微積分
極限、導數、最優化與函數性質。
-
seventh grade > b.12 add and subtract integers fns add: $-1 + -3 = \\sq…
$-4$
-
nth grade > ★ b.12 add and subtract integers add: $-2 + 2 = \\square$ s…
0
-
seventh grade > ★ b.12 add and subtract integers subtract: $-1 - 9 = \\…
$-10$
-
seventh grade > ★ b.12 add and subtract integers fns add: $-5 + 5 = \\s…
0
-
seventh grade > ★ b.12 add and subtract integers fns subtract: $-5 - 1 …
$-6$
-
$y=mx+b$ 4) $y=-\frac{2}{3}x-1$ 5) $y=-x-1$ 6) $y=-2x-4$ 7) $y=-\frac{1…
### Graphs: 4. Line through $(0,-1)$ and $(3,-3)$ 5. Line through $(0,-1)$ and $(1,-2)$ 6. Line through $(0,-4)$ and $(1,-6)$ 7. Line through $(0,-1)$ and $(2,-2)$ 8. Vertical lin…
-
1. determine the average rate of change of $f(x)=x^2 + 4x - 5$ on the i…
$m = 8$
-
seventh grade > ★ b.12 add and subtract integers fns subtract: $-1 - -2…
1
-
seventh grade > ★ b.12 add and subtract integers fns add: -4 + -1 = □ s…
$-5$
-
multiple-choice question to find the average rate of change we will use…
slope $= \frac{16-0}{3-1}$
-
question 5 of 14 step 1 of 2 consider the function: $h(x) = -4x^3 + 3x^…
43
-
venth grade > ★ b.12 add and subtract integers fns add: $3 + -3 = \\squ…
0
-
1. determine the average rate of change of $f(x)=x^2 + 4x - 5$ on the i…
(1, 0) (3, 16)
-
describe how the graph of the function $y = \\frac{4}{7} (x - 1)^2 + 3$…
vertical translation: 3 units up horizontal translation: 1 unit right dilation: Vertical compression by a factor of $\frac{4}{7}$ reflection: No reflection across the x-axis
-
describe how the graph of the function $y = -(x + 4)^2 - 6$ is related …
vertical translation: 6 units down horizontal translation: 4 units left dilation: No dilation (no stretch or compression) reflection: Reflected over the x-axis
-
does the parabola $y=2x^{2}-17x+7$ have a tangent line whose slope is -…
A. The parabola has a tangent line whose slope is -1. The equation of the tangent line is $y = -x -25$ and the point of tangency is $(4, -29)$.
-
1. determine the average rate of change of $f(x)=x^2 + 4x - 5$ on the i…
f(3) = 16
-
describe how the graph of the function is related to the graph of the p…
It is reflected over the x-axis, vertically stretched by a factor of 4, and has no horizontal/vertical shift.
-
question 9 1/1 pt the graph of $y=f(x)$ (solid) and $y=g(x)$ (dashed) i…
$-\infty$
-
compute the right-hand and left-hand derivatives as limits and check wh…
Left-hand derivative at $P(9,6)$: $\frac{1}{6}$ Right-hand derivative at $P(9,6)$: $2$ The function is not differentiable at point $P$.
-
$\\sqrt{128}$
$8\sqrt{2}$
-
9. a tangent function of the form $y = \\tan(bx)$ is defined for all va…
$\frac{1}{4}$ (any value $0<|b|\leq\frac{1}{4}$ is valid, $\frac{1}{4}$ is one example)
-
1. determine the average rate of change of $f(x)=x^2 + 4x - 5$ on the i…
f(1) = 0
-
1. determine the average rate of change of $f(x)=x^2 + 4x - 5$ on the i…
a = 1, b = 3
-
check all that apply: $\frac{sin(2x)}{sin(9x)} =$$square sinleft(\frac{…
$\frac{2}{9}$
-
vocab quiz 2 which statement best explains a key difference between saf…
Safety net programs provide direct assistance, while environmental policies set limits on actions to protect public goods
-
vocab quiz 2 2 of 10 a government limits industrial emissions even thou…
The use of regulatory power to protect environmental and public health
-
1) $y = \\frac{3}{4}x - 2$
The line $y=\frac{3}{4}x-2$ is graphed by plotting the y-intercept $(0, -2)$, using the slope to find a second point $(4, 1)$, and drawing a straight line through these two points.
