Calcul
Limites, dérivées, optimisation et comportement des fonctions.
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question 5. henrietta drew a graph of the function below. $f(x) = 3\\sq…
D. The graph that starts at (0,0) and increases for \( x\geq0 \) (matching the parent function \( y = \sqrt{x} \))
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find the inverse of $f(x)=\frac{2}{3}x - \frac{1}{3}$. the inverse is $…
$g(x) = \frac{3}{2}x + \frac{1}{2}$
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find the inverse of $f(x)=-\frac{1}{2}x + 4$. the inverse is $g(x)=squa…
$g(x) = -2x + 8$ (For graphing: Plot the line through points $(0,8)$ and $(4,0)$ as the inverse function)
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lines from point/slope (diagonal only) score: 2/3 penalty: 1 off questi…
$y = 2x - 6$
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find the inverse of \\( f(x) = 6x \\).\ the inverse is \\( g(x) = \\squ…
$g(x) = \frac{x}{6}$ Graph details: 1. For $f(x)=6x$: Draw a line through $(0,0)$ and $(1,6)$. 2. For $g(x)=\frac{x}{6}$: Draw a line through $(0,0)$ and $(6,1)$.
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solve $y = f(x)$ for $x$. then find the input when the output is $-3$. …
$x = \sqrt[3]{y + 3} - 2$ The input is $-2$ when the output is $-3$.
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question 4 of 7 the graph of an exponential function is shown in the fi…
## Question 3 (table values): | $x$ | $y$ | |-----|-----| | $-2$ | $\frac{5}{16}$ | | $-1$ | $\frac{5}{8}$ | | $0$ | $\frac{5}{4}$ | | $1$ | $\frac{5}{2}$ | | $2$ | $5$ | ## Quest…
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find the rate of change and initial value for the linear function. a) t…
a) The rate of change (slope) is $1$ b) The initial value (y-intercept) is $-7$
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find the rate of change and initial value for the linear function a) th…
a) The rate of change (slope) is $\frac{7}{8}$ b) The initial value (y-intercept) is $-8$
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6. maximum mark: 8 the diagram shows a square prism of length ( l ) cm …
(a) Derived as shown: $l = \frac{k - 2x^2}{4x}$ (b) Proven that the maximum volume occurs when the prism is a cube.
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y = 0.4^x (a) choose the graph that best represents the shape of this f…
(a) Graph 2 (b) positive (c) Domain: $-\infty < x < \infty$ Range: $y > 0$ (d) x-intercept(s): None y-intercept(s): $(0, 1)$ (e) As x increases, y approaches 0. As x decreases, y …
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7. mr. yung orders 3 pizzas. he cuts the pizzas into the number of equa…
1. (Visual: Mushroom pizza split by 1 center line; Pepperoni pizza split by 4 center lines; Cheese pizza split by 2 center lines) 2. (Visual: 1 half of the Mushroom pizza shaded) …
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find the approximate value of h(-2) for the function below. h(x) = 22e^…
D. 70.98
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solve the following system of equations graphically on the set of axes …
The solution (intersection point) is $(6, 6)$. To graph: 1. For $y=-\frac{1}{6}x+7$, plot $(0, 7)$ and $(6, 6)$, then draw the line through them. 2. For $y=2x-6$, plot $(0, -6)$ a…
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(1 point) \\(\\circ\\ y = \\frac{9}{4}x + \\frac{11}{8}\\) \\(\\circ\\ …
$y=\frac{11}{8}x+\frac{9}{4}$ (the second option)
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y = 2x + 3\ y = -2x + 15
The solution is \( x = 3 \), \( y = 9 \) (or the ordered pair \( (3, 9) \))
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the new deal brings new opportunities (pages 504 - 505) how did the new…
- **Expanded opportunity**: Many New Deal agencies did not discriminate in hiring, which gave women more job opportunities (e.g., more women were appointed to important federal jo…
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the new deal affects many groups before you read in the last section, y…
to question 1 (Describe two ways that the New Deal expanded and limited opportunities for women): - **Expanded opportunities**: - More women were appointed to important federal jo…
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match each exponential function to its graph. $h(x) = 1.5^x$ $q(x) = 2.…
- Top - left graph: \( j(x)=4.5^x \) - Top - right graph: \( q(x)=2.5^x \) - Bottom - left graph: \( m(x)=3.5^x \) - Bottom - right graph: \( h(x)=1.5^x \)
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what was joseph stalins goal in creating a command economy? to graduall…
D. to outproduce capitalist nations
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what is 0.1·20? 10% of 20 = 0.1·20 = \\square
\(2\)
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1. what long - term issue did reconstruction fail to resolve? a. the ro…
1. b. Racial equality and justice 2. d. His violation of the Tenure of Office Act 3. b. End of Reconstruction 4. c. Resistance from Southern states 5. d. To limit the president's …
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graph the following linear equation. $y = 3x + 7$ step 2 of 3: plot the…
The \(y\)-intercept of the line \(y = 3x+7\) is the point \((0,7)\), so we plot the point \((0,7)\) on the graph (on the \(y\)-axis at \(y = 7\)).
