Cálculo
Límites, derivadas, optimización y comportamiento de funciones.
-
3. (3pts) let $f(x)$ be a function that satisfies the following. \\\\li…
$f(x)$ has horizontal asymptote(s) at $\boldsymbol{y=6}$ and vertical asymptote(s) at $\boldsymbol{x=3}$
-
2. let $g(x) = \\begin{cases} 3x - 5 & \\text{if } 0 \\leq x < 1 \\\\ 1…
(a) $\boldsymbol{-2}$ (b) $\boldsymbol{-2}$ (c) $\boldsymbol{-2}$
-
1. (4pts) find the value of the constant ( k ) that makes ( f(x) ) cont…
$\frac{23}{6}$
-
2. $y = \\frac{4}{3}x - 4$
The line passes through points $(0, -4)$ and $(3, 0)$, and extends infinitely in both directions on the coordinate grid.
-
7. (5pts) for the given function, find all vertical asymptotes and hori…
Horizontal Asymptote: $\boldsymbol{y=\frac{1}{2}}$ Vertical Asymptote(s): $\boldsymbol{x=\frac{\sqrt{2}}{2}}$ and $\boldsymbol{x=-\frac{\sqrt{2}}{2}}$
-
6. (2pts) for each pair of functions, circle the function that dominate…
a. $10e^{0.1x}$ b. $2x^4$
-
evaluate the integral. \\(\\int \\sin^3 x \\, dx\\) \\(\\int \\sin^3 x …
$-\cos x + \frac{1}{3}\cos^3 x + C$
-
3. (4pts) give the equation of the function graphed to the right: $f(x)…
$f(x) = -|x+3| + 1$
-
1. find a function that passes through (1, 6) and (3, 24) where the fun…
(a) $f(x)=9x-3$ (b) $f(x)=3(2)^x$
-
7, the cube root of 68604^10 over 54
The problem as presented is unclear due to potential typos or ambiguity. If we assume the expression is \(\frac{\sqrt[3]{68604^{10}}}{54}\), it can be rewritten as \(\frac{68604^{…
-
use transformations to graph the function. \\( v(x) = -(x + 4)^2 - 2 \\…
1. Reflect the graph of $f(x)=x^2$ over the x-axis 2. Shift the resulting graph 4 units to the left 3. Shift the resulting graph 2 units downward
-
graph the function by applying an appropriate reflection. $k(x) = -\fra…
The graph of $k(x)=-\frac{1}{x}$ is the hyperbola of $y=\frac{1}{x}$ reflected over the $x$-axis (or $y$-axis), with branches in the second and fourth quadrants, asymptotes at $x=…
-
the parent function for $g(x)=\\sqrt{x + 2}-4$ is $f(x)=\\sqrt{x}$. par…
The point $(0, 0)$ on $f$ corresponds to $(-2, -4)$ on $g$. The point $(1, 1)$ on $f$ corresponds to $(-1, -3)$ on $g$. The point $(9, 3)$ on $f$ corresponds to $(7, -1)$ on $g$.
-
use translations to graph the given function.\\( g(x) = sqrt{x + 2} - 4…
$f(x)=\sqrt{x}$
-
identify function transformations g is a transformation of f. the graph…
B. \( f(x + 2) \)
-
use translations to graph the given function.\\( g(x) = \\sqrt{x + 2} -…
\(f(x)=\sqrt{x}\)
-
use translations to graph the given function. \\( g(x) = sqrt{x + 2} - …
$f(x) = \sqrt{x}$
-
mary creates a table of values for a function and plots the points. she…
linear
-
question 1 (2 points) which is an affective strategy for improving one’…
Question 1: limiting sociocentricity Question 2: concrete → transitional → formal
-
add & subtract fractions & mixed numbers solve by finding a common deno…
1. $6\frac{1}{10}$ 2. $4\frac{47}{72}$ 3. $\frac{5}{14}$ 4. $6\frac{1}{9}$ 5. $2\frac{3}{8}$ 6. $3\frac{5}{6}$ 7. $6\frac{7}{12}$ 8. $1\frac{2}{5}$ 9. $7\frac{1}{3}$ 10. $3\frac{5…
-
use the aleks calculator to approximate \\(\\sqrt{119}\\). round your a…
$\boxed{10.91}$
-
r(x) = \\begin{cases} x^2 - 4 & \\text{for } x \\leq 2 \\\\ 5x - 10 & \…
The second rule defines a line with slope 5 and y-intercept $(0, -10)$. Since $x>2$, the leftmost point $(2, 0)$ is graphed as an open dot.