-
steps for graphing 1 start by placing a point at the y-ic_ 2 from that …
2
-
y-intercept = $\boldsymbol{3}$ slope = $\boldsymbol{\frac{3}{2}}$ equat…
-3
-
graph the following features: - slope = 2 - y-intercept = $-2$ answer a…
The line $y=2x-2$ is graphed by plotting $(0, -2)$ and $(1, 0)$, then drawing a straight line through these points and extending it.
-
graphing sine, cosine and tangent ariel gaspar lopez 9 of 14 enter an e…
$f(x)=3.5\cos(x)$
-
name: _______ period____ find the slope, y-intercept of the line, and t…
1. $m=-\frac{4}{3}$, $b=\frac{20}{3}$, Equation: $y=-\frac{4}{3}x+\frac{20}{3}$ 2. $m=-\frac{3}{4}$, $b=-\frac{19}{4}$, Equation: $y=-\frac{3}{4}x-\frac{19}{4}$ 3. $m=0$, $b=3$, E…
-
which concept describes the idea that government and government officia…
rule of law
-
$24div(3+5)\times2$
6
-
the constitution regulates government powers byproviding guides and lim…
providing guides and limits to the government's power.
-
8. $32 + 12 \\div 4$
12
-
7. $(18 - 6) \\div 3 + 4$
8
-
question ⓘ governments may choose to censor access to the internet in a…
Preventing access to video or photo sharing services
-
3. twelve divided by the difference of 8 and 2
2
-
solve each problem paying careful attention to the order of operations.…
$(12 - 4) \div 2 = 4$ $9 + 2 - 6 = 5$ $3 + 2 \times 7 = 17$ $10 \div 2 - 1 = 4$ $9 - 6 \div 2 = 6$ $24 \div 2 - 8 = 4$ $(2 + 6) \times 7 = 56$ $12 - 12 \div 3 = 8$ $(4 + 6) \div 5…
-
2) $12 + 4^2$
28
-
28) $f(x)=-x^2 - 4x + 1$; find $f(1)$
$-4$
-
which best describes emersons central message to his contemporaries in …
One should follow one's conscience instead of what others dictate.
-
1 multiple choice 1 point what do we know about the family structure of…
1. They partnered with a spouse of their choice, raised small nuclear families, and occasionally separated and remarried. 2. Socities adopted male-dominated, extended families wit…
-
27) $f(x)=x^2 - 2x - 1$; find $f(2)$
$-1$
-
Question was provided via image upload.
$\frac{2}{5}$ ### Model Explanation (for the visual model): 1. Draw a rectangle, divide it vertically into 5 equal parts, shade 3 parts to represent $\frac{3}{5}$. 2. Divide the s…
-
read the excerpt from hemingways a farewell to arms. \it could not be w…
are still loaded with meaning.
-
key features of graphs 6. name: even degree or odd degree? end behavior…
Even Degree or Odd Degree? Even Degree End Behavior: As \(x\to\infty\), \(f(x)\to-\infty\); As \(x\to-\infty\), \(f(x)\to-\infty\) X-Intercepts: \((-6.861, 0)\), \((5.238, 0)\) Y-…
-
$f(x)=3x + 5$; find $f(-3)$ 28) $f(x)=-x^2 - 4x + 1$;
$-4$ Note: The second function $f(x)=-x^2-4x+1$ is incomplete (the value to evaluate is missing), so only the solution for $f(x)=3x+5; \text{Find }f(-3)$ is provided. If you provi…
-
25) $f(x) = -3x$; find $f(-3)$
9
-
slt12: key features of graphs name: 4. even degree or odd degree? end b…
Even Degree or Odd Degree? Odd Degree End Behavior: As $x\to-\infty$, $f(x)\to-\infty$; as $x\to+\infty$, $f(x)\to+\infty$ X-Intercepts: $(-1.8541, 0)$, $(0, 0)$, $(4.8541, 0)$ Y-…
-
evaluate each function for the given value. 24) $f(x) = -x^2 - 6x - 7$;…
$-2$
-
brain breaker #5: what would you do about the petition if you were the …
1. Brain Breaker #5: I would first review the colonial petition's grievances thoroughly, then negotiate a compromise that reduces the tax burden on colonists while upholding limit…
-
2. even degree or odd degree? end behavior: x-intercepts: y-intercept: …
Even Degree or Odd Degree? Odd Degree End Behavior: As $x\to+\infty$, $f(x)\to-\infty$; As $x\to-\infty$, $f(x)\to+\infty$ X-Intercepts: $(-2.84, 0)$, $(1, 0)$, $(2.52, 0)$ Y-Inte…
-
• the correct answer is: problem 3 $(5 + 3)^2 - 4 \\times 2$ student wo…
