微積分
極限、導関数、最適化、関数挙動。
-
graph all vertical and horizontal asymptotes of the rational function. …
Vertical asymptote: $x = 1.5$ (a vertical dashed line at $x=1.5$ on the graph) No horizontal asymptote
-
what is the y-intercept of the polynomial $f(x)$ defined below? write t…
2
-
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 \(\boldsymbol{4}\) different real zeros and \(\boldsy…
-
the polynomial function $f(x)$ is graphed below. fill in the form below…
The degree of \(f(x)\) is \(\boldsymbol{4}\) and the leading coefficient is \(\boldsymbol{\text{positive}}\). There are \(\boldsymbol{2}\) different real zeros and \(\boldsymbol{1…
-
which graph represents the function $f(x) = \\frac{x^2 - 16}{x - 4}$?
The top-right graph (with an open circle at (4, 8) and closed point at (-4, 0))
-
use the graph of $y = f(x)$ to answer the following. part: 0 / 9 part 1…
$0$
-
(c) $h(t) = \\frac{1}{\\sqrt3{t - 5}}$ the domain in interval notation …
$(-\infty,5) \cup (5,\infty)$
-
find the value of k that transforms the graph of f(x) into graph g. the…
The value of \( k \) is \( -2 \), and the transformation is a vertical shift of the graph of \( f(x) \) down by 2 units.
-
write the domain in interval notation. part 1 of 3 (a) ( f(t) = sqrt3{t…
$(-\infty, \infty)$
-
11. determine the values of x for which the function f(x) = -3(x + 4)^2…
$x = -6$ and $x = -2$
-
find the sum. simplify if necessary \\(\\frac{2}{4} + \\frac{7}{8} = ?\…
1
-
identifying characteristics of a function and its inverse the following…
The true statements are: - The domain of \( h^{-1}(x) \) is the range of \( h(x) \). - The \( x \)-coordinate of the \( x \)-intercept of \( h^{-1}(x) \) is the \( y \)-coordinate…
-
find the sum. simplify if necessary. \\(\\frac{4}{5} + \\frac{1}{4} = ?…
1
-
determine the domain and range of the function. part 1 of 2 the domain …
$(-\infty, 2)$
-
the function ( f ) is defined as follows. ( f(x) = 2x^2 - 5 ) if the gr…
$h(x)=2x^2 - 1$
-
select the correct answer. which of these modes of narration does emily…
B. frame narrative
-
adding & subtracting decimals a. \\(\\begin{array}{r}.56\\\\ -.12\\\\ \…
a. $0.43$ b. $0.76$ c. $2.97$ d. $5.0$ e. $92.9$ f. $2.7$ g. $40.4$ h. $1.0$ i. $67.6$ j. $18.38$ k. $3.84$ l. $12.27$ m. $1.18$ n. $2.10$ o. $3.71$ p. $10.12$
-
(9) find the real roots of $y = x^3 - 3x^2 + x - 3$ by inspecting the g…
3
-
9) choose the best answer. given the equation, ( y = x^2 + 4 ), the ran…
1. The real root is $\boldsymbol{1}$ 2. $\boldsymbol{No\ real\ roots}$
-
10) what is $f(g(x))$? $f(x) = 3x + 5$ and $g(x) = 5x - 1$ $\\bigcirc$ …
$f(g(x)) = 15x + 2$ --- ### Question 11
-
determine the x- and y-intercepts for the given function. write your an…
x-intercept(s): $(9, 0)$ y-intercept(s): $(0, -3)$
-
determine the x- and y-intercepts for the given function. write your an…
x-intercept(s): $(3, 0)$ y-intercept(s): $(0, -15)$
-
12. the function ( f(x)=ln x ) is transformed so that the transformed f…
D. $g(x) = \ln(x - 5) + 3$ --- ### For Question 13:
-
a line has a slope of 7 and a y-intercept of -6. write its equation in …
\(y = 7x-6\)
-
find and simplify f(x + h). simplify your answer. f(x) = -8x² + 9x - 7 …
$-8x^2 - 16xh - 8h^2 + 9x + 9h - 7$
-
evaluate the function $g(x)=\frac{1}{x}$ for the given value of $x$. if…
Undefined
-
evaluate the function $f(x)=\\sqrt{x + 1}$ for the given value of $x$. …
2
-
the statement $f(-8) = -2$ corresponds to what ordered pair? the statem…
$(-8, -2)$
-
21. $y = x^2 + 2x + 1$ vertex: $x = \\frac{-b}{2a} = \\frac{-2}{2(}$
Vertex: $(-1, 0)$
-
identify the transformations of the graph of the parent function that p…
### Problem 2: Transformations: Reflection over $x$-axis, vertical shrink by $\frac{1}{2}$, shift up 4 units. Asymptote: $x=0$ ### Problem 3: Transformations: Vertical shrink by $…
-
10) choose the correct graph of $y = |x - 1| + 2$.
