Calculus
Limits, derivatives, optimization, and behavior of functions.
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evaluate the function graphically. find ( f(6) )
\( f(6)=0 \)
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evaluate the function graphically. find ( f(-6) )
\( f(-6)=8 \)
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evaluate the function graphically. find ( f(3) )
2
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evaluate the function graphically. find $f(-3)$
\(f(-3)=-6\)
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evaluate the function graphically. find $f(-5)$
\( \boldsymbol{2} \)
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evaluate the function graphically.
If evaluating \( f(-5) \), the value is \( 4 \). (Note: If the specific \( x \)-value to evaluate was not fully clear from the image, but based on the dot's position at \( x=-5 \)…
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a. the function has a minimum value of -2. b. the function has a maximu…
C. The function has a maximum value of 1.
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if ( g(x) = f(4x) ), which statement is true? a. the graph of function …
C. The graph of function $f$ is compressed horizontally by a scale factor of $\frac{1}{4}$ to create the graph of function $g$
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remy says: to determine the value of 0.27 ÷ 0.003, i can divide 270 by …
Yes
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problem 4 calculate $3.5 \\div 0.005$.
\(700\)
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problem 1 determine the value of $1.4\\div0.2$.
7
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5. in the indonesian government places a $500 tax on every japanese car…
5. A. To eliminate tariffs and promote economic cooperation 6. B. Quota 7. A. To pressure the government over human rights concerns
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trade in southeast asia the strait of malacca is considered one of the …
1. A. Singapore 2. A. Narrow waterway that is easy to control or block 3. B. Specialization 4. A. To eliminate tariffs and promote economic cooperation
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use the area model to find the product. 1. $24 \\times 0.71 = $ _______…
7 tenths, 1 hundredth $24 \times 0.71 = 17.04$
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the image shows a line on a coordinate grid. the options are: ① $y = 4x…
$\boldsymbol{y=4x+1}$ (Option D)
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question 5 $4\\cdot5^3$ 60 500 729 8000 question 6 $6 + 2(3 - 8) + 5$ 2…
Question 5: B. 500 Question 6: C. 1
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which scenario best fits the graph shown below? a machine at a factory …
A machine at a factory can spool 5 yards of twine per minute. The inputs are the number of minutes that have passed and the outputs are the number of yards of twine remaining to b…
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which function is graphed here? graph of a line \\(\\circ f(x) = -\\fra…
$f(x)=-\frac{1}{3}x+2$ (the second option)
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what is the y - intercept of the equation $y = 15x + 75$? 15 75 - 5 $-\…
1. B. 75 2. 15
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which is the sum of $8\\frac{3}{4}+2\\frac{1}{2}$? (1 point) $\\bigcirc…
B. \(11\frac{1}{4}\)
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item #3 what is \\(\\frac{5}{6} - \\frac{3}{8}\\)? choose the answer in…
$\frac{11}{24}$ (corresponding to the option: $\boldsymbol{\frac{11}{24}}$)
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question 40 not yet answered marked out of 1.00 flag question one reaso…
d. Great Depression a. cannot be taken away by a government without due process of law a. exceptions for job-related discrimination
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question 28 not yet answered marked out of 1.00 p flag question the pri…
Question 28: b. protect individual freedoms and rights Question 29: d. Social Security Administration Question 30: b. Gilded Age, World War I, Great Depression, Cold War
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question 22 not yet answered marked out of 1.00 p flag question how did…
Question 22: d. It confirmed the commitment of the United States to aid nations resisting communism. Question 23: a. Presidential veto power Question 24: a. It gave citizens a voi…
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5) $-5x + 5y = -5$ $10x - 4y = -14$
The solution to the system of equations is \(x=-3\) and \(y = - 4\)
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find the zero.\ $f(x) = 27x^3 - 27x^2 + 9x - 1$
$x=\frac{1}{3}$ (a repeated zero with multiplicity 3)
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33. for what value of the constant ( c ) is the function ( f ) continuo…
\( \frac{2}{3} \)
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the value of one share of stock, in dollars, t hours after 12 p.m. is m…
\( f'(t) = (-0.1 + 1.6t) \cdot 1235e^{0.04t} + (14 - 0.1t + 0.8t^2) \cdot 49.4e^{0.04t} \) ### Part B: How fast is the total value changing at 5 p.m.?