The student failed to follow the order of operations (PEMDAS/BODMAS) by not calculating the sum inside the parentheses $(5+3)$ first. Instead, they incorrectly calculated $3^2$ be…
-
solve each equation making sure to follow the order of operations. $2 \…
1. $2 \times 8 + 7$: 23 2. $2 + 3 \times 9$: 29 3. $4 + 10 \div 2$: 9 4. $9 - 2 + 3$: 10 5. $(3 + 2) \times 9$: 45 6. $8 \div (2 + 2)$: 2 7. $6 \div 2 - 1$: 2 8. $1 + 3 \times 5$:…
-
8 mark for review the industrialization of japan in the nineteenth cent…
D. A policy of imperial expansion that sought to take advantage of the political and military weakness of neighboring Asian states
-
the exponential function $g(x)=3^{x - 1}-4$ is a transformation of the …
B. $g(x)$ is translated 6 units down. E. $g(x)$ is translated 1 unit to the right.
-
thursday 2/5 what went wrong? - order of operations directions: each pr…
What went wrong? The student added before doing the required division step after calculating the exponent, violating the order of operations. Correct solution: $\frac{28}{3}$ (or …
-
question determine whether the following graph represents a function. a…
Not a Function
-
which of the graphs shown has a constant rate of change? a. graph w onl…
D. Graph X only
-
determine whether the function represents exponential growth or decay. …
The function $y = 500 \cdot 4^x$ represents exponential **growth**. Rewriting the base in terms of the rate of growth or decay results in the function $y = 500 \cdot \boldsymbol{(…
-
1. which of the following is equivalent to $76 \\div 9$? a) $\\frac{9}{…
1. B. $8\frac{4}{9}$ 2. A. 6 3. B. 72 inches 4. C. $10^3$
-
write an equation for the function whose graph is shown to the right. t…
$y=(x-2)^2 + 1$
-
find the slope of the line that passes through (1, 9) and (5, 4). simpl…
$\frac{-5}{4}$
-
find the slope of the line that passes through (5, 2) and (10, 5). simp…
$\frac{3}{5}$
-
write an equation for the function whose graph is shown to the right. t…
$y=(x-2)^2 - 1$
-
find the slope of the line that passes through (3, 8) and (8, 4). simpl…
$\frac{-4}{5}$
-
find the slope of the line that passes through (9, 10) and (6, 12). sim…
$-\frac{2}{3}$
-
determine the intervals where the function is increasing and decreasing…
Increasing intervals: $(0, 3)$ Decreasing intervals: $(-\infty, 0)$, $(3, \infty)$
-
divide fractions & mixed numbers - clue 1 crack the code by completing …
Completed fraction division results (with matching letters): 1. $\frac{7}{10} \div 1\frac{1}{6} = \boldsymbol{\frac{3}{5}}$ (S) 2. $\frac{5}{6} \div 1\frac{1}{2} = \boldsymbol{\fr…
-
i want you to remember, rate of change is the same thing as slope of a …
$\boldsymbol{\frac{y_2-y_1}{x_2-x_1}}$ (the first option)
-
answer as $x \\to \\infty, f(x) \\to -\\infty$ and as $x \\to -\\infty,…
as \(x \to \infty, f(x) \to \infty\) and as \(x \to -\infty, f(x) \to \infty\)
-
describe the behavior of this graph shown.a. as the input increases, th…
B. As the input increases, the output decreases for all values of x.
-
use a graphing utility with the standard viewing window to graph the fu…
The left graph (the one symmetric across the origin, passing through (0,0), with a peak in the second quadrant and a trough in the fourth quadrant)
-
move at least one of the 3 guide points below to complete the graph of …
1. Move the blue starting point from $(0,0)$ to $(2,0)$. 2. Move the first red point from $(1,1)$ to $(3,1)$. 3. Move the second red point from $(4,2)$ to $(6,2)$. The graph will …
-
which transformations to the graph of $j(x)$ would result in the graph …
horizontal compression by a factor of $\frac{1}{4}$ , and a translation 27 units down
-
review the expressions for $j(x)$ and $j(-x)$ $j(x)=\\frac{220}{x^3}$ $…
j(x) is an odd function.
