Cálculo
Límites, derivadas, optimización y comportamiento de funciones.
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composite functions & inverses perform the indicated operation. 1) $f(x…
$f(g(x)) = 3x^2 - 9x - 2$ $g(f(x)) = 9x^2 - 21x + 10$
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1.9.3 quiz: finding vertical asymptotes question 4 of 10 at what value …
C. 1
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ponential growth functions the graph represents the function $f(x)=10(3…
- The graph will increase at a slower rate - The y-values will continue to increase as x increases
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which of the following correctly identifies the factor $k$ for the vert…
B. $k=\frac{1}{4}$
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simplifying fractions grade 5 fractions worksheet simplify the fraction…
1. $\frac{1}{5}$ 2. $\frac{1}{2}$ 3. $\frac{1}{10}$ 4. $\frac{4}{5}$ 5. $\frac{3}{4}$ 6. $\frac{2}{3}$ 7. $\frac{1}{2}$ 8. $\frac{11}{12}$ 9. $\frac{1}{2}$ 10. $\frac{1}{5}$ 11. $…
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upton sinclairs the jungleinvestigated ______ and brought about the pas…
1. the meat packing industry 2. censored
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the graph represents the function $f(x)=10(2)^x$ how would the graph ch…
- The y-values will each be less than their corresponding x-values - The graph will increase at a slower rate - The y-values will continue to increase as x increases Note: Based o…
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consider the following two functions. original: $f(x)=|x| + 1$ final: $…
Option #2: a vertical compression
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complete this assessment to review what youve learned identify the fact…
$\frac{1}{2}$
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use the given zero to find all the zeros of the function. (enter your a…
For \(h(x) = 4x^3 - 13x^2 + 28x + 30\): \(2-\sqrt{6}i, 2+\sqrt{6}i, -\frac{3}{4}\) For \(f(x) = x^3 + 5x^2 + 24x + 20\): \(-2-4i, -2+4i, -1\)
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the graph represents the function $f(x) = 10(1.5)^x$ how would the grap…
- The graph will increase at a slower rate. - The y-values will continue to increase as x increases.
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ponential growth functions what are the domain and range of the functio…
The domain includes all real numbers, and the range is $y > 0$
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what are the domain and range of the relation in the graph? the domain …
The domain includes all non-negative numbers, and the range is $y \geq 0$
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question 1 of 3 select the correct answer from each drop-down menu. the…
The parent function of the function represented in the table is exponential. If function $f$ is vertically compressed by a factor of $\frac{1}{4}$, the $f(x)$-values will be divid…
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bra 1b - standard (15261) tial growth functions ramon is graphing the f…
The fourth graph (with the point (0, 3) plotted)
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shawna is graphing the function $f(x) = 3(4)^x$. she begins by plotting…
The graph with the point plotted at $(0, 3)$ (the rightmost option, labeled IV) is the correct initial step.
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exponential growth functions which is the graph of $f(x) = 5(2)^x$?
The fourth graph (rightmost one, passing through (0,5) and (1,10))
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exponential growth functions keshawn is asked to compare and contrast t…
- The range of $g(x)$ is $y > 0$ - The domain of both functions is all real numbers
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here is the graph of $g(r)$. determine the average rate of change for e…
| Interval | Average Rate of Change | |------------------------|------------------------| | $r=-2$ to $r=1$ | $\frac{-1}{3}$ | | $r=-2$ to $r=5$ | $\frac{-4}{7}$ | | $r=-2$ to $r=…
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you estimated the answer to be 8. where can you place the decimal point…
$8.36$
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$\\begin{array}{r}38\\\\×22\\hline76\\\\+760\\hline□□□\\end{array}$
8 3 6
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now solve for the second partial product, and look at one place value a…
The second partial product is 760, so the blanks are filled with $\boldsymbol{6}$ and $\boldsymbol{0}$ (resulting in the line showing 760, with the 7 under the placeholder "1").