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find f(x) for the function f(x) = \\frac{x + 9}{x^2 - 7x + 2}. f(x) =
\( \frac{-x^2 - 18x + 65}{(x^2 - 7x + 2)^2} \)
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the term coined by mark twain to describe the period of rapid economic …
1. Gilded Age 2. laissez-faire 3. Standard Oil 4. steel 5. horizontal integration 6. Sherman Antitrust Act 7. Captains of Industry 8. power 9. Gospel of Wealth 10. monopoly 11. ri…
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what was the purpose of the sherman antitrust act? a. to encourage hori…
1. b. To limit monopolies 2. d. By using horizontal integration 3. c. Robber barons and captains of industry
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enter the correct answer. find the product. $2\\frac{1}{2} \\times \\fr…
1
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differentiate ( y = ln(10 - x - 5x^2) ).( y = )
\( y'=\frac{-1 - 10x}{10 - x - 5x^{2}} \) (or \( \frac{10x + 1}{5x^{2}+x - 10} \))
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compute the derivative of the function ( y = sqrt{x^7 - 40x} ) using th…
\(\frac{7x^{6}-40}{2\sqrt{x^{7}-40x}}\)
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evaluate \\( \\frac{d}{dt} e^{-4t^2 + 3t + 7} = \\)
\( (-8t + 3)e^{-4t^2 + 3t + 7} \) (or \( e^{-4t^2 + 3t + 7}(-8t + 3) \))
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4. a) given the graph of f(x), graph the inverse relation. explain your…
s: a) To graph the inverse relation, reflect each point \((x,y)\) on \(f(x)\) over \(y = x\) (swap \(x\) and \(y\) to get \((y,x)\)) and plot these points. For example, if \((x_1,…
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express the function \\(\\frac{1}{x - 1}\\) in the form \\(f \\circ g\\…
\( f(x)=\frac{1}{x} \)
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complete the table for the function $y = 7^x$. | $x$ | $y$ | | --- | --…
### Completed Table: | $x$ | $y$ | |-----|-----| | -1 | $\frac{1}{7}$ | | 0 | 1 | | 1 | 7 | | 2 | 49 | ### Key Plotting Points: Two suitable points to graph the function are $(0, …
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answer the following true or false: let $f(x) = x^2 - 7x + 3$. the slop…
True
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question 7 estimate the instantaneous rate of change of $g(t) = \\frac{…
\( -1.000 \)
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7. below are the graphs of the functions f and g. the graph of y = f(x)…
$\lim_{x\to1^-} \frac{-4x^2 -5x +2}{f(x)} = +\infty$ $\lim_{x\to1^+} \frac{-4x^2 -5x +2}{f(x)} = -\infty$ $\lim_{x\to1} \frac{-4x^2 -5x +2}{f(x)}$ does not exist
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complete the table for the function $y = 3^x$. now, graph the function.…
Completed table: | x | y | |----|------| | -1 | $\frac{1}{3}$ | | 0 | 1 | | 1 | 3 | | 2 | 9 | For the graph: Plot the points $(0,1)$ and $(1,3)$ on the coordinate grid, then draw …
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question 8 estimate the instantaneous rate of change at ( x = 3 ) your …
\( 8 \) (or a value close to 8, depending on more precise graph reading, but 8 is a good estimate here)
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(int_{0}^{8} \frac{dx}{sqrt{1 + x}})
\( 4 \)
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complete each equation. 8 × 20 = ?
160
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use the area model to find $8 \\times 26$. step 1: use place value to b…
First, correct the breakdown: $26 = 20 + 6$ The final product is $208$
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use the area model to find $8 \\times 26$. step 1: use place value to b…
For the blanks: $20$ and $6$ Final product: $208$
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fill out the table for the following linear equation: $y = 2x - 2$ grap…
The filled table (with example x - values 0, 1, 2) is as above, and the graph is drawn using the plotted points.