-
form: 9. $g(x) = 15x - 9$
The graph of $g(x)=15x-9$ is a straight line passing through $(0, -9)$ and $(1, 6)$, with a steep positive slope of 15.
-
question 8 the graph below is the function $f(x)$ determine which one o…
$\boldsymbol{\lim_{x \to a} f(x) \text{ exists.}}$
-
write the equation of this line in slope-intercept form.
$y=\frac{1}{3}x$
-
11. higher order thinking without multiplying, decide which symbol belo…
$<$ --- ### For Question 12:
-
which is the graph of $y = \\sqrt3{2x}$?
This graph is **not** the graph of \(y = \sqrt[3]{2x}\). The correct graph of \(y = \sqrt[3]{2x}\) is an increasing function defined for all real \(x\), passing through the origin…
-
review the graph of $f(x) = \\sqrt3{x}$ and the graph of the transforme…
- $-f(x + 4)$
-
start start in 3-8, without multiplying, decide which symbol belongs in…
3. $>$ 4. $=$ 5. $<$ 6. $>$ 7. $<$ 8. $>$ 9. $\frac{5}{6} \times \frac{1}{4}, \frac{5}{6} \times \frac{6}{6}, \frac{5}{6} \times 1\frac{8}{9}, \frac{5}{6} \times 10\frac{1}{12}$ 1…
-
writing equations in slope-intercept formexample 1write an equation of …
1. $y = \frac{1}{4}x + \frac{5}{4}$ 2. $y = \frac{1}{2}x - \frac{7}{2}$ 3. $y = -\frac{1}{3}x + 6$ 4. $y = -x + 3$ 5. $y = \frac{1}{7}x + \frac{17}{7}$ 6. $y = -\frac{3}{4}x - \fr…
-
divide. give the exact answer, written as a decimal. $\\dfrac{2.1}{2}$
1.05
-
1. what are premium deposits in a variable annuitys subaccounts applied…
1. c. accumulation units 2. b. when the contract is the funding vehicle for a qualified plan 3. b. the insurer's general account
-
divide. give the exact answer, written as a decimal. $\\dfrac{\\square}…
1.6
-
graph the inverse of the provided graph on the accompanying set of axes…
Plot the points $(3, -10)$, $(2, -5)$, $(1, 0)$, $(0, 5)$, $(-1, 10)$ on the axes, then draw a straight line through them to get the inverse graph.
-
complete the sentences about the functions $f(x) = 5x + 12$ and $g(x) =…
For small values of $x$, the function with greater values is $\boldsymbol{f(x) = 5x + 12}$. For instance, $\boldsymbol{f(0)=12}$ whereas $\boldsymbol{g(0)=3}$. As the value of $x$…
-
find the inverse function in slope-intercept form (mx+b): $f(x)=3x+6$
$f^{-1}(x) = \frac{1}{3}x - 2$
-
find the inverse function in slope-intercept form ($mx+b$): $f(x) = x +…
$f^{-1}(x) = x - 9$
-
divide. give the exact answer, written as a decimal. 75.14 ÷ 5 =
15.028
-
multiple choice 8 points which graph description best matches: $f(x) = …
A vertical asymptote at $x = 0$ and an x-intercept at $x = 1$
-
what is the domain of the following rational function? $f(x) = \\frac{2…
$\{x|x eq 1\}$
-
divide. give the exact answer, written as a decimal. $overline{5)589.58…
117.916
-
given the rational function, $f(x) = \\frac{(x-2)(x+1)}{(x-2)}$, what i…
3
-
what is the horizontal asymptote of the following rational function? $f…
$y=0$