微積分
極限、導関数、最適化、関数挙動。
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think about the division expression $\frac{2}{5} div \frac{3}{5}$. do y…
Less than 1, because only part of $\frac{3}{5}$ fits into $\frac{2}{5}$.
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chapter 2 → lesson 8: add, subtract, multiply, & divide decimals 1. at …
1. A. 11.92 seconds 2. C. 9.982 3. B. 14.5 ft 4. D. 10.17 5. A. 2.18
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based on the declaration of independence, which statement best describe…
B. Government is necessary in any society to protect the rights of the citizens.
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exam: retail industry fundamentals (july 2024 release) question 43 of 5…
D. Make tasks easier and faster to complete for employees and customers.
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4. the graph of $y=3x$ is shown below. a constant is added to the equat…
From top to bottom, the missing values are: $\boldsymbol{-6}$, $\boldsymbol{-3}$, $\boldsymbol{0}$, $\boldsymbol{3}$
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finding slope from a graph date___________ period____ find the slope of…
1) Slope: $-\frac{3}{5}$; Points: $(-6, 4)$, $(4, -2)$ 2) Slope: $\frac{1}{2}$; Points: $(-4, -2)$, $(2, 1)$ 3) Slope: $-\frac{5}{6}$; Points: $(-4, 2)$, $(2, -3)$ 4) Slope: $-\fr…
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find the difference. $\frac{1}{3} - \frac{1}{12} = \frac{?}{?}$
$\frac{1}{4}$
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find the difference. $\frac{1}{2} - \frac{1}{10} = \frac{1}{10}$ done s…
$\frac{2}{5}$ Note: The partially filled answer $\frac{1}{10}$ in the image is incorrect; the correct numerator after subtraction is 4, which simplifies to $\frac{2}{5}$.
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4) find the difference. $\frac{1}{5}-\frac{1}{10}=\frac{\boxed{?}}{\box…
$\frac{1}{10}$ (Top box: 1, Bottom box: 10)
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first, find an equivalent expression with whole number divisor: $117\\d…
$4.5$
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which expression is equivalent to $3,400 \\div 2$ find the quotient. $3…
1700
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theo says the standard algorithm shows that 34theo had trouble because …
3,400 ÷ 2
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before prof. ribleys challenging, calculus exam, everyone hoped to make…
Remove the comma between challenging and calculus.
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the \zoot suit\ riots of 1943 were a series of fashion shows in hollywo…
highlighted the limits of racial tolerance during World War II.
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find slope the slope of a line is the ratio of change in the y-coordina…
1. $1$ 2. $-2$ 3. Undefined 4. $\frac{4}{3}$ 5. $-\frac{2}{7}$ 6. $0$ 7. $\frac{4}{5}$ 8. $-\frac{3}{4}$ 9. $0$ 10. $r=-4$ 11. $r=3$ 12. $r=6$ 13. $r=-5$ 14. $r=11$ 15. $r=\frac{2…
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look at this graph: what is the y-intercept?
4
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what is $lim_{h \to 0} \frac{8left(\frac{1}{2}+h ight)^8 - 8left(\frac{…
$\frac{1}{2^{\frac{7}{8}}}$ (or $\frac{1}{\sqrt[8]{128}}$)
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iii. $int_{1}^{7} f(x) dx = 14$ find $f(x)$. show your work. 60. the gr…
(a) $g(4) = -1$, $g(-2) = -\frac{9}{2}$ (b) $1$ (c) The absolute minimum value is $-\frac{9}{2}$, since it is the smallest value of $g(x)$ evaluated at critical points and endpoin…
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look at this graph: what is the minimum value of this function?
-3
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20 multiple choice 10 points write the equation of a function $g(x)$ wh…
$\boldsymbol{\frac{1}{3}|x + 5| + 7}$ (corresponding to the last option)
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look at this graph: what is the minimum value of this function?