The correct graph is the third option (the V-shaped graph with vertex at (1, 2), passing through (0, 3) and (2, 3)).
-
y = 3x - 2; y = 4x + 3; y = 6/5x + 1.5
1. For $y=3x-2$: Line through $(0,-2)$, $(1,1)$, $(2,4)$ 2. For $y=4x+3$: Line through $(0,3)$, $(1,7)$, $(-1,-1)$ 3. For $y=\frac{6}{5}x-3$: Line through $(0,-3)$, $(5,3)$, $(-5,…
-
question: state the equation of the oblique (diagonal) asymptote for th…
\( y = 3x+3 \) (the option: \( y = 3x+3 \))
-
question: state the equation (if any) of the horizontal asymptote for t…
\( y =-\frac{2}{5} \) (corresponding to the option \( y=-2/5 \))
-
the americas. on december 2, 1823, monroe issued the monroe doctrine. m…
Spanish colonies were encouraged to revolt because the Monroe Doctrine (1823) declared the Americas off - limits to new European colonization, reducing the likelihood of new Spani…
-
evaluate the function $h(x) = -7$ for the given value of $x$. simplify …
$-7$
-
square grids $y = \\frac{1}{4}x - 1$ $y = -x + 2$ $y = x + 1$ $y = 4/2 …
Each line is plotted as follows: 1. $y=\frac{1}{4}x-1$: Line through $(0,-1)$ and $(4,0)$ 2. $y=-x+3$: Line through $(0,3)$ and $(1,2)$ 3. $y=x+1$: Line through $(0,1)$ and $(1,2)…
-
which of the following correctly solves the equation $ln(3) = ln(12 - 1…
\(x=\frac{3}{4}\) (corresponding to the option \(x=\frac{3}{4}\))
-
which graph represents the function $f(x) = \\frac{2}{x - 1} + 3$?
The top-left graph (the first option)
-
reasoning 7. the function $f(x)=|x - 7| + 5$ cannot have any zeros. why…
La fonction \(f(x) = |x - 7| + 5\) n'a pas de zéros car la valeur absolue \(|x - 7|\) est toujours supérieure ou égale à 0, donc \(|x - 7| + 5 \geq 5\) pour tout \(x\), et une fon…
-
9. the function ( f(x) ) is represented by the graph. the function ( g …
b) \( f(-2) < g(-2) \), c) \( f(4) > g(4) \), d) \( f(2) > g(2) \)
-
applications 6. the side profile of a roof has the equation shown below…
12 feet
-
5. for each absolute value function below, graph the function and then …
### Part (a): \( y = |x + 3| - 6 \) #### Step 1: Trouver le point de virage La fonction de valeur absolue est de la forme \( y = |x - h| + k \), où \( (h, k) \) est le point de vi…
-
why did the founding fathers create a weak central government under the…
C. to prevent abuse of power by the national government
-
limited government is the concept that a governments power over its cit…
A. the Bill of Rights
-
determine which graph represents a reflection across the x - axis of $f…
The bottom graph (the third graph shown) represents the reflection across the $x$-axis of $f(x)=3(1.5)^x$.