-
reasoning a signal generator is used to generate signals for a lab expe…
2
-
answer the following questions about how opportunity costs affect the p…
a. increasing. b. some resources are better at producing certain goods while others are better at producing different goods. c. Monti decides to pick up an extra shift at work and…
-
graph the function. \\( r(x) = \\begin{cases} \\,\\,\\,x^2 - 4 & \\text…
The first rule defines a **parabola** with vertex $(0, -4)$.
-
find the asymptote and y-intercept of the following function. y = -3·4^…
Asymptote: $y = 0$ y-intercept: $y = -3$
-
subtract. \\(\\frac{1}{2} - \\frac{7}{8}\\) write your answer in simple…
\(-\frac{3}{8}\)
-
what long - term effect did the watergate scandal have on the u.s. gove…
D. It made Americans less confident and more distrustful in their government.
-
add. $-\frac{2}{3} + \frac{4}{7}$ write your answer in simplest form.
\(-\frac{2}{21}\)
-
graph the function. $r(x)=\\begin{cases}x^2 - 4 & \\text{for } x \\leq …
The graph consists of: 1. The left half (and vertex) of the parabola $y=x^2-4$ for $x \leq 2$, including the point $(2,0)$. 2. The ray of the line $y=3x-6$ for $x > 2$, starting f…
-
r(x) = \\begin{cases} x^2 - 4 & \\text{for } x \\leq 2 \\\\ 3x - 6 & \\…
The second rule defines a **line** with slope $\boldsymbol{3}$ and y-intercept $\boldsymbol{(0, -6)}$. The leftmost point $(2, 0)$ is graphed as an open dot.
-
graph the function. ( r(x) = \begin{cases} x^2 - 4 & \text{for } x leq …
The vertex is $(0, -4)$ To complete the graphing process (for full context): 1. For $r(x)=x^2-4$ ($x\leq2$): Plot the vertex $(0,-4)$, find additional points e.g., $x=2$ gives $r(…
-
you have a device that monitors the voltage across a lamp in a certain …
a decreasing
-
indicate which intervals are increasing, decreasing, or constant (there…
### 1. Intervals that are Decreasing To determine decreasing intervals, we check where the function's \( y \)-value decreases as \( x \) increases (the graph moves downward from l…
-
indicate which intervals are increasing, decreasing, or constant. which…
A. (1), F. (5)
-
for the function f whose graph is given, state the following. (a) \\(\\…
### Part (a) # Explanation: ## Step1: Analyze end - behavior as \(x\to\infty\) As \(x\) approaches positive infinity (\(x\to\infty\)), we look at the right - most part of the grap…
-
fill in the table using this function rule. $y = 3x - 4$ | x | y | | -6…
When \( x = -6 \), \( y = -22 \); when \( x = -3 \), \( y = -13 \); when \( x = 0 \), \( y = -4 \); when \( x = 3 \), \( y = 5 \) So the filled table (row by row for \( y \)) is: …
-
indicate which intervals are increasing, decreasing, or constant. which…
B. (3)
-
evaluate $4\\cdot7$. $4\\cdot7 = \\square$
28
-
select all of the even functions. r(x) = 6x⁴ - 7x² - 2 b(x) = -5x⁴ - 9 …
# Explicación: ## Paso 1: Definir función par Una función $f(x)$ es par si cumple $f(-x) = f(x)$ para todo $x$ en su dominio. Esto se verifica cuando solo existen potencias pares …
-
katie took a plane to visit her grandparents for the summer. at the air…
$3(x + 6) = 102$
-
a. transformations of quadratic functions 1. what is the equation of th…
a. $y=-x^2+3$
-
plot the point on this function with an x - value of 0. what is the y -…
14
-
drag the tiles to the correct boxes to complete the pairs. match each b…
- The business owners' personal assets are protected from liabilities, but the business is not a separate tax entity. → limited liability corporation - A single individual is pers…
-
graph the equation shown below by transforming the given graph of the p…
To graph \( y=\sqrt[3]{-x}+5 \): 1. Start with the parent function \( y = \sqrt[3]{x} \). 2. Reflect the graph of \( y = \sqrt[3]{x} \) over the \( y \)-axis (to get \( y=\sqrt[3]…
-
f(x) = \\begin{cases} (x - 2)^2 - 1 & \\text{for} & x < 2 \\\\ 1 & \\te…
$f(7)$ is undefined, as 7 is not in the domain of the function $f(x)$.
