微积分
极限、导数、最优化与函数性质。
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use tools a company models its revenue in dollars using the function ( …
Los precios posibles (de menor a mayor) son aproximadamente \(\$0.36\) y \(\$0.86\) (valores aproximados después de resolver la ecuación \( 70000(x - x^4)=20000 \) en el dominio \…
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evaluate the factorial expression. (6 - 4)! (6 - 4)! = \\square
\(2\)
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23 multiple choice the bipartisan campaign reform act lowered limits on…
D. Raised limits on hard money (assuming the options are labeled A to D as: A. Lowered limits on soft money, B. Raised limits on soft money, C. Lowered limits on hard money, D. Ra…
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given the function f(x) = (x + 1)^3, complete parts a through c. (a) fi…
### Part (a) # Explanation: ## Step1: Replace \( f(x) \) with \( y \) We start with the function \( f(x)=(x + 1)^3 \). Replace \( f(x) \) with \( y \), so we have \( y=(x + 1)^3 \…
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unit 3: polynomial functions 3.1.a independent practice & hw 1. convert…
### Problem 1: Convert \( f(x) = 3(x - 5)(x + 7)(x - 1) \) to standard form, find \( x \)-intercepts and \( y \)-intercept. #### Step 1: Find \( x \)-intercepts To find \( x \)-in…
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use the graph to determine open interval on which the function is incre…
A. The function is increasing on the interval(s) \((0, \infty)\)
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most youths who join gangs have already been involved in delinquency an…
B. Those involved with gangs are more likely to be cut off from their families. D. Being involved with a gang increases the likelihood of dropping out of school. E. Once a person …
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alexander leans a 20-foot ladder against a wall. if the ladder reaches …
\(20.8^\circ\)
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most youths who join gangs have already been involved in delinquency an…
- using drugs - skipping school - being arrested
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1.9 rational functions & vertical asymptotes ap precalculus name: ca #2…
# Explanation: ## Step 1: Factorizar el numerador y el denominador Para \( f(x)=\frac{x^{2}-25}{x^{2}-8x + 15} \), factorizamos: - Numerador: \( x^{2}-25=(x - 5)(x + 5) \) (difere…
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use a graphing calculator to solve the equation by graphing. if necessa…
\(-1.46\), \(1.14\) (rounded to the nearest hundredth)
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3. write an equation in slope intercept form for a line with a slope of…
\(y = 2x+3\) (depends on the actual \(y\) - intercept value, but following the formula) ### Problem 11
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2. write about how to solve this problem. 9 - 0.6
To solve \(9 - 0.6\), first rewrite \(9\) as \(9.0\) (to match the decimal places of \(0.6\)). Then subtract: \(9.0 - 0.6 = 8.4\). The result is \(8.4\).
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question 37 of 40 the population of a country was 954,000 in 2009 with …
\( 954000(1.0005)^t \) ### Part (b)
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part 2 of 2 there \\underline{\\hspace{2cm}} \\( x \\)-intercept(s) to …
is one
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match each polynomial function to its graph. $f(x) = -2x^3 + 42x^2 - 28…
\( f(x)=-2x^{3}+42x^{2}-288x + 640 \) matches the right graph. \( g(x)=-x^{3}-24x^{2}-192x - 512 \) matches the left graph.
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given the function f(x)=x³ - 4, complete parts a through c. (a) find an…
(for part a): \( f^{-1}(x)=\sqrt[3]{x + 4} \) ### Part (b)
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use a graphing calculator to solve the equation by graphing. if necessa…
\(x\approx1.09\)
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the function $y = f(x)$ is graphed below. plot a line segment connectin…
The average rate of change is \(-\frac{15}{2}\) (or - 7.5)
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suppose $f(x) = (x - 3)^2 - 3$. a) evaluate $f(0)$. b) evaluate $f(1)$.…
\( 6 \) ### Part (b)
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g. i can calculate which type of function (linear vs. exponential) is b…
Option 1: An account that grows by 11% each year will create the largest birthday present.
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unit 3: polynomial functions 3.3.b independent practice & hw 1. classif…
(1a): Classification: 10th - degree trinomial Degree: 10 Leading coefficient: \(3\) End Behavior: As \(x\to\pm\infty\), \(f(x)\to\infty\) ### Part 1b: \( k(x) = -10x^3 + 4x^2 - 5x…
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does the graph represent a function that has an inverse function? choos…
No
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32. ccss reason abstractly each game at a carnival costs $0.50, or you …
Inequality: \( 0.50x > 15 \) Solution: \( x > 30 \) Interpretation: If you play more than 30 games, paying $15 for unlimited play is less expensive than paying $0.50 per game.