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determine whether the following sentence is true or false. $f \\circ g$…
A. False
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homework 1: 1.1-1.4 review score: 15/17 answered: 12/13 question 13 use…
114 square units
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homework 1: 1.1-1.4 review score: 10/17 answered: 7/13 question 8 using…
$x^3$
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homework 1: 1.1-1.4 review score: 9/17 answered: 6/13 question 7 if \\(…
140
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(int_{0}^{8} \frac{dx}{sqrt{1 + x}})
\( 4 \)
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homework 1: 1.1-1.4 review score: 8/17 answered: 5/13 question 6 if \\(…
$4.5$
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homework 1: 1.1-1.4 review score: 7/17 answered: 4/13 question 5 given …
$-\frac{38}{11}$
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write the standard form of the equation of the parabola that has the in…
\(y = -\frac{1}{4}(x - 6)^2 + 3\) (or \(y=-\frac{1}{4}x^{2}+3x - 6\)) ### Problem 2 (Vertex: (-6, -2); point: (-7, 0))
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homework 1: 1.1-1.4 review score: 5/17 answered: 2/13 question 3 evalua…
4
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homework 1: 1.1-1.4 review score: 4/17 answered: 1/13 question 2 evalua…
4
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score on last try: 2 of 4 pts. see details for more. at least one score…
$f(x) = -\frac{1}{2}x + 4$ $\text{area} = \frac{13}{4}$ (or 3.25)
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use a graphing utility to graph the quadratic function. $f(x) = 2x^2 - …
- vertex: \( (6, 0) \) - axis of symmetry: \( x = 6 \) - x-intercept: \( (6, 0) \) - standard form: \( f(x) = 2(x - 6)^2 \)
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use a graphing utility to graph the quadratic function. $f(x) = x^2 + 1…
vertex: \((-5, -13)\) axis of symmetry: \(x = -5\) x - intercept (smaller x - value): \((-5 - \sqrt{13}, 0)\) x - intercept (larger x - value): \((-5 + \sqrt{13}, 0)\) standard fo…
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which equation is represented by the graph below?answer\\(\\boldsymbol{…
$y = 3^{-x} - 4$
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which equation is represented by the graph below? answer \\( y = 3^{x -…
$\boldsymbol{y = 3^x + 2}$ (Option B)
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3. identify the vertical and horizontal asymptotes of $f(x) = \\frac{5x…
B. $x = 0, x = -2, x = 2, y = 0$
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a line has a slope of -1 and passes through the point (-12, 11). write …
$y=-x - 1$
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a line has a slope of 0 and passes through the point (7, 19). write its…
$y=19$
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graph below? answer \\( y = 2^{-x - 2} \\) \\( y = -2^{-x} - 2 \\) \\( …
# Explanation: ## Step1: Test x=0 on each option For $y=2^{-x}-2$: $y=2^{0}-2=1-2=-2$ For $y=2^{-x-2}$: $y=2^{-0-2}=2^{-2}=\frac{1}{4}$ For $y=-2^{-x}-2$: $y=-2^{0}-2=-1-2=-3$ For…
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a line has a slope of 6 and passes through the point (-2, -16). write i…
$y = 6x-4$
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2. consider $f(x) = \\frac{1}{x^2 - 2}$. evaluate $\\lim\\limits_{x\\to…
D. $-\infty$
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compute.\ $-4.53 + \\left(-5.34\ ight) = \\square$\ $-6.8 + 19.5 = \\sq…
$-4.53 + (-5.34) = -9.87$ $-6.8 + 19.5 = 12.7$
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compute. -4.368 - 3.86 = 16.37 + (-29.786) =
$-4.368 - 3.86 = -8.228$ $16.37 + (-29.786) = -13.416$
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fill in the blank the system of linear equations is shown below: $3x + …
$(6, 5)$
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compute. 39.4 + (-7.2) = 3.9 - 36.24 =
$39.4 + (-7.2) = 32.2$ $3.9 - 36.24 = -32.34$
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multiple-choice problems 1. evaluate \\(\\lim\\limits_{x\\to -\\infty} …
1. B. 2 2. C. $\infty$
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which outcome best explains how justinian’s codification affected the e…
It ensured more consistent application of laws
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12. v(x) = 2(x² - 5)
\( v(x)=2x^{2}-10 \)
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expand the expression and simplify. \\(\\ln(5e^2)\\). do not give a dec…
$2$ + $\ln(\boldsymbol{5})$
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compare the graph to its parent function ( f(x) = x^2 ). 2. ( f(x) = -4…
\( -4 \)
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5. $y = 2(2^x - 1)$
The graph is an exponential curve passing through $(0,0)$, $(1,2)$, $(-1,-1)$, approaching the horizontal asymptote $y=-2$ as $x \to -\infty$, increasing for all real $x$.
