Question 1

Find a function $g$ that agrees with $f$ for $x \neq 25$ and is continuous on $\Re$.
$$f ( x ) = \frac { 5 - \sqrt { x } } { 25 - x }$$

Accepted Answer

The answer of Find a function $g$ that agrees with...

Question 2

Find the range of the function.  y=2+cos⁡xy = 2 + \cos xy=2+cosx 
Select the correct answer.

Accepted Answer

A)    (−∞,∞) ( - \infty , \infty ) (−∞,∞)  
B)    (2,∞) ( 2 , \infty ) (2,∞)  
C)    [−1,1][ - 1,1 ][−1,1] 
D)    (−1,3) ( - 1,3 ) (−1,3)  
E)    [1,3][ 1,3 ][1,3]

Question 3

You are given $\lim _ { x \rightarrow a } f ( x ) = L$ and a tolerance $\varepsilon$. Find a number $\delta$ such that $| f ( x ) - L | < \varepsilon$ whenever $0 < | x - a | < \delta$.
$\lim _ { x \rightarrow 3 } 4 x = 12 ; \quad \varepsilon = 0.01$

Accepted Answer

The answer of You are given \(\lim _ { x...

Question 4

Find  aaa , such that the function  f(x) =4x+a−x2f ( x )  = 4 x + \sqrt { a - x ^ { 2 } }f(x) =4x+a−x2​  has the domain  (−4,4) ( - 4,4 ) (−4,4)  .

Accepted Answer

A)    a=−16a = - 16a=−16 
B)    a=4a = \sqrt { 4 }a=4c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5,-10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8,-50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0,35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5,-221l0 -0c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422s-65,47,-65,47zM834 80h400000v40h-400000z'/>​ 
C)    a=−4a = - \sqrt { 4 }a=−4c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5,-10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8,-50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0,35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5,-221l0 -0c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422s-65,47,-65,47zM834 80h400000v40h-400000z'/>​ 
D)    a=16a = 16a=16 
E)    a=4a = 4a=4

Question 5

Find the value of  lim⁡x→0+f(x) \lim _ { x \rightarrow 0 ^ { + } } f ( x ) limx→0+​f(x)  
 f(x) =11+61/xf ( x )  = \frac { 1 } { 1 + 6 ^ { 1 / x } }f(x) =1+61/x1​

Accepted Answer

A)   0
B)    −0.7- 0.7−0.7 
C)    −0.7- 0.7−0.7 .
D)    −0.6- 0.6−0.6 .
E)    0.160.160.16 .

Question 6

How would you define  f(7) f ( 7 ) f(7)   in order to make  fff  continuous at 7 ?
 f(x) =x2−2x−3x−7f ( x )  = \frac { x ^ { 2 } - 2 x - 3 } { x - 7 }f(x) =x−7x2−2x−3​

Accepted Answer

A)    f(3) =−8f ( 3 )  = - 8f(3) =−8 
B)    f(7) =12f ( 7 )  = 12f(7) =12 
C)    f(7) =0f ( 7 )  = 0f(7) =0 
D)    f(7) =−12f ( 7 )  = - 12f(7) =−12 
E)   None of these

Question 7

Find the limit. $$\lim _ { x \rightarrow 2 } \frac { x ^ { 2 } + 2 x - 12 } { x - 2 }$$

Accepted Answer

6

Question 8

Determine whether  fff  is even, odd, or neither.
 f(x) =4x2x4+5f ( x )  = \frac { 4 x ^ { 2 } } { x ^ { 4 } + 5 }f(x) =x4+54x2​

Accepted Answer

A)   neither
B)   odd
C)   even

Question 9

Which of the given functions is discontinuous?

Accepted Answer

\[f ( x ) = \left\{ \begin{arr...

Question 10

Consider the following function. $$f ( x ) = \left\{ \begin{array} { c c } 
3 - x & x < - 1 \
x & - 1 \leq x < 3 \
( x - 3 ) ^ { 2 } & x \geq 3
\end{array} \right.$$
Determine the values of $a$ for which $\lim _ { x \rightarrow a } f ( x )$ exists.

Accepted Answer

The answer of Consider the following function. \[f ( x...