-
graph these equations: y = 4x - 1 y = 4x - 9 click to select points on …
To graph \( y = 4x - 1 \): Plot \( (0,-1) \), then use slope \( 4 \) (up 4, right 1) to get more points (e.g., \( (1,3) \), \( (2,7) \) etc.) and draw the line. To graph \( y = 4x…
-
13. 0/1 points find an equation of the tangent line to the curve at the…
$y = -\frac{47}{14}x + \frac{51}{14}$ (or in standard form: $47x + 14y = 51$)
-
use the graph of ( f(x) ) to evaluate the following: the average rate o…
\( -\frac{2}{5} \)
-
find the exact location of all the relative and absolute extrema of the…
- \( f \) has a relative minimum (and absolute minimum) at \( (x,y)=(1, - 8) \) (smallest \( x \) - value for minimum). - \( f \) has an absolute maximum at \( (x,y)=(3,0) \) (lar…
-
which number is closest to \\(\\sqrt{22}\\) ? 3.9 5.1 4.6 4.1
4.6
-
caleb uses the standard algorithm to find 438 ÷ 6. part of his work is …
\(3\)
-
how many times does 2 go into 7? 3 times, with a remainder of 1 how man…
9 times, with a remainder of 1
-
1. $\frac{3}{4} - \frac{1}{4} =$ 2. $\frac{60}{90} - \frac{30}{90} =$ 3…
$\frac{1}{2}$ ### Problem 2
-
adding and subtracting fractions (unlike denominators) 1. \\(\\frac{4}{…
$\frac{11}{20}$ ### Problem 2: $\boldsymbol{\frac{25}{18} - \frac{2}{9} - \frac{1}{6}}$
-
adding and subtracting (like denominators) 1. \\(\\frac{4}{5} + \\frac{…
$\frac{2}{5}$ ### Problem 2
-
which number is closest to $-sqrt{271}$? -15.6 -16.4 -15.7 -17.1
-16.4
-
which number is closest to \\(\\sqrt{203}\\) ? 13.9 13.6 14.2 15.5
14.2
-
which number is closest to $-sqrt{190}$? -13.7 -14.3 -13.3 -12.8
-13.7
-
which number is closest to $-sqrt{152}$? -11.8 -11.5 -12.3 -12.6
-12.3
-
which number is closest to \\(\\sqrt{103}\\) ? 10.6 \\quad 10.7 \\quad …
10.1
-
which number is closest to $-sqrt{80}$? -8.9 8.9 -9.2 9.2
-8.9
-
which number is closest to \\(\\sqrt{126}\\) ? 11.2 10.8 11.6 12.4
11.2
-
10. what does it mean when f(x) = g(x) = h(x)?
It means that for a given \( x \) (in the common domain of \( f \), \( g \), and \( h \)), \( f(x)=g(x) \) and \( g(x) = h(x) \) (so \( f(x)=h(x) \) as well), i.e., the three func…
-
9. complete the tables for $f(x) = x$ and $g(x) = x^3$ and $h(x) = x^5$…
### Part a: For \( f(x) = x \) # Explanation: ## Step1: When \( x = -1 \) Substitute \( x = -1 \) into \( f(x) = x \), so \( f(-1) = -1 \). ## Step2: When \( x = 0 \) Substitute \…
-
what is the absolute value of the complex number $-4 - sqrt{2}i$? $circ…
$3\sqrt{2}$ (corresponding to the second option)
-
2 how many three - quarters are there in 3 wholes? $3\\div\\frac{3}{4}=…
4
-
(b) $\frac{1}{6} div 2 = \frac{1}{2}$ of $\frac{1}{6}$ =
\(\frac{1}{12}\)
-
use the graph of f in the figure to do the following. 2. find the value…
a. $x=2$ b. $x=2, x=3$
-
dividing by a fraction is the same as multiplying by the fraction’s rec…
21
-
determine the graph of f from the graph of f. choose the correct graph …
C. (The graph with $y=-1$ on $(-8,0)$ and $(2,8)$, $y=1$ on $(0,2)$, with open circles at the segment endpoints)
-
find $9 \\div 5$. how many times does 5 go into 9? 1 time(s), with a re…
8 time(s), with a remainder of 0
-
how many times does 5 go into 9? 1 time(s), with a remainder of 4 there…
tenths
-
find $9\\div5$. how many times does 5 go into 9? \\boxed{} time(s), wit…
1 time(s), with a remainder of 4
-
how many times does 2 go into 10? 5 times, with a remainder of 0 have y…
Yes. The remainder is 0 and there are no other digits to bring down.
