Calcul
Limites, dérivées, optimisation et comportement des fonctions.
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evaluate the expression. -1 × (4 + 15 × -11 ÷ -3)
$-59$
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amples write the equation of the function with the given transformation…
\( y=(x - 4)^2-7 \) ### Problem 6:
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11. which points are solutions to the inequality $y < -\frac{1}{2}x + 4…
The points that are solutions to \(y < -\frac{1}{2}x + 4\) are \((-2, -3)\) and \((1, -5)\). If the inequality were \(y \leq -\frac{1}{2}x + 4\), \((4, 2)\) would also be a soluti…
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eq: what is a parent function? how do we apply transformations to paren…
Let's solve these problems one by one. We'll start with the "State the parent function and the types of transformations" section, then move to "Write the equation of the function …
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question 4 of 8 which shows the correct setup to multiply the decimals?…
A. $\begin{align} &3345\\ &\underline{\times\ \ 64} \end{align}$ (and the identical second option, as they match the correct integer setup for decimal multiplication)
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evaluate the expression. 15 ÷ -3 + -13 × -5 - -18
83
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8 -48.6 - 13.4
\(-62\)
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evaluate the expression. (5 + -9 ÷ 3) × -3
$-6$
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how did consumers weaken the economy in the late 1920s? ○ consumers onl…
B. Consumers bought too many goods they could not afford.
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use the change of base formula to rewrite the logarithm in terms of the…
First part (rewritten form): $\frac{\ln(77)}{\ln(6)}$ Second part (evaluated value): $2.4247$
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15 $-\frac{7}{12} + \frac{1}{2}$
$-\frac{1}{12}$
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use the change of base formula to rewrite the logarithm in terms of the…
First, the rewritten form using natural logarithm is $\frac{\ln(36)}{\ln(9)}$. When evaluated and rounded to four decimal places, the value is $1.6309$.
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do now ** homework is to complete the packet ** 1) given the functions …
### Part (a) #### For function \( f(x) = x^2 - 2x + 5 \) ## Step1: Find \( f(-1) \) and \( f(2) \) To find \( f(-1) \), substitute \( x = -1 \) into \( f(x) \): \( f(-1) = (-1)^2 …
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1. $y = 3x + 1$ (and a coordinate grid chart)
To graph \( y = 3x + 1 \), plot points like \((0,1)\), \((1,4)\), \((-1,-2)\) and draw a straight line. (If calculating \( y \) for a specific \( x \), follow the substitution ste…
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on questions 1 - 9, graph each linear equation in the space provided. 1…
### For \( y = 3x + 1 \) # Explanation: ## Step1: Identify the slope and y-intercept The equation is in slope - intercept form \( y=mx + b \), where \( m \) is the slope and \( b …
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part of the graph of the function f(x) = (x + 4)(x − 6) is shown below.…
The vertex of the function is at (1,-25). The graph is negative on the entire interval -4 < x < 6.
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which is the graph of $f(x) = -(x + 3)(x + 1)$? (four graphs are shown …
The second graph (top middle, downward-opening parabola with x-intercepts at (-3, 0) and (-1, 0), y-intercept at (0, -3))
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add: -44 + 65 =
21
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add: -29 + -77 =
$-106$
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select the correct text in the passage. which phrase indicates a limit …
He started out with a sample size of 300 people
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add: -41 + 75 = sub
34
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add: 63 + 21 = submit
84
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add: -2 + -8 = 〇. submit
$-10$
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add: 3 + -5 = 〇. submit
$-2$
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determining key aspects of a quadratic function the graph of the functi…
maximum value The vertex is $(-1, 0)$ The function is positive: nowhere The domain is all real numbers The range is $y \leq 0$ The y-intercept is $(0, -1)$
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determine the domain on which the following graph of $f(x)$ is negative.
$(-\infty, -7) \cup (1, \infty)$
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analyzing a quadratic function the graph of the function $f(x) = (x + 6…
The axis of symmetry is x = -4. The domain is all real numbers. The function is negative over (-6, -2).