$-7$
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submission $f(x)=\\begin{cases}(x + 2)^2 \\text{ if } x < -1\\\\|x| + 1…
The correct graph is the second (right-hand) graph with closed points at $(-1, 2)$, $(0, 1)$, $(1, 2)$, an open point at $(-1, 1)$ and $(1, -1)$, the parabola for $x<-1$, V-shape …
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11. choose the best answer. choose the correct graph that sketches $f(x…
The correct graph is the top-right option (with dashed curve $y=4^x$, shading above it; solid curve $y=3+\log x$, shading below it, with overlapping shaded region as the solution …
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match the functions to the graph: a. $ln(x + 2)$ b. $2 + ln x$ $f(x)$ _…
$f(x) = \ln(x+2)$ $g(x) = 2+\ln x$
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3. the deadly woodland hopping mouse has terrorized the people of west …
1. The mouse does NOT jump from (0,0). When $x=0$, $y=-12$, meaning the model starts 12 feet below the defined ground reference, so the mouse must jump from an elevated position (…
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quadratic inverse let $f(x)=3(x+1)^2-6$. 17 multiple choice 6 points fo…
## Question 17: A. $x \geq -1$ ## Question 18: D. $\sqrt{\frac{x+6}{3}} - 1$
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piecewise function use technology to graph the function, then answer th…
### For Question 11: Continuous ### For Question 12: $-1$
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*see answer key. the mental math section should not be duplicated for t…
1. $7$ 2. $25$ 3. $10$ 4. $\frac{2}{9}$ 5. $100$ 6. $\frac{3}{10}$ 7. $-15$ 8. $-8$ 9. $0.05$ 10. $\approx 60\%$ (or $\approx 63\%$ for a closer estimate)
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\the character you appear to us in, is truly ridiculous. your friends, …
It contains sentences with varied structures.
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11 fill in the blanks of g(x) to translate the function g(x) 1 unit dow…
First blank: $+3$, Second blank: $-1$ The completed function is $\boldsymbol{(x + 3)^2 - 1}$
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5 the function $h(t) = -16t^2 + 32t + 24$ models the height h, in feet,…
The initial velocity is $\boldsymbol{32}$ feet per second The initial height of the ball is $\boldsymbol{24}$ feet
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the graph of $y = 2^{x}$ is displayed here. a what is the y-intercept o…
No
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1. the graph of $y=2^x$ is displayed here. 1a what is the $y$-intercept…
$y=1$
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17. $(6-7i)^2$ 18. $(2-5i)(2+5i)$
17. $-13 - 84i$ 18. $29$
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5. $y = \\frac{1}{2}|x|$ 6. $y = $
The graph is a V-shaped curve with vertex at $(0,0)$, passing through $(-4,2)$, $(-2,1)$, $(2,1)$, $(4,2)$, and following $y=\frac{1}{2}x$ for $x\geq0$ and $y=-\frac{1}{2}x$ for $…
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what is the range of the function $f(x)=-(x+3)^2 + 7$?○ all real number…
all real numbers less than or equal to 7
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the function $f(x) = -x^2 - 4x + 5$ is shown on the graph. which statem…
The range of the function is all real numbers less than or equal to 9.
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which is $f(6)$ for the quadratic function graphed? -2 -0.5 1.5 4
D. 4
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which function has a minimum and is transformed to the right and down f…
D. $g(x)=8(x-3)^2-5$
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the first steps in writing $f(x)=3x^{2}-24x+10$ in vertex form are show…
D. $f(x) = 3(x - 4)^2 - 38$
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common core math ii a-cr - rla what is the vertex of $g(x)=-3x^2 + 18x …
(3, 29)
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the function $f(x) = x^2$ has been translated 9 units up and 4 units to…
g(x) = (x - 4)² + 9
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what is the equation of the translated function, $g(x)$, if $f(x)=x^2$?…
D. $g(x) = (x + 4)^2 + 6$
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what value represents the vertical translation from the graph of the pa…
3
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11) use synthetic division to evaluate the polynomial $y=-11 + x^2 + x^…
The coordinate is $(3, -2)$ --- ### Question 12
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omatically graded, and you will receive instant feedback on your perfor…
$x$ $-1$
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the graph of the function $f(x)=-(x + 3)(x - 1)$ is shown below. which …
B. The function is negative for all real values of x where $x < -3$ and where $x > 1$.
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the graph of the function $f(x) = (x +2)(x + 6)$ is shown below. what i…
The domain is all real numbers, and the range is all real numbers greater than or equal to $-4$.