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solve the following equation for x: \\(\\ln(x + 9) + \\ln(x + 3) = \\ln…
\(-2\)
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the population of a city is modeled by the equation $p(t) = 230,000 + 7…
The rate of change of the population after 5 years is 7000 people per year.
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what is the domain of this quadratic function?
The domain of the quadratic function is all real numbers, which can be written as \( (-\infty, \infty) \) (or \( \{x | x \text{ is a real number}\} \)).
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for the given cost function ( c(x) = 72900 + 300x + x^2 ) find: a) the …
The cost at the production level 1050 is \( \boldsymbol{1490400} \). ### Part (b)
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solve for a positive value of x.\\(\\log_{4}(64) = x\\)
3
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the number of mybook members, in millions, can be approximated by the f…
The number of Mybook members is changing at a rate of 133 million members per year in 2017.
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in exercises 27–32 find a parametrization for the curve. 28. the line t…
A possible parametrization is \(x=-3 + 8t\), \(y=-3 + 4t\) for \(t\in\mathbb{R}\) (or equivalent forms like \(x=-3+2t\), \(y=-3 + t\) for \(t\in\mathbb{R}\))
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in exercises 61–64, solve the problem without using a calculator. 61. m…
A. \((-3, -2)\)
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and identify the graph of the parametric curve. in exercises 11–26, use…
The equation after eliminating the parameter is \( x = 4 - y^2 \) (or \( y^2 = 4 - x \)), and the graph is a parabola opening to the left.
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and identify the graph of the parametric curve. in exercises 11–26, use…
The equation after eliminating the parameter is \( x=(y - 1)^{2} \), and the graph is a parabola opening to the right with vertex at \( (0,1) \).
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and identify the graph of the parametric curve. in exercises 11–26, use…
The rectangular equation after eliminating the parameter is \( y = -\frac{1}{3}x+\frac{17}{3} \) (or equivalent forms like \( x + 3y=17 \)), and the graph of the parametric curve …
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y = 2x² - 20x + 18
The vertex of the parabola \( y = 2x^2-20x + 18 \) is \( (5,-32) \)
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y - x² = 18 - 20x
\( y = x^2 - 20x + 18 \)
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what is the slope of the line represented by the equation $y = \\frac{4…
\(\frac{4}{5}\) (corresponding to the option \(\boldsymbol{\frac{4}{5}}\))
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use a graphing utility to graph the equation. use a standard setting. a…
x - intercept \((x,y)=(-5,0)\) y - intercept \((x,y)=(0,5)\)
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two functions are graphed on the coordinate plane. which represents whe…
\( f(-4) = g(-4) \) and \( f(0) = g(0) \) (the second option: \( f(-4) = g(-4) \) and \( f(0) = g(0) \))
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if f(x) = 5x + 40, what is f(x) when x = -5? -9 -8 7 15
15 (assuming there was a typo and \( x = - 5 \) instead of \( x=-52 \), as the calculation with \( x=-5 \) gives 15 which is an option)
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what is the inverse of the function $f(x) = 2x - 10$?\ \\(\\bigcirc\\) …
$h(x) = \frac{1}{2}x + 5$ (the fourth option)
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the function g(x) is graphed. which statements about the function are t…
B. $g(0)=0$ D. $g(1)=1$ E. $g(-1)=1$
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which is true regarding the graphed function f(x)? $f(0) = 3$ $f(5) = -…
B. $f(5) = -1$
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the point (-3, -5) is on the graph of a function. which equation must b…
A. $f(-3) = -5$
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waterworks is a company that manufactures and sells paddleboards. its p…
In order to make a profit, Waterworks must produce more than $\boldsymbol{2000}$ and fewer than $\boldsymbol{10000}$ paddleboards.