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graph the equation. y = x + 3 use the graphing tool to graph the equati…
To graph \( y=x + 3 \): 1. Plot the y - intercept at \( (0,3) \) (since when \( x = 0 \), \( y=0 + 3=3 \)). 2. Plot the x - intercept at \( (-3,0) \) (since when \( y = 0 \), \( 0…
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expand \\( \\log_{2} \\frac{3x^2(x + 2)}{(x - 3)} \\)
$\log_2 3 + 2\log_2 x + \log_2 (x + 2) - \log_2 (x - 3)$
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writing an equation given two points partner worksheet each partner wri…
For the points \((1,5)\) and \((3,11)\), the equation of the line in slope - intercept form is \(y = 3x + 2\)
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solve the following elementary exponential equation. 1000^{-x} = 10^{4x…
\(x = 2\)
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11. projectile recall that the acceleration due to earth’s gravity is 3…
-6 ft/s ### Part (b)
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19) rewrite in a different form (reescribe de otra forma): a) ( x^{\fra…
- For \(x^{\frac{3}{4}}\): \(\sqrt[4]{x^{3}}\) (or \((\sqrt[4]{x})^{3}\)) - For \(\sqrt[4]{a^{5}}\): \(a^{\frac{5}{4}}\) (or \(a\sqrt[4]{a}\))
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3.3.a independent practice & hw 1. classify each polynomial below by de…
### Part a: \( f(x) = 8x^2 - 2x + 9x^3 - 2 \) # Explanation: ## Step 1: Simplify the polynomial First, we arrange the terms in descending order of exponents: \( f(x) = 9x^3 + 8x^2…
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4. interpret logarithmic functions in terms of time that it takes for a…
The time \( t \) is given by \( t=\frac{\ln(70)}{\ln(3)} \) (or \( t = \log_3(70) \) using the definition of logarithm \( \log_b(a)=\frac{\ln(a)}{\ln(b)} \))
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16^{1/2} ?
\(4\)
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2. interpret the exponential function as growth of an initial quantity …
The function describing the population growth is \( P(t) = P_0 \cdot 3^t \) (where \( t \) represents time in years, \( P_0 \) is the initial population, and \( P(t) \) is the pop…
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solve the following logarithmic equation, using a calculator if necessa…
$x = 35$
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11 which function has a point of discontinuity at x = 3 when graphed? a…
D. \(f(x)=\frac{x + 2}{x^{2}-9}\)
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consider the following polynomial function. $f(x) = x^2 - 3x - 4$ step …
The parabola \( f(x)=x^2 - 3x - 4 \) (opening upwards, roots at \( x=-1 \) and \( x = 4 \)) is positive for \( x < - 1 \) or \( x>4 \) (graph above x - axis) and negative for \( -…
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the radical expression below has a radical in the denominator. fill in …
\(6b^3\)
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1. sketch the graph of an exponential function using transformations an…
- Domain: \( (-\infty, \infty) \) - Range: \( (-\infty, 2) \) - Horizontal Asymptote: \( y = 2 \)
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question 16 of 64 step 1 of 2 no time limit consider the following poly…
two (corresponding to the option "two")
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simplify. (-10 - 4i)10 write your answer in the form a + bi.
\(-100 - 40i\)
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express your answer as a decimal. 606 \\div 15 = \\square
40.4
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each large square is a whole. divide. hint: use the image to help visua…
4
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consider the following polynomial. h(x) = -2x² + 4x - 11 step 2 of 2: d…
For \( h(x)\to\) \(\boldsymbol{-\infty}\) as \( x\to-\infty\) and \( h(x)\to\) \(\boldsymbol{-\infty}\) as \( x\to\infty\)
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use transformations of the graph of f(x)=2^x to graph the given functio…
- **Asymptote Equation**: \( y = 2 \) - **Domain of \( g(x) \)**: \( (-\infty, \infty) \) - **Range of \( g(x) \)**: \( (2, \infty) \) - **Graph Description**: The graph of \( g(x…
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multiply. 30 × 2,000 = \\boxed{}
\(60000\)
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radical expressions 16^(1/2) simplify ?
