微積分
極限、導數、最優化與函數性質。
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use a graphing tool to solve the equation below for x. $-3^{(-x)} - 6 =…
A. \(x\approx2.50\)
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use a graphing tool to solve the equation below for x. $-3^{(-x)} - 6 =…
A. \(x\approx2.50\)
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select the correct answer. how many real solutions exist for this syste…
C. two
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what is the range of the absolute value function shown in the graph? op…
C. \(-6\leq y<\infty\)
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all exponential functions can be written in many forms. write the funct…
\( f(t)=\boldsymbol{740\times(1.3364)^{t}} \) (or \( f(t) = 740b^{t} \) with \( b\approx1.3364 \))
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match each equation of the piecewise function represented in the graph …
To solve this, we analyze each segment of the piecewise function by examining the domain (x - values) and the corresponding graph: ### 1. Segment from \( x = 0 \) (closed dot) to …
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all exponential functions can be written in many forms. write the funct…
\( f(t) = 490.0000(2)^{\frac{t}{2.4754}} \) (or with more precise rounding during calculation, but following the steps above gives this result)
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3 select all the correct answers. exponential function f is represented…
The correct statements are: - The functions have the same y - intercept. - Both functions are increasing on all intervals of \(x\). - Both functions approach \(-\infty\) as \(x\) …
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2 select the correct answer. exponential function f is represented by t…
A. Both functions are decreasing on \([0, 3]\), and function \( f \) is decreasing at a faster rate.
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what are the features of the function $f(x) = 3^x - 4$ graphed below? g…
The function \( f(x) \) is an **exponential** function with a **horizontal** asymptote of \( y = - 4 \). The range of the function is \( (-4,\infty) \), and it is **increasing** o…
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what are the features of the function $f(x) = \\log_{2}(x + 2)$ graphed…
The function \( f(x) \) is a \(\boldsymbol{\text{logarithmic}}\) function with a \(\boldsymbol{\text{vertical}}\) asymptote of \(\boldsymbol{x=-2}\). The range of the function is …
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select the correct answer from each drop - down menu. the function f is…
(4,87)
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a quantity with an initial value of 790 decays continuously at a rate o…
194.81
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a quantity with an initial value of 110 grows continuously at a rate of…
\( 113.35 \)
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5 select the correct answer from each drop - down menu. the function f …
To solve this, we analyze the function from the table and apply transformations: ### Step 1: Identify the Parent Function First, we check the pattern of \( f(x) \). Let’s test \( …
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select the correct answer. consider the function $f(x) = 2^x$ and the f…
A. The graph of \( g(x) \) is the graph of \( f(x) \) shifted 4 units to the left.
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select the correct answer. in which direction must the graph of $f(x) =…
D. right
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2 enter the correct answer in the box. the function ( f(x) = 7^x + 1 ) …
\( 3 \)
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select the correct answer. which function is decreasing and approaches …
B. f(x) = -3(6)^x + 2
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select the correct answer. what are the solutions of this quadratic equ…
D. $x = -4 \pm \sqrt{13}$
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select all the correct answers. which of the following statements are t…
The extreme value is at the point (3, -7), The solutions are \(x = 3 \pm \sqrt{7}\), The graph of the quadratic equation has a minimum value.
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select the correct answer. this table represents a quadratic function. …
C. The value of a is positive, so the vertex is a minimum.
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5 select the correct answer. if function ( g(x) = x^2 + 2 ) is a transf…
C. \((0,2)\)
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4.2 3. complete each table of values. a) $y = x + 1$\ \ | $x$ | $y$ |\ …
### Question 3 (already completed correctly): a) For $y=x+1$: $x=1, y=2$; $x=2, y=3$; $x=3, y=4$; $x=4, y=5$ b) For $y=x-1$: $x=2, y=1$; $x=4, y=3$; $x=6, y=5$; $x=8, y=7$ ### Que…
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find the domain of the function below. $f(x) = \\sqrt{\\frac{x^2 + 13x …
The domain of the function is \([-7,-6]\cup(-4,1)\cup(2,\infty)\)
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which is the minimum or maximum value of the given function? graph of a…
