Cálculo
Límites, derivadas, optimización y comportamiento de funciones.
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transform the solid black function to match the dotted function. $y = |…
The first box (horizontal shift) is 2, the second box (vertical shift) is 1. So the answer is 2 (in the first box) and 1 (in the second box).
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4.7 with calcchat® and calcview® make a connection in exercises 1–4, ma…
## Matching Exercises 1-4: 1. $f(x)=(x-1)^2(x+2)$: Graph A 2. $h(x)=(x+2)^2(x+1)$: Graph B 3. $f(x)=(x-1)(x-2)(x+2)$: Graph D 4. $g(x)=(x+1)(x-1)(x+2)$: Graph C ## Graphing Exerci…
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use the drawing tools to complete the graph. sketch a graph of a polyno…
The graph is possible. A possible polynomial is \(f(x)=-x^4 - 1\). The graph is a degree - 4 polynomial (even degree) with a negative leading coefficient, so it opens downward. It…
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7. use the graph to determine the formulas for the different pieces of …
### Part a) Analyzing Each Piece of the Graph #### Step 1: Left - Most Linear Piece (x < 0) We observe two points on this line: let's assume the points are \((-2, 6)\) and \((0, 2…
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the function $y = f(x)$ is graphed below. what is the average rate of c…
$\frac{60}{7}$
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7. use the graph to determine the formulas for the different pieces of …
To solve this problem, we analyze the graph (even though it's partially visible, we can infer the typical structure of a piecewise function with three parts: a line on the left, a…
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what is the slope of the line that passes through the points (10, 8) an…
\(-2\)
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what is the slope of the line that passes through the points (3, 2) and…
\(\frac{1}{4}\)
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directions: use the reading to fill in the blanks. 1. in the early 1800…
To solve these fill - in - the - blank questions, we need to recall relevant historical knowledge, especially about the U.S. government structure and early American political hist…
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what is the slope of the line that passes through the points (9, 5) and…
\(-\frac{5}{6}\)
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the function $y = f(x)$ is graphed below. what is the average rate of c…
9
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given the function $f(x) = -x^2 + 5x + 14$, determine the average rate …
$-2$
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2. \\begin{array}{r}5\\ - 3\\frac{5}{6}\\\\ hline \\end{array}
\(1\frac{1}{6}\)
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given the function $g(x) = x^2 + 6x + 1$, determine the average rate of…
2
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evaluate. -4(-2)(5)
40
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draw a line representing the ise\ and a line representing the un\ of th…
The slope of the line is \(3\).
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complete the table. $f(q)=|-q + 8|+3$ | $q$ | $f(q)$ | | ---- | ---- | …
| $q$ | $f(q)$ | |-----|--------| | 6 | 5 | | 7 | 4 | | 8 | 3 | | 9 | 4 |
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complete the table. $f(k) = 2|k + 5| + 1$ | $k$ | $f(k)$ | | ---- | ---…
| $k$ | $f(k)$ | |-----|--------| | -6 | 3 | | -5 | 1 | | -4 | 3 | | -3 | 5 |
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complete the table. $f(c)=|-c|$ | $c$ | $f(c)$ | | ---- | ---- | | -50 …
| $c$ | $f(c)$ | |-----|--------| | -50 | 50 | | -25 | 25 | | 0 | 0 | | 25 | 25 |
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16·3 =? (10·3) + (6·3) □ + □
First box (10×3 result): 30 Second box (6×3 result): 18 Final total: 48
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63 ÷ 7 = 110 ÷ 10 =
63 ÷ 7 = 9 110 ÷ 10 = 11
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4-7. copy each expression and simplify it. show all of your steps. home…
\( 7.18 \) ### Part b: \( 6.1 - 1.536 \)
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divide. 0.6)13.2 = \\boxed{}
22
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solve the following system of inequalities graphically on the set of ax…
(2, 2) (or other valid points like (0, 0), (3, 2) is invalid, (0, 3) is valid, (2, 3) is valid as 3 < 5 and 3 ≥ 4/3*2 - 1 = 8/3 - 1 = 5/3 ≈ 1.666. Let's confirm (2,3): 3 < -4/3 + …
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use the change of base formula to compute \\(\\log_{6} \\frac{1}{8}\\).…
-1.161
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solve for x. \\(\\ln 16 = \\ln(2x + 1)\\) \\(x = \\square\\)
$7.5$ (or $\frac{15}{2}$)
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solve for x. \\(\\log_{5}(2x - 4) = 2\\) \\(x = \\square\\)
$\frac{29}{2}$ (or 14.5)
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9878 + 462
10340
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complete the table. $f(m)=|m|$ | $m$ | $f(m)$ | | --- | --- | | $-2$ | …
| $m$ | $f(m)$ | |-----|--------| | -2 | 2 | | -1 | 1 | | 0 | 0 | | 1 | 1 |
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solve for x. \\log_{7}x = -2 simplify your answer as much as possible. …
$\frac{1}{49}$
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complete the table. $f(j) = |j|$ | $j$ | $f(j)$ | | ---- | ---- | | $-5…
| $j$ | $f(j)$ | |-----|--------| | -5 | 5 | | 0 | 0 | | 5 | 5 | | 10 | 10 |
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solve the following system of equations graphically on the set of axes …
$(-2, -1)$
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graph and determine the solution of the system of equations. x + 4y = 0…
All points on the line $y = -\frac{1}{4}x$ (infinitely many solutions, as the two equations are identical when simplified).