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find the vertex. f(x) = 3x² - 6x + 2 (?, )
$(1, -1)$
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16. slope (m) = y-intercept (b) = equation: 17. slope (m) = y-intercept…
slope (m) = \(-3\) y-intercept (b) = \(-2\) equation: \(y = -3x - 2\) ### Problem 17
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identifying key aspects of quadratic functions place each of the key as…
For $h(x)=(x-1)^2$: range: $\{y|y \geq 0\}$ decreasing over $(-\infty, 1)$ increasing over $(1, \infty)$ For $g(x)=-(x+1)(x-1)$: range: $\{y|y \leq 1\}$ increasing over $(-\infty,…
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find the solution to the system of equations. you can use the interacti…
$x = -2$ $y = 5$
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7) if $\\ln \\frac{\\sqrt{x}}{y^3} = a\\ln x - b\\ln y$, find the value…
$\frac{1}{2}$
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find the product. $4.8 \\times 10,000 = \\square$
\(48000\)
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what is the slope of this line? simplify your answer and write it as a …
3
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determine the domain on which the following function is decreasing.
The function is decreasing on the interval \((-\infty, 4)\) (or \(x < 4\)).
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solve the following system of equations graphically on the set of axes …
The solution (intersection point) is $\boldsymbol{(-6, -1)}$ To plot: 1. For $y=-\frac{2}{3}x-5$: plot $(0, -5)$ and $(3, -7)$, draw the line through them. 2. For $y=\frac{1}{3}x+…
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find the product. 0.75 × 100,000 = ?
\(75000\)
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multiple choice question indira is listening to an online presentation.…
Indira should not engage in multitasking because it has "switch costs," which can hinder cognition, productivity, memory, and creativity.
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the remaining 3 tenths have been unbundled for 30 hundredths. divide 30…
The top box is 2, the middle boxed pair is 0.22, and the bottom boxed pair is 0.08. The completed division shows $\frac{8}{11} \approx 0.72$ with a remainder of 0.08.
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the decimal representation of \\(\\frac{8}{11}\\) will be less than 1, …
The filled-in long division is: $$ \begin{array}{r} 0.7 \\ 11 \enclose{longdiv}{8.0} \\ \underline{-7.7} \\ 0.3 \end{array} $$ So the tenths place is 7, the subtracted value is 7.…
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name: finding slope (mixed) maze directions: begin at square (a) below.…
Path: A → E → I → J → F → C → G → D → H → FINISHED!
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which of the following could be a graph of the function below? $f(x) = …
A. <The graph with x-intercepts at x=-2 and x=6, opening upwards at both ends, and dipping below the x-axis between the intercepts>
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given the function below, fill in the table of values, use the table of…
### Completed Table: | $x$ | $\sqrt[3]{x}$ | $y = \frac{1}{4}\sqrt[3]{x}$ | |-----|---------------|-------------------------------| | $-8$ | $-2$ | $-\frac{1}{2}$ | | $-1$ | $-1$ …
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select all of the following graphs which represent y as a function of x…
- Top-left empty graph (the first grid with no curve) - Top-right linear graph (the downward-sloping line) - Middle-right wave graph (the oscillating curve) - Bottom-left polynomi…
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question 1-2 selected response: 1 point for correct answer only. examin…
$\boldsymbol{x = 3}$ is a triple root of the function.
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question 1-1 drop down: 1 point for correct answer only. what is the en…
As $x \to -\infty$, $f(x) \to -\infty$ and as $x \to +\infty$, $f(x) \to +\infty$
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question 2-2 sam and riley have been in a relationship for 3 months. th…
○ responsibility.