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part - a (multiple choice - non calculator) 1. what is the slope of the…
A. 2 ### Question 2
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homework 16: section 3.4 score: 77.5/160 answered: 8/16 question 8 give…
(a) \(\boldsymbol{24}\) (b) \(\boldsymbol{0}\)
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graph the function. identify a and compare 1. $f(x) = 5x^2$ $a = $ ____…
5
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question a new car is purchased for 23700 dollars. the value of the car…
$\$4687.86$
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homework 16: section 3.4 score: 67.5/160 answered: 7/16 question 7 give…
\(x^2 + 15x + 54\) ### Part (b)
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17. find the equation of a line parallel to y = 3x - 4 that passes thro…
$y=3x-25$
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moreover, our gracious will and pleasure is... that if any person or pe…
B. The slave trade will not be allowed in the new colony.
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homework 16: section 3.4 score: 57.5/160 answered: 6/16 question 6 give…
\( 49 \) ### Part (b)
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9. when does an individual begin to feel esteem and gain self - respect…
An individual begins to feel esteem and gain self - respect when their lower - level needs (physiological, safety) are met, they achieve personal goals, receive positive recogniti…
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use the quadratic function $f(x)=\frac{1}{3}x^2 + 6x + 4$ to answer the…
\((-9, - 23)\) ### Part b)
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use the graphs to evaluate the expressions below. $f(g(5)) = square$ $g…
\( 5 \) ### For \( g(f(1)) \):
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for the function ( f ) whose graph is given, state the following. (a) (…
To solve the problem, we analyze the graph of the function \( f(x) \) for the given limits and asymptotes. ### Part (a): \( \lim_{x \to \infty} f(x) \) As \( x \) approaches \( \i…
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use the quadratic function ( f(x)=\frac{1}{3}x^2 + 6x + 4 ) to answer t…
\((-9,-23)\)
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let $g(x)=\\begin{cases}-6x^2 + x & \\text{if } x < 3 \\\\ a & \\text{i…
B. There is no value of \( a \) for which \( g \) is continuous at \( 3 \) because \( \lim_{x ightarrow3^{-}}g(x)=\boldsymbol{-51} \) and \( \lim_{x ightarrow3^{+}}g(x)=\boldsymbo…
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let $g(x)=\\begin{cases}-6x^2 + x & \\text{if } x < 3 \\\\ a & \\text{i…
13 ### Part c
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let $g(x)=\\begin{cases}-6x^2 + x & \\text{if } x < 3 \\\\ a & \\text{i…
\(-51\)
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evaluate the following limit. \\lim_{x\\to 0} \\frac{\\cos x - 1}{\\sin…
\( -\frac{1}{2} \)
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at what points is the function $y = \\frac{\\sin x}{5x - 5}$ continuous…
\((-\infty, 1)\cup(1, \infty)\)
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consider continuous functions f and g. then complete the statement. fun…
greater than
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find the vertex of the graph of the quadratic function. determine wheth…
\((2, -6)\)
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determine the intervals on which the following function is continuous. …
\((-\infty, \infty)\)