-
there are no more digits in the dividend to bring down. how can you con…
5 times, with a remainder of 0
-
how many whole loaves does each person get? 1 what can you do to contin…
4
-
what is the quotient? 4,860 ÷ 12 = \\boxed{}
405
-
what is the quotient? 855 ÷ 5 = \\boxed{} \\longdiv{855}{5}
171
-
what is the quotient? 1,521 ÷ 3 = \\overline{\\quad\\quad} \\begin{arra…
507
-
continue dividing. what is the quotient? $568\\div4=\\square$ \\\\begin…
142
-
what was noahs mistake? noah forgot to write a 0 in the ones place. the…
Noah didn't divide the ones. He needs to bring down the 8 and keep dividing.
-
noah says that 560 ÷ 4 is equal to 14. his work is shown below. is noah…
C. No, \(560\div4\) should be much greater than \(14\).
-
what is the quotient? 2,585 ÷ 11 = \\boxed{}
235
-
what is the next digit in the quotient? \\overline{\\begin{array}{r}3? …
0
-
what is the quotient? 3,135 ÷ 15 =
209
-
use the standard algorithm to find 407 ÷ 11. how many times does 11 go …
37
-
use the standard algorithm to find 407 ÷ 11. how many times does 11 go …
7 times, with a remainder of 0
-
how can you find the first digit in the quotient? divide 40 by 11. the …
The number of times is 3, and the remainder is 7. So the first box is 3 and the second box is 7.
-
how many times does 7 go into 9? time, with a remainder of ? \\(\\begin…
1 time, with a remainder of 2
-
caleb uses the standard algorithm to find 438 ÷ 6. part of his work is …
7 represents 7 tens (the number of groups of 6 tens in 43 tens), and 1 represents 1 ten (the remainder when 43 tens is divided by 6). ### Second Sub - Question (What should Caleb …
-
find 114 ÷ 2. what is the quotient? 114 ÷ 2 = \\square
\(114\div2 = \boxed{57}\)
-
find $114\\div2$. divide the ones by 2. how many ones can go in each gr…
7 can go in each group, with 0 left over.
-
place-value blocks standard algorithm what is the quotient? 72 ÷ 3 = \\…
24
-
place - value blocks standard algorithm think about dividing 12 ones in…
4 ones (corresponding to the option: 4 ones)
-
question 68 0.5 pts which describes the information processing model? ○…
Information passes through discrete stages to form memories.
-
d. $y = x - 4$ | $x$ | $y$ | | --- | --- | | -3 | -7 | | 1 | -3 | | 6 |…
A straight line passing through the points $(-3, -7)$, $(1, -3)$, and $(6, 2)$ is graphed on the coordinate plane, representing the equation $y=x-4$.
-
below is the graph of function ( g(x) ). estimate as close as possible …
\( 3 \)
-
evaluate $f(x) = -5x^2 + 8x - 2$ at the indicated values $f(3) = $ $f(1…
\( f(3) = -23 \) \( f(1) = 1 \) \( f(a + 6) = -5a^2 - 52a - 134 \)
-
the one-to-one functions g and h are defined as follows. $g = {(-1, 6),…
s: - \( g^{-1}(3)=\boldsymbol{2} \) - \( h^{-1}(x)=\boldsymbol{-\frac{x + 3}{4}} \) (or \( \frac{-x - 3}{4} \)) - \( (h^{-1}\circ h)(-1)=\boldsymbol{-1} \)