-
7. the graph shown represents the function ( h(x) = p(x) cdot q(x) cdot…
\( p(x)=x \), \( q(x)=x - 6 \), \( r(x)=x - 9 \) (or other linear functions corresponding to the roots of \( h(x) \))
-
this is the legal notion that the power of government is limited and re…
First concept: Rule of Law (legal notion limiting government power by law, not individual whims). Second concept: Procedural Due Process (government actions follow established rul…
-
write each decimal as a fraction or mixed number in simplest form. \\(1…
\(\frac{3}{40}\)
-
15/40 match each polynomial function to its graph. m(x)=x³+3x²+2x+1 a(x…
1. $m(x)=x^3+3x^2+2x+1$ matches the leftmost cubic graph (rising right, falling left) 2. $h(x)=-x^3+3x+...$ matches the second cubic graph from the left (falling right, rising lef…
-
part b which excerpt from the play most clearly supports the answer to …
A. Juliet. How camest thou hither, tell me, and wherefore? The orchard walls are high and hard to climb, And the place death considering who thou art.... Romeo. With love's light …
-
exponential - growth - and - decay $g(t)$ increases by 9 $g(t)$ increas…
\( g(t) \) increases by 9 (the option: \( g(t) \) increases by 9)
-
★ \we hold these truths to be self - evident, that all men are created …
B. limited government
-
how are the two functions $f(x) = 0.7(6)^x$ and $g(x) = 0.7(6)^{-x}$ re…
$g(x)$ is the reflection of $f(x)$ over the $y$-axis.
-
which graph represents a reflection of $f(x) = 6(0.5)^x$ across the $x$…
The middle graph (the second one, with the curve below the x-axis passing through (0, -6)) represents the reflection.
-
the function $f(x) = \\frac{3}{4}(10)^{-x}$ is reflected across the $x$…
$(2, -\frac{3}{400})$
-
add. 3.98 + 3.16 + 4.2
$11.34$
-
went camping with each other. if i wasnt at my house, i was at his hous…
D. He realizes the limits of his own knowledge.
-
add. 1.8 + 4.35 + 7.88
14.03
-
subtract. \\begin{array}{r} 26.46\\ -\\ 1.6\\ \\hline \\end{array} \\bo…
24.86
-
subtract. 79.64 - 58.18
\(21.46\)
-
subtract. \\begin{array}{r} 98.39 \\\\ -\\ 7.44 \\\\ \\hline \\end{arra…
\(90.95\)
-
which exponential function has an initial value of 2? (there is a table…
The exponential function represented by the bottom graph (with y-intercept at 2) has an initial value of 2.
-
!! your goal is to earn 10 points. 3. a) how many points of intersectio…
2 ### 3b)
-
sketch the graph of each linear inequality. 17) $y > 2x - 4$ 18) $y \\g…
### Problem 17: \( y > 2x - 4 \) # Explanation: ## Step 1: Graph the boundary line The inequality is \( y > 2x - 4 \). First, consider the boundary line \( y = 2x - 4 \). This is …
-
if the function ( g ) is defined by ( g(x)=\frac{x}{x + 1} ), which of …
\( g(10) < g(20) \) (the first option)
-
which is the graph of $f(x) = 100(0.7)^x$?
The top (first) graph with points $(0,100)$ and $(2,30)$ (approximating the exponential decay of $f(x)=100(0.7)^x$) is the correct graph.
-
h(x) = 3·4^x choose 1 answer: a graph a b graph b c graph c
A. <The graph with y-intercept at (0,3), passing through (1,12), approaching 0 as x approaches negative infinity>
-
choose the graph of the function. $g(x) = 2 \\cdot 4^x$ choose 1 answer…
A. <The graph passing through (0, 2) and (1, 8), with exponential growth approaching 0 as x approaches negative infinity>
-
choose the function that is graphed below. choose 1 answer: a ( y = 5 c…
C. $y = 5 \cdot 2^x$
-
choose the graph of the function. $f(x) = 2 \\cdot 3^x$ choose 1 answer…
A. <The graph passing through (0,2), rising steeply for positive x, and approaching 0 for negative x>
-
choose the function that is graphed below. choose 1 answer: a ( y = 6 c…
A. $y = 6 \cdot 2^x$
-
formative assessment look to the graph below and identify the key featu…
- y - intercept: \((0, 5)\) - x - intercept: \((2, 0)\) - Slope: \(-\frac{5}{2}\) (mark 'Negative') - Domain: \((-\infty,\infty)\) (or all real numbers) - Range: \((-\infty,\infty…
-
6. write the equation of the line shown on in slope - intercept form.