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comparing graphs of radical functions which of the following graphs hav…
The three graphs with the same domain are: - \( y = \sqrt{x} \) - \( y = 4\sqrt{x} \) - \( y=\sqrt{x}+4 \)
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graphing transformations of quadratic functions the graph of the functi…
$g(x) = -(x+4)^2 + 3$ *(Note for graphing: The vertex of $g(x)$ is at $(-4, 3)$, it opens downward, with the same width as $f(x)=x^2$)*
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comparing graphs of radical functions which of the following graphs are…
The two functions with identical graphs are \(y =-\sqrt[3]{x}\) and \(y=\sqrt[3]{-x}\) (i.e., the options \(y =-\sqrt[3]{x}\) and \(y=\sqrt[3]{-x}\)). In the given options, we sho…
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13. what is the purpose of a credit score? * a) to determine your eligi…
a) To determine your eligibility for a loan or credit card ### Question 14
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give the intervals of increase and decrease for the graph above. warnin…
(a) Increasing on the interval(s) \( (-\infty, -2) \) and \( (1, \infty) \) (b) Decreasing on the interval(s) \( (-2, 1) \)
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score on last try: 0.5 of 2 pts. see details for more. next question ge…
(a) Increasing on the interval(s) \((-\infty, - 2)\) and \((1,\infty)\) (or in the graph's visible domain, \((-5,-2)\) and \((1,5)\)) (b) Decreasing on the interval(s) \((-2,1)\)
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1. the position of a particle moving in the xy - plane is given by the …
C. 2 only
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look at this graph: graph of a parabola opening upwards with vertex in …
-7
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the following transformations were done to $f(x) = x^3$: up by 2 and fl…
Equation of transformed function: $\boldsymbol{-x^3 - 2}$ or $\boldsymbol{-x^3 + 2}$ Domain: $\boldsymbol{(-\infty, \infty)}$
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a parent function and transformed function are shown: $y = \\sqrt3{x}$ …
The three correct answers are: - compressed by a factor of 0.4 - translated 2 units right - reflected over the \( x \)-axis
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slope $m = \\frac{y_2 - y_1}{x_2 - x_1}$ $m = \\frac{14 - (-7)}{9 - (-5…
$\frac{3}{2}$
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what is the average rate of change of $g(x)$ over the interval $3, 6$? …
B. -2
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find the equation of the line that is parallel to y = 2x - 7 and contai…
\( y = 2x+12 \) (So the first box is 2 and the second box is 12)
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graph the function $f(x) = x$ after it has been vertically shifted 3 un…
The graph is the straight line of $y = x + 3$, passing through points like $(-2,1)$, $(0,3)$, and $(2,5)$, drawn using the line tool on the grid.
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find the equation of the line passing through the points (5,21) and (-5…
\( y = 5x-4 \)
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evaluating functions given the function, evaluate. be sure to use the o…
a. $g(8) = -129$ b. $f(6) = 16$ c. $k(4) = 2$ d. $h(3) = 23$
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does the equation $x - y^2 = 144$ define $y$ as a function of $x$? \\bi…
no
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the functions r and s are defined as follows. r(x) = -x - 1 s(x) = -x² …
$-34$
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the functions q and r are defined as follows. q(x) = -x + 1 r(x) = x² +…
6
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does the equation $x^2 + y = 141$ define $y$ as a function of $x$? \\bi…
yes
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does the equation \\( y = \\sqrt{x + 7} \\) define \\( y \\) as a funct…
yes
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multiple choice question indira is listening to an online presentation.…
Indira should not engage in multitasking because it has "switch costs," which can hinder cognition, productivity, memory, and creativity.
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let ( l^{-1} ) be the inverse function of ( l ). take ( x ) to be an ou…
The amount of time (in minutes) it takes to have x liters of liquid.
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what protections does the credit card act of 2009 provide?