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complete the table to vertically stretch the parent function $f(x)=x^3$…
The completed table values are: - Missing coefficient: $3$ - $y$ when $x=1$: $3$ - $y$ when $x=2$: $24$ Filled table: | $x$ | $y=3x^3$ | |-----|----------| | 0 | 0 | | 1 | 3 | | 2…
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valeria and thiago disagree about the domain of $f(x)$.- valeria says t…
Correct choice: Valeria's
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problem 8: spiral review here is the graph of $g(r)$. determine the ave…
| Interval | Average Rate of Change | |----------|------------------------| | $r=-2$ to $r=1$ | $\boldsymbol{-\frac{1}{3}}$ | | $r=-2$ to $r=5$ | $\boldsymbol{-\frac{4}{7}}$ | | $…
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find the rate of change and initial value for the linear function. the …
Rate of change: $-1$ Initial value: $5$
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using the correct order of operations $8 \\times (10 - 6) \\div 2 + 4$
20
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graph the equation $y = -x^2 - 4x + 5$ on the accompanying set of axes.…
Plotted points: $(-5,0), (-4,5), (-2,9), (0,5), (1,0)$ Equation of the axis of symmetry: $x=-2$
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ons worksheet -- order of operations simplify each expression usin $(3 …
2
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graph the equation $y = -x^2 - 14x - 48$ on the accompanying set of axe…
Points to plot: $(-9,-3), (-8,0), (-7,1), (-6,0), (-5,-3)$ Equation of the axis of symmetry: $x=-7$
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graph the equation $y = x^2 - 8x + 7$ on the accompanying set of axes. …
The vertex of the parabola is $\boldsymbol{(4, -9)}$ The 5 points to plot are: $(0,7)$, $(1,0)$, $(4,-9)$, $(7,0)$, $(8,7)$
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ian finds the area of the rectangle shown by adding 4+4+4+4+4+4.ray fin…
1. C. Both Ian’s and Ray’s methods are correct. 2. D. 3×6, because the order of the numbers does not matter in multiplication
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graph the equation $y = -x^2 - 12x - 35$ on the accompanying set of axe…
### Plotted Points: $(-7,0), (-5,0), (-6,1), (-8,-3), (-4,-3)$ ### Equation of Axis of Symmetry: $x=-6$
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graph the equation $y = x^2 - 10x + 16$ on the accompanying set of axes…
The 5 points to plot are: $(0,16)$, $(2,0)$, $(5,-9)$, $(8,0)$, $(10,16)$ The roots of $x^2-10x+16=0$ are $x=2$ and $x=8$
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graph the equation $y = -x^2 - 10x - 24$ on the accompanying set of axe…
### 5 Points to Plot: $(-7, -3)$, $(-6, 0)$, $(-5, 1)$, $(-4, 0)$, $(-3, -3)$ ### Equation of Axis of Symmetry: $x=-5$
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question graph the equation $y = x^2 - 10x + 16$ on the accompanying se…
Plotted points: $(1,7)$, $(2,0)$, $(5,-9)$, $(8,0)$, $(9,7)$ Equation of the axis of symmetry: $x=5$
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6. $4\\frac{1}{5}-2\\frac{1}{4}=$
$1\frac{19}{20}$
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name: kaliah salinasdate: feb 10 20267.3 exponential functions: charact…
a) Day 3 number of bacteria: 1500 b) Day 6 number of bacteria: 187500 c) $f(x) = 12 \cdot 5^x$ d) Exponential growth y-intercept: $(0, 12)$ --- ### Problem 2
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graph the function. $g(x) = \\frac{3}{4} \\cdot 2^x$
The graph is an increasing exponential curve with a horizontal asymptote at $y=0$, passing through $(0, 0.75)$ and $(2, 3)$, approaching 0 as $x \to -\infty$ and growing without b…
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$d(t) = \\frac{5}{6}x + 4$ evaluate $d(12)$ type answer here. © math by…
14
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f(x) = -2x + 5 evaluate f(-4) type answer here.
13
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at says \type answer here.\ if you answer correctl you get to the \fini…
$-10$
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directions: study the information and graphs, read each question, and c…
13. A. Revolving credit stayed lower and steadier than in previous years, and non-revolving credit spiked upward. 14. A. Consumer resources and confidence are down, so fewer peopl…
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$g(y) = y^2 - 3y$ evaluate $g(6)$
18
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$h(x) = -\frac{1}{3}x+4$ evaluate $h(0)$ type answer here.
$4$
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$f(x) = -3x - 4$ evaluate $f(-2)$
$2$
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question if $f(x)$ is an exponential function of the form of $y = ab^x$…
205.5
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if $f(x)$ is an exponential function of the form of $y = ab^{x}$ where …
$21.5$
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question if $f(x)$ is an exponential function of the form of $y = ab^{x…
21.2
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graph the following function. $y = 5 \\cdot 2^{x}$ show your work here …
- Horizontal asymptote: $y=0$ - Plotted points: $(-2, 1.25)$, $(-1, 2.5)$, $(0, 5)$, $(1, 10)$ - The graph is an increasing exponential curve that approaches the x-axis (from abov…
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multiple-choice question using the function below. $g(x)=2(6)^x$ calcul…
$m = 35$
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question write an exponential function in the form $y = ab^x$ that goes…
$y=13(2)^x$
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graph this function: $f(x) = -2x - 16$
The graph is a straight line passing through the points $(-8, 0)$ and $(0, -16)$, with a slope of $-2$, extending across the provided coordinate grid.