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$4x^{2}+9y^{2}=72$ $2x - y = 4$ which of the following is a solution to…
D. (3/5, -14/5)
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which of the following is the equation of a parabola with focus (0, 2) …
$y = \frac{1}{8}x^2$
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draw a graph of $f(x) = \\frac{x - 9}{-x + 3}$ by first placing the hor…
1. Vertical asymptote: $x=3$ (dashed vertical line at $x=3$) 2. Horizontal asymptote: $y=-1$ (dashed horizontal line at $y=-1$) 3. Plot the point $(0, -3)$, then sketch the hyperb…
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draw a graph of $f(x) = \\frac{-3x}{x-2}$ by first placing the horizont…
1. Vertical asymptote: $x=2$ (dashed vertical line at $x=2$) 2. Horizontal asymptote: $y=-3$ (dashed horizontal line at $y=-3$) 3. Plotted point: $(0, 0)$ The graph is a hyperbola…
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draw a graph of $f(x) = \\frac{-4}{2x - 4}$ by first placing the horizo…
1. Vertical asymptote: $x=2$ (dashed vertical line at $x=2$) 2. Horizontal asymptote: $y=0$ (dashed horizontal line along the x-axis) 3. Plot the point $(0, 1)$, then draw the hyp…
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write an equation for the function graphed below $y = $ question help: …
$\boldsymbol{y = -1 - \frac{12}{(x+3)(x-4)}}$ or $\boldsymbol{y = \frac{-x^2 + x}{(x+3)(x-4)}}$
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0/1 pt 3 98 details write an equation for the function graphed below $y…
$y=\frac{8(x-2)}{x^2 - 2x - 8}$
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0/1 pt 3 99 details write an equation for the function graphed below $y…
$\boldsymbol{y=\frac{6(x-2)}{(x+3)(x-4)}}$ (or $\boldsymbol{y=\frac{6x-12}{x^2 - x -12}}$)
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11. evaluate each limit, if it exists. a) $lim_{x \\to 2} \\frac{(2+x)^…
a) $8$ b) $6$ c) $-14$ d) $\frac{1}{9}$ e) $-32$ f) $-1$
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and cube root functions and equations which is the graph of the cube ro…
The second graph (the one with an upward-sloping S-shape, passing through the origin, where positive x-values correspond to positive y-values and negative x-values correspond to n…
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cube and cube root functions and equations the graph of the parent func…
$(-3, -4)$
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the graph of the parent function $f(x) = x^3$ is translated to form the…
A. The topmost graph with inflection point at (1, 2)
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cubic and cube root functions and equations which is the graph of the f…
The top-most graph (Option C)
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cubic and cube root functions and equations the function $f(x) = \\sqrt…
The second graph from the top (the one where the curve goes from the upper left to the lower right, decreasing across the plane)
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c157d (11) $68\\div8=$ (12) $68\\div9=$ (13) $69\\div3=$ (14) $69\\div7…
(11) $8.5$ (or $8$ remainder $4$) (12) $\frac{68}{9}\approx7.56$ (or $7$ remainder $5$) (13) $23$ (14) $\frac{69}{7}\approx9.86$ (or $9$ remainder $6$) (15) $8.625$ (or $8$ remain…
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(1) $61\\div7=$ (2) $64\\div2=$ (3) $65\\div9=$ (4) $67\\div8=$ (5) $69…
1. $8\frac{5}{7}$ (or 8 remainder 5) 2. $32$ 3. $7\frac{2}{9}$ (or 7 remainder 2) 4. $8\frac{3}{8}$ (or 8 remainder 3) 5. $7\frac{2}{3}$ (or 7 remainder 6) 6. $8\frac{7}{8}$ (or 8…
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cubic and cube root functions and equations the graph of $f(x)=x^3 - 6x…
one real number solution, three non-real number solutions
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cube and cube root functions and equations the graph of the cube root p…
$f(x) = \sqrt[3]{x+6}-1$
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12. $\\begin{cases} y = -x + 4 \\\\ y = 2x - 5 \\end{cases}$ solution:
The solution to the system is $(3, 1)$ To graph the lines: 1. For $y=-x+4$: plot the y-intercept $(0,4)$ and use slope $-1$ to find another point (e.g., $(4,0)$), then draw the li…
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11. $\begin{cases} y = \frac{2}{3}x + 3 \\ y = -2x - 5 end{cases}$ solu…
The solution to the system is $(-3, 1)$ To graph: 1. For $y=\frac{2}{3}x+3$: plot the y-intercept $(0,3)$, then use slope $\frac{2}{3}$ (rise 2, run 3) to plot another point, draw…
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5) $y=3x-4$ $y=-\frac{1}{2}x+3$
The solution to the system is $(2, 2)$. To graph: 1. For $y=3x-4$: plot the y-intercept $(0, -4)$, then use slope 3 to plot $(1, -1)$, draw the line. 2. For $y=-\frac{1}{2}x+3$: p…
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go graph each system of equations and identify t 9. $\begin{cases} y = …
The solution to the system is the intersection point $(1, 1)$. To graph: 1. For $y=-3x+4$: plot $(0,4)$ and $(\frac{4}{3},0)$, draw the line. 2. For $y=4x-3$: plot $(0,-3)$ and $(…
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what radical function is represented in the graph? $f(x)=\\square$ (sim…
$f(x)=\sqrt{x+1}+3$
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4. $y \\geq \\frac{1}{4}x - 5$
1. Draw a solid line for $y = \frac{1}{4}x - 5$ using intercepts $(20, 0)$ and $(0, -5)$. 2. Shade the entire region above (and including) this solid line.