4
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use the elementary properties of logarithms to solve the following equa…
\(x=\frac{16}{1}\) (or simply \(16\))
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question 7 of 24 step 1 of 1 no time limit solve the following elementa…
\(x = 4\)
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find equations for the vertical asymptotes, if any, for the following r…
\( x = -1 \)
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consider the following polynomial inequality. $x^2(x + 6)(x - 8) > 0$ s…
\(x=-6,0,8\)
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write the slope - intercept form of the equation for the line passing t…
\( y=\frac{4}{17}x+\frac{49}{17} \) (the fourth option: \( y=\frac{4}{17}x+\frac{49}{17} \))
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code: ______ name: hugo andre t. galang section: 9 - mdl 4 - dec 2025 g…
To graph the inverse of a function, we use the property that the graph of the inverse function \( f^{-1}(x) \) is the reflection of the graph of \( f(x) \) over the line \( y = x …
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how does the system of checks and balances ensure that no single branch…
It allows each branch to review and limit the actions of the others
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4.1.5) graph the function on the coordinate plane below. include three …
To create the mapping: 1. Identify ordered pairs from the graph (e.g., \((-6, -3)\), \((-3, -1)\), \((0, 0)\), \((6, 4)\) - values may vary based on precise graph reading). 2. Dra…
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find the horizontal asymptote of $f(x) = \\frac{2x^2 + 3x + 6}{x^2 + 1}…
\( y = 2 \) (corresponding to the option with \( y = 2 \))
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graph the equation and give the intercepts. 2x - 3y = 6 ○ (0,-2) and (3…
\( (0, -2) \) and \( (3, 0) \)
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question 4 (multiple choice worth 5 points) (oa 03r mc) find the vertic…
A. \( x=-1,1 \) (assuming the first option is labeled as A with \( x=-1,1 \))
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consider the following polynomial function. $f(x) = x^2 - 3x - 4$ step …
To sketch the graph: The parabola \( f(x)=x^{2}-3x - 4 \) (opening upwards) is positive (above the x - axis) for \( x < - 1 \) and \( x>4 \), and negative (below the x - axis) for…
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evaluate the expression. \\log_{0.4} 14.1 \\approx \\square (type an in…
$-2.89$ (rounded to two decimal places, or more precise value as per calculation)
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move one answer to each box. restriction of state-level discrimination …
- Restriction of state - level discrimination: expanded individual rights and equality - Equal protection clause: expanded individual rights and equality - Citizenship for all bor…
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solve the following elementary exponential equation. 16^{-x} = 8 answer…
\(-\frac{3}{4}\)
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use common logarithms or natural logarithms and a calculator to evaluat…
(The answer depends on the specific logarithm expression. For example, if the expression is \(\log_{5}12\), the answer is approximately \(1.544\); if it is \(\log_{3}8\), the answ…
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solve the following logarithmic equation, using a calculator if necessa…
$x = 7.3$
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complete the table and then graph the function. $y = -4x + 14$ | x | y …
For \( x = 1 \), \( y = 10 \); for \( x = 2 \), \( y = 6 \); for \( x = 3 \), \( y = 2 \). So the completed table has \( y \)-values 10, 6, 2 for \( x = 1, 2, 3 \) respectively.
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evaluate the expression. \\log_{0.2} 11.3 \\approx \\square
\(\approx - 1.51\) (rounded to two decimal places, or more precise value as per calculation)
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solve the following elementary exponential equation. $9^x - 3 = 0$ answ…
\(\frac{1}{2}\)
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problems #13-16: sketch the graph of the inverse function for each func…
The function \( f(x)=\sqrt[3]{x - 4} \) is one - to - one and has an inverse. The domain of \( f(x) \) is all real numbers (\( (-\infty,\infty) \)).
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find equations for the vertical asymptotes, if any, for the following r…
none
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log_f \\frac{\\sqrt{s} t^6}{r^2} = \\square (simplify your answer.)