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complete the expression 481 -180 ← 18 × dropdown 301 -180 ← 18 × 121 - …
Top blank: 10, Second blank: 10, Third blank: 5, Bottom blank: 1
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example 1 determine the consecutive integer values of x between which e…
Let's solve these problems one by one. We'll use the Intermediate Value Theorem, which states that if a function \( f(x) \) is continuous on an interval \([a, b]\), and \( f(a) \)…
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which function has a maximum at (2, 0)?
The function represented by the purple graph (second option from left)
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identify a root options: (0,0), (-1,9), (0,-8), (-4,0)
D. (-4,0)
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which function has a maximum at (2, 0)?
The function represented by the orange graph (third option, with vertex at (2, 0))
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the picture shows the $4.88 josephine spent on a package of 4 pens. dra…
Each pen costs $\$1.22$
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the function g is defined as follows. $g(x) = -2x^2 + 4$ if the graph o…
\( f(x)=-2x^{2} \)
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calculators are allowed on this portion of the test. 1. the number of p…
$V = 50000(0.97)^t$
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find the product in simplest radical form. \\(\\sqrt3{-13} \\cdot \\sqr…
$\sqrt[3]{26}$
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write the expression in simplest radical form. \\sqrt3{945}
$3\sqrt[3]{35}$
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determine whether the system of equations has no solution, one solution…
one solution, (2, -1)
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which event challenged president thomas jeffersons beliefs about the co…
A. the Louisiana Purchase
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donna is going to rent a truck for one day. there are two companies she…
The inequality is \( 84 < 75 + 0.60m \) and the solution is \( m > 15 \). So when the number of miles driven \( m \) is greater than 15, Company A will charge less than Company B.
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table of values and use the table values to graph. $y = -3x - 5$ | $x$ …
For \(x=-3\): - \(-3x\) value: \(9\) - \(y = -3x - 5\) value: \(4\) The complete table is: | \(x\) | \(-3x\) | \(y=-3x - 5\) | |-------|---------|---------------| | \(-3\) | \(9\)…
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write a cubic function whose graph is shown.
$y = x^3 - 7x^2 + 10x$
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consider the line ( 9x + 6y = -3 ). what is the slope of a line paralle…
Slope of a parallel line: \(-\frac{3}{2}\) Slope of a perpendicular line: \(\frac{2}{3}\)
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consider the line -4x - 5y = 3. what is the slope of a line perpendicul…
Slope of a perpendicular line: \(\frac{5}{4}\) Slope of a parallel line: \(-\frac{4}{5}\)
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finding asymptotes in exercises 1–4, find all ve asymptotes of the grap…
Let's solve each function for its vertical asymptotes (I'll assume "ve" in the problem is a typo for "vertical"). A vertical asymptote occurs where the function is undefined (deno…
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given the function below, fill in the table of values and use the table…
For \( x = -3 \), \( y = -4 \); for \( x = -2 \), \( y = -4 \); for \( x = -1 \), \( y = -4 \); for \( x = 0 \), \( y = -4 \); for \( x = 1 \), \( y = -4 \); for \( x = 2 \), \( y…
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question given the function below, fill in the table of values and use …
The table is filled with \( y = 5 \) for all given \( x \)-values. The graph is a horizontal line at \( y = 5 \) passing through the plotted points \((-3, 5)\), \((-2, 5)\), \((-1…
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the graph of a function f is shown. how many real zeros does f have? re…
3 real zeros.
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given the function below, fill in the table of values and use the table…
For \( x=-3 \), \( y = 5 \); for \( x=-2 \), \( y = 5 \); for \( x=-1 \), \( y = 5 \); for \( x=0 \), \( y = 5 \); for \( x=1 \), \( y = 5 \); for \( x=2 \), \( y = 5 \); for \( x…
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the function $y = f(x)$ is graphed below. what is the average rate of c…
$-4$
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-42 ÷ (-1) ÷ 3
14
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the function $f(x)$ is graphed below. how many points on the graph repr…
1
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(4×3×8 + 9 + 9)
114
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is this point a max or min? max min
max
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describe the transformation from the graph of f to the graph of h. 9. f…
9. The graph of $h(x)$ is a horizontal compression of the graph of $f(x)$ by a factor of $\frac{1}{4}$. 10. The graph of $h(x)$ is a vertical compression of the graph of $f(x)$ by…
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describe the transformation from the graph of f to the graph of g. 1. $…
1. The graph of $g$ is the graph of $f$ shifted down 2 units. 2. The graph of $g$ is the graph of $f$ shifted right 3 units. 3. The graph of $g$ is the graph of $f$ shifted left 4…
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3 for each graph of a polynomial function, state the minimum degree, st…
The zeros of \( f(x)=-\frac{1}{6}P(x) \) are \( x=-2 \) (multiplicity 3) and \( x = 1 \) (multiplicity 2). ### Part 4c(iii): Zeros of \( h(x)=P(x - 10) \)
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*24. write \\(\\frac{1}{2}\\) and \\(\\frac{1}{5}\\) as fractions with …
$\frac{7}{10}$
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evaluate the function for the given value of x.\\(g(x) = x^6 - 64x^4 + …
$-43$
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document 4 le gouvernement libéral de lomer gouin adopte une loi limita…
Since no specific question is provided about these documents, it's not possible to give a targeted answer. If you want to analyze these documents (for example, about historical co…
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3. the median home price in a country over the period january 2011 to j…
The average rate of change is 11.2 thousand dollars per year.