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khsd department of instructional services grade 11 argumentative synthe…
## The Case for a Four-Day School Week: Balancing Learning, Well-Being, and Sustainability To the Local School Board, As districts across the nation grapple with declining student…
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11. what are the values of x where the graph of the rational function $…
D. $x = -3$ and $x = 4$
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use any method to evaluate the integral $int \frac{242 dw}{w^{2}sqrt{12…
$-\frac{2\sqrt{121-w^2}}{w} + C$
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5. for what x-value(s) is the function shown below discontinuous? $x=0$…
x = 0 and x = 1
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3 calculate the vertical asymptote(s) of the rational function $f(x)=\\…
C. $x=-2, x=4$
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$\\frac{x^2 - 5x + 6}{x - 2}$ and test the solution(s) by analyzing the…
$\boldsymbol{x=4}$
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a ball is thrown into the air from the edge of a 48-foot-high cliff so …
Average rate of change = 40 feet per second Interpretation: Between 0 and 2.5 seconds, the ball's height increases by an average of 40 feet each second as it travels upward to its…
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5. scarcity impacts opportunity costs because most resources are limite…
trash
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the plot below represents the function $f(x)$ solve $f(x) = 2$ $circ$ 4…
○ -2
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below is the graph of function $f(t)$. estimate as close as possible th…
$-3$
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choose the function that expresses the relationship $15x + 4y^3 = 4$ as…
$f(x) = \sqrt[3]{\frac{4 - 15x}{4}}$
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find the average rate of change for $f(x) = -x^2 + 4x + 3$ on the inter…
The average rate of change is $-3$. On the interval $[2, 5]$, the value of the function $f(x)$ decreases by an average of 3 for each 1-unit increase in $x$.
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11/22 why might something like medicine be produced abroad? higher regu…
Lower production costs and specialized manufacturing capabilities.
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for the function $f(x) = \\frac{-4x + 1}{8x - 9}$, evaluate $f(1)$. $f(…
$3$
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given $f(x)=6x - 9$ a) evaluate $f(3)$ $f(3) = $ b) solve $f(x)= - 27$ …
a) $9$ b) $-3$
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1. identify where the following graph is positive or negative *if it is…
Positive: $(-\infty, -4) \cup (-2, \infty)$ Negative: $(-4, -2)$
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given the function $f(x) = 6x^2 + 7x - 7$. calculate the following valu…
$f(0) = -7$ $f(2) = 31$ $f(-2) = 3$ $f(x+1) = 6x^2+19x+6$ $f(-x) = 6x^2-7x-7$
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find the average rate of change for $f(x) = 3x^2 - 1$ on the interval 1…
The average rate of change is 15.
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homework assignment 3.7: rational functions score: 3/12 answered: 3/12 …
1) $\boldsymbol{(0, -\frac{1}{10})}$ 2) $\boldsymbol{(-1, 0)}$ and $\boldsymbol{(-\frac{1}{3}, 0)}$ 3) $\boldsymbol{-2}$ and $\boldsymbol{\frac{5}{2}}$ 4) $\boldsymbol{\frac{3}{2}…
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find the horizontal asymptote of $f(x) = \\frac{-2x + 4x^3 - 1}{-5x^3 +…
$y = -\frac{4}{5}$
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for each function, determine the long run behavior.$\frac{-9x^{3}+1}{-6…
1. $\frac{-9x^3 + 1}{-6x^3 + 2}$ has: a Horizontal asymptote at y=3/2 2. $\frac{x^3 + 1}{x^4 + 2}$ has: a Horizontal asymptote at y=0 3. $\frac{0x^4 + 1}{-10x^3 + 2}$ has: a Horiz…
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6. identify where the following graph is positive or negative *if it is…
Positive: $(-8, -4) \cup (5, \infty)$ Negative: $(-\infty, -8) \cup (-4, 5)$
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4) the continuous function $f$ is defined on the interval $-4 \\leq x \…
a) $g(0) = 4\pi$ $g'(0) = 3$ $g''(0) = 1$ b) The x-coordinate is $\frac{3}{2}$. Justification: $g'(x)=f(x)$, so $g'(x)=0$ at $x=\frac{3}{2}$. For $0<x<\frac{3}{2}$, $f(x)>0$ so $g…
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3. describe a real-world situation where you would need to divide a fra…
Word Problem: You have $\frac{3}{4}$ of a cup of chocolate chips. Each cookie requires $\frac{1}{8}$ of a cup of chocolate chips. How many full cookies can you make? Final Result:…
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given the function $f(x) = 3x^2 - 8x + 1$. calculate the following valu…
$f(-2)=29$ $f(-1)=12$ $f(0)=1$ $f(1)=-4$ $f(2)=-3$
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when $f(x) = 9x^2 - x - 1$, evaluate $f(-4)$ $f(-4) = \\boldsymbol{\\sq…
147
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incorrect 2 tries left. please try again. persevere graph the system of…
9 units$^2$
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2 find the difference, $-21.52 - (-8.86)$
$-12.66$