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consider the definite integral $int_{0}^{1} xe^{4x^{2}+b}dx$, where $b$…
a) $4x^2 + b$ b) $8x dx$ c) Lower limit: $b$, Integrand: $\frac{1}{8}e^u$, Upper limit: $4+b$ d) $\frac{1}{8}e^b(e^4 - 1)$ (or $\frac{e^{4+b} - e^b}{8}$)
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20. given the exponential function: $f(x) = 5 \\cdot 2^{x-2} + 1$, expl…
- The factor 5 vertically stretches the parent exponential function $2^x$ by a factor of 5. - The $-2$ in the exponent shifts the parent function 2 units to the right. - The $+1$ …
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graph this function:$f(x) = -2x - 16$graph this function:$f(x) = \\frac…
1. For $f(x) = -2x - 16$: - Y-intercept: $(0, -16)$ - X-intercept: $(-8, 0)$ - Draw a straight line through these two points, extending across the grid. 2. For $f(x) = \frac{1}{2}…
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how did regents v. bakke change affirmative action policies?○ it struck…
It struck down the use of strict racial quotas.
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plot the point on this function with an x - value of 0. what is the y -…
14
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graph the equation shown below by transforming the given graph of the p…
To graph \( y = |x|+3 \), shift the graph of \( y = |x| \) (with vertex at \( (0,0) \), points like \( (1,1),(-1,1),(2,2),(-2,2) \) etc.) 3 units upward. The new vertex is \( (0,3…
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subtract. \\(\\frac{1}{2} - \\frac{7}{8}\\) write your answer in simple…
\(-\frac{3}{8}\)
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question given the definitions of $f(x)$ and $g(x)$ below, find the val…
47
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find the inverse of $f$. $f(x)=x^3 - 5$ $\bigcirc \\ f^{-1}(x)=\\sqrt3{…
$f^{-1}(x) = \sqrt[3]{x + 5}$ (the last option)
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answer $y = 3(x - 4)^2 - 2$ $y = 3(x + 4)^2 - 2$ $y = -3(x - 4)^2 - 2$ …
\(y = -3(x - 4)^2 - 2\) (the second option in the lower - left group of equations)
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write the domain and range of the function using interval notation. not…
The domain is: \([-4, 4]\) The range is: \([-4, -2]\)
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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 $\boldsymbol{x=3}$
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2. let $g(x) = \\begin{cases} 3x - 5 & \\text{if } 0 \\leq x < 1 \\\\ 1…
(a) $\boldsymbol{-2}$ (b) $\boldsymbol{-2}$ (c) $\boldsymbol{-2}$
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1. (4pts) find the value of the constant ( k ) that makes ( f(x) ) cont…
$\frac{23}{6}$
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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.
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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 $\boldsymbol{x=-\frac{\sqrt{2}}{2}}$
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6. (2pts) for each pair of functions, circle the function that dominate…
a. $10e^{0.1x}$ b. $2x^4$
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evaluate the integral. \\(\\int \\sin^3 x \\, dx\\) \\(\\int \\sin^3 x …
$-\cos x + \frac{1}{3}\cos^3 x + C$
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3. (4pts) give the equation of the function graphed to the right: $f(x)…
$f(x) = -|x+3| + 1$
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1. find a function that passes through (1, 6) and (3, 24) where the fun…
(a) $f(x)=9x-3$ (b) $f(x)=3(2)^x$
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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^{…
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use transformations to graph the function. $m(x) = 6\\sqrt3{x}$
The graph of $m(x)=6\sqrt[3]{x}$ is a vertical stretch by a factor of 6 of the parent cube root function $f(x)=\sqrt[3]{x}$, passing through points $(-8,-12)$, $(0,0)$, and $(8,12…
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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
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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=…
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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 $g$.
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use translations to graph the given function.\\( g(x) = sqrt{x + 2} - 4…
$f(x)=\sqrt{x}$
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identify function transformations g is a transformation of f. the graph…
B. \( f(x + 2) \)
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use translations to graph the given function.\\( g(x) = \\sqrt{x + 2} -…
\(f(x)=\sqrt{x}\)
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use translations to graph the given function. \\( g(x) = sqrt{x + 2} - …
$f(x) = \sqrt{x}$
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mary creates a table of values for a function and plots the points. she…
linear
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question 1 (2 points) which is an affective strategy for improving one’…
Question 1: limiting sociocentricity Question 2: concrete → transitional → formal
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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…
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reasoning a signal generator is used to generate signals for a lab expe…
2
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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.
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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…
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graph the function. \\( r(x) = \\begin{cases} \\,\\,\\,x^2 - 4 & \\text…
The first rule defines a **parabola** with vertex $(0, -4)$.
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find the asymptote and y-intercept of the following function. y = -3·4^…
Asymptote: $y = 0$ y-intercept: $y = -3$
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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.
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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…
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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.
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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(…
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you have a device that monitors the voltage across a lamp in a certain …
a decreasing
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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…
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indicate which intervals are increasing, decreasing, or constant. which…
### For the "Which intervals, if any, are decreasing?" question: To determine decreasing intervals, we analyze the graph's slope: - A function is decreasing when as \( x \) increa…
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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…
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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: …
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indicate which intervals are increasing, decreasing, or constant. which…
B. (3)