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solve the following system of inequalities graphically on the set of ax…
Point: \((-6, 0)\) (Other valid points like \((-8, 0)\) also work, but \((-6,0)\) is the intersection and a clear solution.)
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undreds of thousands of americans were left without homes because of th…
1. c. protecting 2. a. finally 3. For "safeguarding": "protect the land"; For "ultimately": "It took many more years before the land fully recovered" 4. The Dust Bowl displaced th…
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1/16 readworks article \why humans cant live off sunlight\ as part of a…
B. sunlight, sugar, and water
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which act addressed in article i of the constitution is a limit of cong…
B. a bill of attainder
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what is the slope of this line? simplify your answer and write it as a …
\(1\)
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17. critique reasoning jake said you compare two fractions with the sam…
Jake is correct. When two fractions have the same denominator, each fraction represents parts of a whole that are all the same size. The numerator tells you how many of those equa…
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evaluate. write your answer as a whole number or as a simplifie \\(\\fr…
\(\frac{4}{27}\)
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this equation describes a relationship between x and y. $y = 2x$ comple…
1. The completed table values are correct as provided: - $x=3, y=6$ - $x=4, y=8$ - $x=5, y=10$ - $x=6, y=12$ 2. The correct graph is the right-hand grid (the one with the cursor p…
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15. the height ( h ), in metres, of a diver relative to the water level…
8 seconds
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find the value of the exponential expression. for example, 0.1⁴ = 0.000…
0.064
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5. determine the zeros of the function $f(x) = -3(x + 1)^2 + 12$. 6. de…
The zeros of the function are \( x = 1 \) and \( x = -3 \). ### Question 6: Determine the \( y \)-intercept of \( f(x) = -\frac{1}{2}(x + 4)^2 + 9 \).
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select the correct answer. find the value of h(-7) for the function bel…
A. 138.7
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m is the \\underline{slope} write the equation of a line given the writ…
$y=-2x + 5$ ### Problem 3:
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which of these choices shows how to correctly evaluate $0.03^3$? a) $0.…
B) $0.03^3 = 0.03 \times 0.03 \times 0.03 = 0.000027$
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select the correct answer. find the inverse of function f. f(x) = 9x + …
C. \( f^{-1}(x)=\frac{1}{9}x - \frac{7}{9} \)
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9.6 notes – writing linear equations in slope-intercept form identify t…
\(y=-2x + 5\) ### Problem 2:
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determine the domain of the following graph: answer attempt 1 out of 2 …
$-3 < x < 8$ (or in interval notation: $(-3, 8)$)
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graph this line: slope = 0 y-intercept = 0 click to select points on th…
The line $y = 0$ (the $x$-axis) is graphed by plotting points with $y$-coordinate $0$ (e.g., $(0,0)$, $(1,0)$, $(-1,0)$) and drawing a horizontal line through them.