Question 11

Find the domain of the function.  f(x) =7x+1x2f ( x )  = \frac { 7 x + 1 } { x ^ { 2 } }f(x) =x27x+1​

Accepted Answer

A)    (−∞,0) ( - \infty , 0 ) (−∞,0)  
B)    (−∞,−17) ∪(−17,∞) \left( - \infty , - \frac { 1 } { 7 } \right)  \cup \left( - \frac { 1 } { 7 } , \infty \right) (−∞,−71​) ∪(−71​,∞)  
C)    (−∞,17) ∪(17,∞) \left( - \infty , \frac { 1 } { 7 } \right)  \cup \left( \frac { 1 } { 7 } , \infty \right) (−∞,71​) ∪(71​,∞)  
D)    (−∞,0) ∪(0,∞) ( - \infty , 0 )  \cup ( 0 , \infty ) (−∞,0) ∪(0,∞)

Question 12

Estimate the value of the following limit by graphing the function $f ( x ) = \frac { ( 5 \sin x ) } { ( \sin \pi x ) }$. $\lim _ { x \rightarrow 0 } \frac { 5 \sin x } { \sin \pi x }$ Round your answer correct to two decimal places.

Accepted Answer

The answer of Estimate the value of the following limit...

Question 13

Let
  5\end{array} ight.">f(x) ={x−4 if x≤5kx2−24x+46 if x>5f ( x )  = \left\{ \begin{array} { c c } x - 4 & 	ext { if } x \leq 5 \k x ^ { 2 } - 24 x + 46 & 	ext { if } x > 5\end{array} ight.f(x) ={x−4kx2−24x+46​ if x≤5 if x>5​ 
Find the value of  kkk  that will make  fff  continuous on  (−∞,∞) ( - \infty , \infty ) (−∞,∞)  .

Accepted Answer

A)   5
B)   46
C)    −4- 4−4 
D)   3

Question 14

Determine whether $f$ is even, odd, or neither.
$$f ( x ) = \frac { 8 x ^ { 2 } } { x ^ { 4 } + 1 }$$

Accepted Answer

even

Question 15

Graph the function by hand, not by plotting points, but by starting with the graph of one of the
standard functions and then applying the appropriate transformations. $$y = 4 + 2 x - x ^ { 2 }$$

Accepted Answer

The answer of Graph the function by hand, not by...

Question 16

The graph of the function  f(x) =x2−11x+7f ( x )  = x ^ { 2 } - 11 x + 7f(x) =x2−11x+7  has been stretched horizontally by a factor of 2 . Find the function for the transformed graph.

Accepted Answer

A)    g(x) =x2−11x+72g ( x )  = \frac { x ^ { 2 } - 11 x + 7 } { 2 }g(x) =2x2−11x+7​ 
B)    g(x) =2x2−22x+14g ( x )  = 2 x ^ { 2 } - 22 x + 14g(x) =2x2−22x+14 
C)    g(x) =x2−22x+284g ( x )  = \frac { x ^ { 2 } - 22 x + 28 } { 4 }g(x) =4x2−22x+28​ 
D)    g(x) =4x2−22x+7g ( x )  = 4 x ^ { 2 } - 22 x + 7g(x) =4x2−22x+7

Question 17

Evaluate the limit. $$\lim _ { x \rightarrow 9 } \frac { 3 - \sqrt { x } } { x - 9 }$$

Accepted Answer

The answer of Evaluate the limit. \[\lim _ { x...

Question 18

Let  F(x) =x−5∣x−5∣F ( x )  = \frac { x - 5 } { | x - 5 | }F(x) =∣x−5∣x−5​ . Find the following limits.
 lim⁡x→5+F(x) ,lim⁡x→5−F(x) \lim _ { x \rightarrow 5 ^ { + } } F ( x )  , \lim _ { x \rightarrow 5 ^ { - } } F ( x ) limx→5+​F(x) ,limx→5−​F(x)

Accepted Answer

A)   both 1
B)   2 and 1
C)   2 and  −1- 1−1 
D)   1 and  −1- 1−1 
E)   both-1

Question 19

Find the range of the function. $y = 2 + \cos x$

Accepted Answer

The answer of Find the range of the function. \(y...