B. The function has a minimum value of -4.
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question 10 of 10 use the quadratic formula to find the solution to the…
B. \(x=\frac{3}{2}\), C. \(x = \frac{3-\sqrt{\frac{9}{4}}}{2}\), E. \(x=\frac{3+\sqrt{\frac{9}{4}}}{2}\) (Note: When \(\Delta = 0\), the two roots (from the \(\pm\) in quadratic f…
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consider the equation below. $log_{4}(x + 3)=log_{2}(2 + x)$ which syst…
A. $y_{1}=\frac{\log(x + 3)}{\log4},y_{2}=\frac{\log(2 + x)}{\log2}$
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which system of equations could be graphed to solve the equation below?…
$y_1=\frac{\log x}{\log 0.5},y_2=\frac{\log 2}{\log 3}+x$ (the last option among the given choices)
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which system of equations could be graphed to solve the equation below?…
B. \(y_1=\log(2x + 1),y_2 = 3x-2\)
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what is the approximate value of x in the equation below?\\(\\log_{5}15…
-1.317 (corresponding to the option: -1.317)
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kim solved the equation below by graphing a system of equations.\\(\\lo…
1.4 (the option corresponding to 1.4, e.g., if the options are A. 0.6, B. 0.9, C. 1.4, D. 1.6, then the answer is C. 1.4)
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the function $f(x)$ is invertible. find $f^{-1}(-2)$. graph of $f(x)$ i…
\( \boxed{0} \)
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complete the text with the best transition. technology is supposed to m…
Moreover, it's true
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find the equation of the exponential function. | x | f(x) | |----|----|…
$f(x)=4\cdot2^x$
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3. \\begin{cases} y = x - 1 \\\\ x + 4y = 16 \\end{cases}
The solution of the system of equations is \( x = 4,y = 3 \) (or the ordered pair \((4,3)\)).
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add. (1) $3\\frac{5}{7} + 2\\frac{5}{14} =$ (2) $\\frac{5}{6} + 2\\frac…
$6\frac{3}{14}$ $2\frac{13}{15}$ $5\frac{43}{48}$ $9\frac{1}{4}$ $\frac{11}{42}$ $9\frac{27}{50}$
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dividing 2 digits \\begin{array}{c|c|c|c|c} \\times & 1 & 2 & 3 & 4 & 5…
1. a. Quotient 5, remainder 1 b. Quotient 8, remainder 2 c. Quotient 7, remainder 3 d. Quotient 9, remainder 1 e. Quotient 5, remainder 5 2. a. Quotient 8, remainder 2 b. Quotient…
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challenge #4 plot a parabola through the points. when you finish, press…
To plot the parabola, use the vertex \((4, -2)\), the y - intercept \((0, 6)\) and the point \((8, 6)\) (found using the axis of symmetry \(x = 4\)) and draw a smooth curve throug…
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a table representing a continuous unrestricted exponential function is …
B. It is decreasing and positive
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a graph of an exponential function w(x) is shown. use the graph to find…
The y - intercept of \(w(x)\) is \(2\) and the horizontal asymptote is \(y = 0\).
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evaluate the function. (see example 1) ( g(x)=\begin{cases}-x + 4, & \t…
\( -1 \)
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evaluate the function. (see example 1) \\( g(x) = \\begin{cases} -x + 4…
\( 5 \) ### Problem 9: Evaluate \( g(0) \)
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the functions f and g are defined as follows. f(x)=2x³ + 6 g(x)=2x - 3 …
$f(-4)=-122$ $g(-7)=-17$
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the functions f and g are defined as follows. $f(x) = -3x^3 - 2$ $g(x) …
$f(-3) = 79$ $g(6) = -14$
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write the prime factorization of 16. use exponents when appropriate and…
$2 \cdot 7$
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(13+3)/r for r=4
4
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what is the role of a judge in the process of obtaining a search warran…
to decide if evidence justified further searching
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why are public lands beneficial for the general public? they increase t…
They increase biodiversity, natural resource protection, and outdoor recreation.
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divide. 75.5 ÷ 1000
\(0.0755\)
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express in simplest radical form. \\(\\dfrac{\\sqrt{450}}{\\sqrt{9}}\\)…
$5\sqrt{2}$
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use the drawing tools to form the correct answer on the graph. plot fun…
The graph has an open point at \((-3, -4)\) with a horizontal line to the left, and a closed point at \((-3, 2)\) with a line \(y = x+5\) (slope 1) to the right.
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which graph represents a parabola whose corresponding quadratic equatio…
(2) The parabola opening upward with vertex above the x-axis
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18 plus what number equals 20? 18 + 15 = ?
The unknown number is 2, and $18 + 2 = 20$
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2.8 plus what number equals 3? 2.8 + 1.5 = ?
The number that makes 2.8 equal 3 when added is 0.2. $2.8 + 1.5 = 4.3$
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finish decomposing 15. 38 + 15 = ? 15 is decomposed into 2 and a box (t…
The missing decomposed number is 13, and $38 + 15 = 53$
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38 plus what number equals 40? 38 + 15 = ? (with a pentagon image and a…
$2$
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writing linear equations given a graph pixel art directions: using the …
1) Slope-intercept form: $y=-x$; Standard form: $x+y=0$ 2) Slope-intercept form: $y=-x+8$; Standard form: $x+y=8$
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what is the slope of this line? simplify your answer and write it as a …
$-4$
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worksheet adding and subtracting fractions 1 add \\(\\frac{1}{4} + \\fr…
$\frac{1}{3}$ ### Second Problem: $\boldsymbol{\frac{1}{6} + \frac{1}{18}}$
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what is the degree? options: even, positive, negative, odd (with a grap…
A. Even
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what is the degree and sign of the leading coefficient for this polynom…
Even Degree - Leading Coeff.