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problem. 19 : calculate the following limit. (if the limit does not exi…
$-\dfrac{1}{3}$
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for the given polynomial p(x) and the given c, use the remainder theore…
$57$
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problem. 13 : evaluate the limit using the appropriate limit law(s). (i…
DNE ### Problem 14
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graph the equation $y = \\frac{1}{2}x + 3$.
To graph \( y=\frac{1}{2}x + 3 \): 1. Plot the y - intercept at \( (0,3) \). 2. Use the slope \( \frac{1}{2} \) to find another point: from \( (0,3) \), move right 2 units and up …
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problem. 5 : determine if the limit approaches a finite number, $\\inft…
\(\frac{3}{10}\) ### Problem 6
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problem. 3 : determine if the limit approaches a finite number, \\(\\in…
\(0\) ### Problem 4
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graph the system of equations, and determine the solutio $y = -dfrac{3}…
The system has no solution, as the two lines are parallel and never intersect.
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graph the equation $y = \\frac{1}{3}x - 2$. slope: $\\frac{1}{3}$ use t…
To plot another point on the line \( y = \frac{1}{3}x-2 \) using the slope \( \frac{1}{3}=\frac{\text{rise}}{\text{run}} \): 1. Start from the y - intercept point \( (0,-2) \). 2.…
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abstract. practice problems for lecture problem. 1 : determine if the l…
1. $18$ 2. $-1$ 3. $\frac{33}{13}$ 4. $-2$
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graph and determine the solution of the system y = 6x - 3 \\(\\frac{1}{…
The system has infinitely many solutions, represented by all points on the line $y = 6x - 3$.
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solve the following. $(4.78 \\times 10^9) \\times (7.24 \\times 10^3)$ …
a. $3.4607 \times 10^{13}$
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graph each equation. estimate the solution of the system of equa y = 2x…
The solution of the system is $x=-2.5$, $y=-1$ (or the point $(-2.5, -1)$)
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question 16 (4 points) solve the following system graphically or algebr…
The solutions are $(2, 0)$ and $(3, 1)$
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graph the system of equations to determine the solution. $y = \\frac{2}…
The solution is $(3, 3)$ (this is the intersection point of the two lines when graphed)
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n identify its domain 5. $f(x) = \\sqrt3{x + 2}$
The domain of \( f(x)=\sqrt[3]{x + 2} \) is all real numbers, which can be written in interval notation as \( (-\infty, \infty) \) or in set - builder notation as \( \{x|x\in\math…
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consider the following. \\(\\lim\\limits_{x \\to 0} \\frac{\\sin(2x)}{x…
### Completed Table: | $x$ | $f(x)$ | |-------|--------| | $-0.1$| 1.9867 | | $-0.01$| 1.9999 | | $-0.001$| 2.0000 | | $0.001$| 2.0000 | | $0.01$| 1.9999 | | $0.1$| 1.9867 | $\lim…
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match each expression to a reasonable estimate. 186 ÷ 6 98 ÷ 2 43 ÷ 4 a…
- \(186 \div 6\) matches \(30\) - \(98 \div 2\) matches \(50\) - \(43 \div 4\) matches \(10\)
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41. 80 + (-60) - 80 + 70
$10$
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rewrite each expression using the then compute.) 2. 9 - 9
$0$
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27. 23 - |11|
12
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decide whether the following problem can be solved using precalculus or…
0.4 miles per mile (the rate of change of elevation at $x=1$ is 0.4)