\(\frac{1}{2}\log_{f} s + 6\log_{f} t - 2\log_{f} r\)
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solve the following elementary exponential equation. \\(100^{-x} = 10^{…
\(\frac{8}{3}\)
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over the interval -1 < x < 2, the graph of the polynomial shown could b…
2. increasing
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find equations for the vertical asymptotes, if any, for the following r…
\(x=\frac{7}{3}\)
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log (1000y)
$3 + \log(y)$ (or $\log(y) + 3$)
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question 16 of 24 step 1 of 1 no time limit write the following logarit…
$9^5 = G$
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find the domain of the logarithmic function. f(x) = log (4 - x) the dom…
\((-\infty, 4)\)
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question 15 of 24 step 2 of 2 consider the following polynomial functio…
- Positive regions: \( x < - 1 \) and \( x>4 \) (plot above x - axis in these intervals) - Negative region: \( -1<x<4 \) (plot below x - axis in this interval)
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test yourself! practice tool the graph of functions f(x) and g(x) are s…
The correct options are \( \boldsymbol{g(x)=-f(x)+3} \) and \( \boldsymbol{g(x)=-|x| + 3} \) (i.e., the fourth and fifth options: \( \boldsymbol{g(x)=-f(x)+3} \), \( \boldsymbol{g…
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f(x) = x² - 3x - 4 step 1 of 2: plot the x-intercepts, if any, of the p…
two (corresponding to the option "two")
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the function f(x) is shown on the graph. what is the equation of f(x)?
The equation of the function $f(x)$ is $f(x)=\begin{cases}2x + 8, & x\lt - 2\\-2x, & x\geq - 2\end{cases}$ or in absolute - value form $f(x)=-2|x + 2|+4$. If we simplify the absol…
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find equations for the horizontal asymptotes, if any, for the following…
\( y = 0 \)
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consider the following polynomial. h(x) = x² - 9x - 7 step 2 of 2: desc…
For \( h(x) \to \) \(\boldsymbol{\infty}\) as \( x \to -\infty \) For \( h(x) \to \) \(\boldsymbol{\infty}\) as \( x \to \infty \)
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convert the following fraction to a decimal. \\(\\frac{3}{4}\\) \\(\\bi…
B. 0.75
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find equations for the vertical asymptotes, if any, for the following r…
\( x = 8 \)
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is the function $y = \\frac{3}{5} - \\frac{3}{2}\\sqrt{x}$ linear or no…
nonlinear
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convert the following fraction to a decimal.\ \\(\\frac{57}{20}\\)\ \\(…
A. 2.85
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your answer assigned the 1928 agreement in which many nations agreed to…
D. The Worlds Organization established after World War I to promote peaceful cooperation among countries. (Note: There is a typo "Worlds" should be "World's" or "World", but this …
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find the slope of the line. what does the slope tell you about the spee…
The slope is \(20\). The speed of the car is \(20\) miles per hour.
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fill in the blank 1 point complete the square. find the vertex and root…
\(2(x + 3)^2 - 8 = 0\), \((-3, -8)\), \(-5\), \(-1\)
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convert the following fraction to a decimal. \\(\frac{9}{16}\\) \\(\\ci…
A. 0.5625
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question 28 the net area of the \\(\\int_{-5}^{5} \\frac{\\sin x}{\\sqr…
0, because the integrand is an odd function.
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question 27 find the indefinite integral: \\( \\int 3x(5x^2 + 3)^7 dx \…
\(\frac{3}{80}(5x^2 + 3)^8 + C\) (the first option: \(\boldsymbol{\frac{3}{80}(5x^2 + 3)^8 + C}\))
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solve the following. \\( \\frac{1}{11} \\div 5 = ? \\) \\( \\circ \\) a…
A. $\frac{1}{55}$
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question what is the value of \\(\\log_{7} \\sqrt4{343}\\)? answer atte…
\(\frac{3}{4}\)
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question 26 find all inflection points of the function: $g(x) = \\frac{…
Inflection points at \( x=-2,2 \) (the option with this text)
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slope intercept form from a graph questions answers customization quest…
\( y =-\frac{1}{2}x-3 \) (assuming the graph has slope \( -\frac{1}{2} \) and y - intercept \( - 3 \))
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refer to the graph of $y = f(x)$ provided to determine the interval(s),…
\( (-3, 3) \) (corresponding to the option "(-3, 3)")
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what is the value of $3^2 + 36 \\div 4 - 1$? 10.25 9.5 17 14
17
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question 20 find \\( \\frac{dy}{dx} \\) when \\( y^2 - 5x = 11 \\). \\(…
\(\boldsymbol{\frac{dy}{dx}=\frac{5}{2y}}\) (the option with this expression, e.g., if it's the last option: "The last option: \(\frac{dy}{dx}=\frac{5}{2y}\)")
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3. add 71 + (-121). 102 50 -102 -50
-50 (corresponding to the option with -50)