor 3, reflection across the x-axis, then a vertical shift up 1 unit
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solve $e^{2x} - 8e^{x} = 20$ select one: a. $x = \\ln(20)$ b. $x = \\ln…
C. $x = \ln(10)$
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select one: a. $f(x) = \\frac{4(x - 3)}{(x + 2)(x - 4)}$ b. $f(x) = \\f…
D. $f(x)=\frac{-9(x-3)}{(x+2)(x-4)}$
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the graph of the function f(x) is given. choose the correct equation fo…
A. $y = -(x + 1)^2(x - 2)$
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time left 1:41:15 a. -2 with multiplicity 1,0 with multiplicity 2, and …
B. $-2$ with multiplicity 1, $0$ with multiplicity 2, and 3 with multiplicity 1
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determine the end behavior of the polynomial function: $y = -x^6 + 4x^8…
A. As $x ightarrow -\infty, f(x) ightarrow -\infty$ and as $x ightarrow +\infty, f(x) ightarrow -\infty$.
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select one: a. $f(x) = -|x - 1| - 4$ b. $f(x) = -|x + 1| - 4$ c. $f(x) …
C. $f(x) = -|x - 1| + 4$
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write an equation for graphed function by using transformations of the …
$y = -|x-1| + 4$
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write a formula for the function $h(x)$ that relates to when the graph …
D. $h(x) = -\sqrt{\frac{1}{5}x}$
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tabular representations for the functions p, q, and r are given below. …
$q(x) = \frac{1}{4}p(x) + 2$ $r(x) = 2p(x) - 1$
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find the inverse of the function: $f(x) = 7x - 2$ select one: a. $f^{-1…
D. $f^{-1}(x) = \frac{x + 2}{7}$
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given the function $f(x) = 3 - 2x^2$, evaluate $dfrac{f(x + h) - f(x)}{…
D. $-4x - 2h$
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find $(f \\circ g)(x)$ for the functions $f(x) = \\sqrt{2x} + 5$ and $g…
C. $(f \circ g)(x) = \sqrt{6x - 8} + 5$
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evaluate $g(-1)$ for the function $g(t) = 4t - 3$. select one: a. 1 b. …
B. $-7$
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9.2) select four reasons why the articles of confederation represented …
9.2) - Congress was unicameral. - Each state had one vote. - Most of the power was housed in the state legislatures. - It provided for legislative, executive, and judicial branche…
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find the solutions of $y = x^2 - 5x - 14$ from its graph.
$x=-2$ and $x=7$
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question 40 find the vertical and horizontal asymptotes of the function…
Vertical asymptote: $x = -4$ Horizontal asymptote: $y = 7$
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question 39 the graph of a rational function, f, is shown here with all…
Domain: $(-\infty,3)\cup(3,\infty)$ Range: $(-\infty,1)\cup(1,\infty)$ (Option: Domain $(-\infty,3)\cup(3,\infty)$; Range $(-\infty,1)\cup(1,\infty)$)
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describe the end behavior of the graph of the following polynomial func…
Rises to the left and rises to the right --- ### Second Problem: Simplify Rational Expression
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graph the parabola: $f(x)=2(x - 3)^2 - 2$
The correct graph is the second one (the middle-top graph with vertex at $(3,-2)$, opening upward, passing through $(2,0)$ and $(4,0)$).