\( y = x + 5 \)
-
ebukas monthly rent is $750. if ebuka pays the rent late, his landlord …
$R(t) = 750(1.04)^t$
-
8. write the equation of the line shown on the grid in slope - intercep…
\(y = 2\) (assuming the lower horizontal line; if the upper one, but the graph shows the lower horizontal line with arrows. Wait, no, looking at the graph again, the horizontal li…
-
algebra: concepts and connections - plc exponential growth functions wh…
2.50
-
1. write the equation of the line shown on the grid in slope - intercep…
$y=\frac{2}{3}x + 4$
-
what does the term new woman mean? (1 point) a woman who has recently b…
a woman who resists limitations of society
-
which equation represents an exponential function that passes through t…
$f(x) = 4(3)^x$
-
when the dragons have lost their most recent game, 200 fans buy tickets…
\( t(w) = 200(1.1)^w \)
-
which is the graph of $f(x) = 2(3)^x$?
The bottom graph (with the marked point (1,6)) is the graph of $f(x)=2(3)^x$.
-
which of these shows the graphs of $y = x$ and $y = x^2$? a) graph b) g…
A) The graph with the upward - opening parabola (\( y = x^2 \)) and the line passing through the origin (representing \( y = x \) or a line through the origin along with the parab…
-
el agua debemos beber el agua para mantener la salud. 1. los tomates 2.…
1. Debemos comer los tomates para mantener la salud. 2. Debemos limitar las grasas para mantener la salud. 3. Debemos comer los plátanos para mantener la salud.
-
which was not one of the problems cities experienced as a result of rap…
B. limited recreation options
-
$\\sqrt3{216} = \\square$
6
-
slope: -3 y - intercept: 0
$y = -3x$
-
compare using >, <, or =. 236 + 10 + 10 98
$236 + 10 + 10 > 98$
-
post-world war i treaties a. ways these actions attempted to prevent wa…
s: - **A. Ways these actions attempted to prevent war**: - Limit of naval arms - Limit territorial expansion - **B. U.S. policy that these actions reflect**: - Isolationist Policy
-
$\\sqrt{1.69} = \\square$
1.3
-
name the excerpt. so it is enacted that this act may be cited as, \an a…
C. build an unlimited arsenal of weapons to fight Japan
-
compare using >, <, or =. 942 842 + 100 + 10
$942 < 842 + 100 + 10$
-
in the years following world war i, the united states adopted isolation…
- Decision not to join the League of Nations - Limiting territorial expansion in the Nine - Power Treaty - Signing the Kellogg - Briand Pact to stop war as “an instrument of natio…
-
select all of the odd functions. $g(x) = -x^3 + 7$ $w(x) = x^4 + 2x^2 -…
- \( p(x) = -x^5 + 2x^3 + 8x \) (select this) - \( m(x) = -4x^5 + x^3 \) (select this) - Deselect \( g(x) = -x^3 + 7 \) and \( w(x) = x^4 + 2x^2 - 9 \).
-
select all of the even functions.
The even functions are \( g(x) \) and \( k(x) \) (assuming the graphs: \( g(x) \) (top - left) and \( k(x) \) (bottom - right) are symmetric about the \( y \)-axis, while \( m(x) …
-
algebra: concepts and connections - plc exponential growth functions re…
The graph will show an initial value that is lower on the y-axis.
-
which graph represents the function? $f(x) = \\frac{1}{x - 1} - 2$
The top-right graph (the second option)
-
which statements are true of the function ( f(x) = 3(2.5)^x )? choose t…
1. The domain of the function is all real numbers. 2. The function is exponential. 3. The function increases by a factor of 2.5 for each unit increase in $x$.
-
algebra: concepts and connections - plc exponential growth functions de…
3
-
d. \\(\\log_{6}(x^{2} - 9) + \\log_{6}(3) = 3\\)\\(\\log_{4}(10) - \\lo…
For $\log_{6}(x^2 - 9)+\log_{6}(3)=3$, $x = 9$ or $x=-9$; for $\log_{4}(10)-\log_{4}(x + 3)=\log_{4}(x)$, $x = 2$