1. Prohibits issuing credit cards to those under 21 without a co - signer (with income) or proof of independent ability to pay. 2. Limits rate hikes on existing balances (except f…
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what to look for when comparing credit cards. 1. 2. 3. 4. 5. 6. what is…
1. Annual Percentage Rate (APR) 2. Annual Fees 3. Rewards Program (e.g., cashback, points) 4. Credit Limit 5. Introductory Offers (e.g., 0% APR) 6. Late Payment Fees ### 2. What i…
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a line with a slope of 1 means that for every increase of 1 in x, y inc…
1
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analyzing functions using a table the function ( f(x) = x^5 + (x + 3)^2…
3
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analyzing graphs of functions which graph shows a function where f(2) =…
The top - most graph (the first one with the orange curve opening upwards, vertex at the origin, and passing through \((2, 4)\)) shows \( f(2)=4 \). (Assuming the first graph is t…
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solve by graphing. \\begin{cases} y = 2x + 3 \\\\ y = x + 1 \\end{cases…
$(-2, -1)$
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what is the equation for the horizontal asymptote of function f? y=2 y=…
y=4
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5 which of the following includes characteristics of capitalism? a. fre…
A. freedom of competition, market economy, supply and demand
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5. extend a concept consider the functions $f(x) = \\log_{4}(2x + 4)$ a…
a) $(3.3550, 1.7104)$ b) $-2 < x \leq -1.5$
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which of these linear functions has a greater slope? function a (a grap…
Function B has a greater slope.
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which of these linear functions has a smaller slope? function a input (…
Function B
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which of these linear functions has a smaller slope? function a a graph…
Function B
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how is the slope of a line calculated from a table? a. by dividing the …
a. By dividing the change in \( y \) by the change in \( x \)
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in the context of linear functions, what does it mean if two lines have…
b. They are parallel
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reconstruction acts of 1867 the reconstruction acts of 1867 sought to p…
B. to limit the rights of ex - slaves (assuming the options are labeled as A: to create a new government, B: to limit the rights of ex - slaves, C: to help many ex - slaves get jo…
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use a graphing calculator to solve the system of equations. $y = -2x^2 …
$(x,y)=(-2.22, 0.78)$ or $(x,y)=(-4.28, -1.28)$
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question 14 if $g(x) = x^2$, then which function represents a transform…
The function representing the transformation is \( f(x) = (x - 2)^2 - 5 \) (or expanded form \( f(x) = x^2 - 4x - 1 \))
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the polynomial function $f(x)$ is graphed below. fill in the form below…
The degree of \(f(x)\) is \(\boldsymbol{5}\) (odd) and the leading coefficient is \(\boldsymbol{\text{positive}}\). There are \(\boldsymbol{3}\) different real zeros and \(\boldsy…
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the graph of $y = f(x)$ is graphed below. what is the end behavior of $…
as \(x \to \infty, y \to \infty\) and as \(x \to -\infty, y \to -\infty\)
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which detail best supports the idea that ethics bowl differs from tradi…
B. Teams ask questions to expand discussion rather than refute opponents
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the graph of $y = f(x)$ is graphed below. what is the end behavior of $…
as \(x ightarrow-\infty,f(x) ightarrow-\infty\) and as \(x ightarrow\infty,f(x) ightarrow-\infty\)
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which detail best supports the idea that ethics bowl differs from tradi…
Teams ask questions to expand discussion rather than refute opponents
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unlimited and limited governments governments around the world can be d…
B. United States
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the graph of $y = f(x)$ is graphed below. what is the end behavior of $…
as \(x \to \infty, f(x) \to -\infty\) and as \(x \to -\infty, f(x) \to -\infty\)
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the function $f(x)$ is graphed below. how many points on the graph repr…
1
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question the function $f(x)$ is graphed below. how many points on the g…
1
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what does the y-intercept of the line tell you about the situation? bet…
Beth was traveling 12 miles per hour when she started braking.
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determine the domain on which the following graph of f(x) is positive.
The domain on which \(f(x)\) is positive is \(-4 < x<0\) (or in interval notation \((-4,0)\))
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skill practice - slope-intercept form a1: $y = 2x + 4$ and $y = -x + 1$…
The solution of the system of equations \( y = 2x + 4 \) and \( y=-x + 1 \) is \( x=-1,y = 2 \) or the ordered pair \( (-1,2) \)
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determine the domain on which the following graph of f(x) is negative.
\( (-\infty, 3)\cup(7, \infty) \)