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select the correct answer. which of the following represents a function…
A
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use the graph to answer the question. identify all of the asymptotes fo…
- $x=2$ - $x=-2$ - $y=2$
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d end behavior use the graph to answer the question. describe the end b…
$f(x) \to 1$ as $x \to \pm\infty$
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f(x) = 2x² + 4x - 9
Assuming the problem is to find the vertex form of the quadratic function \( f(x) = 2x^2 + 4x - 9 \) (a common task with quadratic functions), we can use the method of completing …
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use the graph of ( y = f(x) ) to answer the following. part: 0 / 9 part…
$0$
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find and simplify $f(x + h)$. simplify your answer. $f(x) = -8x^2 - 2x …
$-8x^2 -16xh -8h^2 -2x -2h + 3$
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select the correct answer. find the value of g(7) for the function belo…
D. \( \frac{45}{8} \)
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solve the system by graphing: \\(2y = 10x - 12\\) \\(5x - y = 6\\) how …
Infinitely many solutions
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consider this function. $f(x) = 2x - 2$ which graph represents the inve…
A. W
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13. consider the functions ( f(x) = x + 3 ) and ( g(x) = -x + 1 ) repre…
$s(x) = 4$
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try again your answer is incorrect. rafael is charging his tablet. as t…
$y=10x+30$
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select the correct answer. jamal is comparing his transportation option…
A. (The number line with open circle at 26 and arrow to the left)
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an animal shelter takes in an average of 5 animals per day. the shelter…
B. \( x < 27 \)
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using equations to compare linear functions consider the function and i…
The slope \( a \) of the inverse function is \( \boldsymbol{3} \), and the \( x \) - intercept of the inverse function is at \( x=\boldsymbol{-2} \).
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type the correct answer in the box. use numerals instead of words. a li…
6
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spiral review find the quotient. if necessary, round to the nearest tho…
\(325\)
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spiral review find the quotient. if necessary, round to the nearest tho…
\(8\)
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spiral review find the quotient. if necessary, round to the nearest tho…
\(0.102\)
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spiral review find the quotient. if necessary, round to the nearest tho…
400
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use the graph of $y = f(x)$ to answer the following. part: 0 / 9 part 1…
$0$
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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.
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(b) $g(t) = sqrt3{5 - t}$ the domain in interval notation is .
$(-\infty, \infty)$
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write the domain in interval notation. part 1 of 3 (a) ( f(t) = sqrt3{t…
$(-\infty, \infty)$
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11. determine the values of x for which the function f(x) = -3(x + 4)^2…
$x = -6$ and $x = -2$
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find the sum. simplify if necessary \\(\\frac{2}{4} + \\frac{7}{8} = ?\…
1
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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…
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find the sum. simplify if necessary. \\(\\frac{4}{5} + \\frac{1}{4} = ?…
1
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determine the domain and range of the function. part 1 of 2 the domain …
$(-\infty, 2)$
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the function ( f ) is defined as follows. ( f(x) = 2x^2 - 5 ) if the gr…
$h(x)=2x^2 - 1$
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select the correct answer. which of these modes of narration does emily…
B. frame narrative
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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. $10.12$
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(9) find the real roots of $y = x^3 - 3x^2 + x - 3$ by inspecting the g…
3
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9) choose the best answer. given the equation, ( y = x^2 + 4 ), the ran…
1. The real root is $\boldsymbol{1}$ 2. $\boldsymbol{No\ real\ roots}$
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the function f is defined as follows. $f(x) = -2x^2 + 7$ if the graph o…
$g(x) = -2x^2 + 10$
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10) what is $f(g(x))$? $f(x) = 3x + 5$ and $g(x) = 5x - 1$ $\\bigcirc$ …
$f(g(x)) = 15x + 2$ --- ### Question 11
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determine the x- and y-intercepts for the given function. write your an…
x-intercept: $(9, 0)$ y-intercept: $(0, -3)$
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y = \\frac{2}{3}x + 6 click to select points on the graph.
Key points to plot: \( (0, 6) \) and \( (3, 8) \) (or others like \( (-9, 0) \)), then draw the line.
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determine the x- and y-intercepts for the given function. write your an…
x-intercept(s): $(3, 0)$ y-intercept(s): $(0, -15)$
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12. the function ( f(x)=ln x ) is transformed so that the transformed f…
D. $g(x) = \ln(x - 5) + 3$ --- ### For Question 13:
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a line has a slope of 7 and a y-intercept of -6. write its equation in …
\(y = 7x-6\)
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find and simplify f(x + h). simplify your answer. f(x) = -8x² + 9x - 7 …
$-8x^2 - 16xh - 8h^2 + 9x + 9h - 7$
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evaluate the function $g(x)=\frac{1}{x}$ for the given value of $x$. if…
Undefined
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evaluate the function $f(x)=\\sqrt{x + 1}$ for the given value of $x$. …
2
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the statement $f(-8) = -2$ corresponds to what ordered pair? the statem…
$(-8, -2)$
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21. $y = x^2 + 2x + 1$ vertex: $x = \\frac{-b}{2a} = \\frac{-2}{2(}$
Vertex: $(-1, 0)$
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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 $…
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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)).
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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,…
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question: state the equation of the oblique (diagonal) asymptote for th…
\( y = 3x+3 \) (the option: \( y = 3x+3 \))