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9. what is the zero of the function below? $f(x)=3x - 15$ a. -15 b. 0 c…
C. 5
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solve for x. \\log_{5}x = -3 simplify your answer as much as possible. …
$\frac{1}{125}$
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compute. 7.24 - 12.863 = 7.28 + (-3.65) =
\(7.24 - 12.863=\boldsymbol{-5.623}\) \(7.28+(-3.65)=\boldsymbol{3.63}\)
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compute. -5.39 - 13.4 = 32.6 + (-56.24) =
s: \(-5.39 - 13.4 = \boldsymbol{-18.79}\) \(32.6 + (-56.24) = \boldsymbol{-23.64}\)
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multiply. \\begin{array}{r} 95.8 \\\\ \\times\\ 2.06 \\\\ \\hline \\end…
197.348
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multiply: \\begin{align*} &\\ \\ \\ \\ \\ \\ 9.07 \\\\ &\\times\\ 8.32 …
75.4624
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multiply. 3.57 × 7.8
\(27.846\)
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evaluate. $6 + 4^2 \\div 2$
14
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multiply. 99.5×0.1
\(9.95\)
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multiply. 1.52×0.01
\(0.0152\)
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in exercises 13–26, evaluate the indicated function f(x) = x² − 1 and g…
s: 13. \(\boldsymbol{9}\) 14. \(\boldsymbol{7}\) 15. \(\boldsymbol{1}\) 16. \(\boldsymbol{-1}\)
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divide f(x) by d(x). your answer should be in the following format: \\(…
\( 2x + 2 \)
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early in the great migration of 1910 - 1970, which involved the mass mi…
A. To introduce and illustrate Barrier Williams's integral role in supporting other Black women as their circumstances changed during part of the Great Migration
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divide f(x) by d(x). your answer should be in the following format: \\(…
\( 1 \)
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3-126. simplify each of the following expressions. homework help a. 3 -…
$-7$ ### Part b:
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exact value of recip. quad. angles (radian) time to beat: unlimited gra…
Undefined (Note: None of the provided options 1, 0 are correct, as $\csc(\pi)$ has no real value)
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exact value of recip. quad. angles (radian) time to beat: unlimited gra…
1
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4 select the correct answer. which mode of narration is apparent in the…
C. free indirect speech
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value 3 which sentence best explains the impact of the mongol invasions…
c. The Mongol invasions reshaped many parts of the civilized world like China, Persia, and Russia through attacks, threats, and harsh rule in.
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continue dividing on the algorithm. 9 ones is equivalent to 90 tenths. …
7
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continue dividing on the algorithm. 9 ones is equivalent to 90 tenths. …
The digit in the tenths place of the quotient is 7, the number subtracted is \( 8.4 \) (or 84 tenths), and the remainder is \( 0.6 \) (or 6 tenths). So filling in the boxes: the f…
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write \\(\\frac{6}{8}\\) as a decimal. continue dividing on the algorit…
The digit in the box is 5, and 40 hundredths divided by 8 is 5 hundredths (or 0.05), but in the context of the long division, the next digit of the quotient is 5, so the answer to…
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if a quadratic equation models the path of a basketball shot and the eq…
d. $x = 2.5$
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solve this system of equations by graphing. first graph the equations, …
\((-5, 4)\)
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write \\(\\frac{4}{5}\\) as a decimal. start by filling in the algorith…
0.8
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write \\(\\frac{8}{9}\\) as a decimal. if we continue to divide 8 by 9,…
\(0.\overline{8}\)
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read the excerpt from the fourteenth amendment of the united states con…
C. was the first time the Constitution defined what a citizen is.
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the function $h(t) = -16t^2 + 96t + 6$ represents an object projected i…
3 seconds (corresponding to the option: 3 seconds)
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estimate the difference. round each number to the nearest whole number,…
\(10\)
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look at the graph: what is the equation of the vertical asymptote?
$x=-6$
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look at the graph: what is the equation of the horizontal asymptote?
$y=-5$
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write $19\\frac{3}{5}$ as a decimal. $19\\frac{3}{5}=\\square$
19.4
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write $24\\frac{1}{4}$ as a decimal. $24\\frac{1}{4}=\\square$
24.25
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question move at least one of the 9 guide points below to complete the …
Move the vertex (blue point) from (0,0) to (3,2); keep red points aligned with $y = |x - 3| + 2$ (e.g., left of vertex: (-1,6), (0,5), (1,4), (2,3); right of vertex: (4,3), (5,4),…
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which equation is represented by the graph below? answer \\( y = -2|x +…
y = -2|x + 3| + 6
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the graph of $f(x) = x^2$ is translated to form $g(x) = (x - 5)^2 + 1$.…
The graph of \( g(x) \) is a parabola opening upwards with vertex at \((5, 1)\). (Among the given options, the one with vertex \((5, 1)\) and upward opening is the correct represe…
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question if θ is an angle in standard position and its terminal side pa…
\(9\)
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question between which two consecutive whole numbers does \\(\\sqrt{18}…
Since \( \sqrt{16} = 4 \) and \( \sqrt{25}=5 \), it is known that \( \sqrt{18} \) is between \( 4 \) and \( 5 \).