Question 20

Use the table to evaluate the expression  (f∘g) (6) ( f \circ g )  ( 6 ) (f∘g) (6)  .
 x123456f(x) 321012g(x) 652346\begin{array}{|c|c|c|c|c|c|c|}\hline x & 1 & 2 & 3 & 4 & 5 & 6 \\hline f(x)  & 3 & 2 & 1 & 0 & 1 & 2 \\hline g(x)  & 6 & 5 & 2 & 3 & 4 & 6 \\hline\end{array}xf(x) g(x) ​136​225​312​403​514​626​​

Accepted Answer

A)   5
B)   2
C)   3
D)   4
E)   6

Exam 1: Functions and Models

Find a function ggg that agrees with fff for x≠25x \neq 25x=25 and is continuous on ℜ\Reℜ . f(x)=5−x25−xf ( x ) = \frac { 5 - \sqrt { x } } { 25 - x }f(x)=25−x5−x​​

Correct AnswerverifiedShow Answer

Find the range of the function. y=2+cos⁡xy = 2 + \cos xy=2+cosx Select the correct answer.

Correct AnswerverifiedShow Answer

Correct AnswerverifiedShow Answer

Find aaa , such that the function f(x) =4x+a−x2f ( x ) = 4 x + \sqrt { a - x ^ { 2 } }f(x) =4x+a−x2​ has the domain (−4,4) ( - 4,4 ) (−4,4) .

Correct AnswerverifiedShow Answer

Find the value of lim⁡x→0+f(x) \lim _ { x \rightarrow 0 ^ { + } } f ( x ) limx→0+​f(x) f(x) =11+61/xf ( x ) = \frac { 1 } { 1 + 6 ^ { 1 / x } }f(x) =1+61/x1​

Correct AnswerverifiedShow Answer

How would you define f(7) f ( 7 ) f(7) in order to make fff continuous at 7 ? f(x) =x2−2x−3x−7f ( x ) = \frac { x ^ { 2 } - 2 x - 3 } { x - 7 }f(x) =x−7x2−2x−3​

Correct AnswerverifiedShow Answer

Find the limit. lim⁡x→2x2+2x−12x−2\lim _ { x \rightarrow 2 } \frac { x ^ { 2 } + 2 x - 12 } { x - 2 }limx→2​x−2x2+2x−12​

Correct Answerverified6

Determine whether fff is even, odd, or neither. f(x) =4x2x4+5f ( x ) = \frac { 4 x ^ { 2 } } { x ^ { 4 } + 5 }f(x) =x4+54x2​

Correct AnswerverifiedShow Answer

Which of the given functions is discontinuous?

Correct Answerverified\[f ( x ) = \left\{ \begin{arr...View AnswerShow Answer

Correct AnswerverifiedShow Answer

Find the domain of the function. f(x) =7x+1x2f ( x ) = \frac { 7 x + 1 } { x ^ { 2 } }f(x) =x27x+1​

Correct AnswerverifiedShow Answer

Correct AnswerverifiedShow Answer

Correct AnswerverifiedShow Answer

Determine whether fff is even, odd, or neither. f(x)=8x2x4+1f ( x ) = \frac { 8 x ^ { 2 } } { x ^ { 4 } + 1 }f(x)=x4+18x2​

Correct Answerverifiedeven

Graph the function by hand, not by plotting points, but by starting with the graph of one of the standard functions and then applying the appropriate transformations. y=4+2x−x2y = 4 + 2 x - x ^ { 2 }y=4+2x−x2

Correct Answerverified11eb9093_a3c0_b6bd_bccc_0115fe2dbf8d_TB8681_00

The graph of the function f(x) =x2−11x+7f ( x ) = x ^ { 2 } - 11 x + 7f(x) =x2−11x+7 has been stretched horizontally by a factor of 2 . Find the function for the transformed graph.

Correct AnswerverifiedShow Answer

Evaluate the limit. lim⁡x→93−xx−9\lim _ { x \rightarrow 9 } \frac { 3 - \sqrt { x } } { x - 9 }limx→9​x−93−x​​

Correct AnswerverifiedShow Answer

Let F(x) =x−5∣x−5∣F ( x ) = \frac { x - 5 } { | x - 5 | }F(x) =∣x−5∣x−5​ . Find the following limits. lim⁡x→5+F(x) ,lim⁡x→5−F(x) \lim _ { x \rightarrow 5 ^ { + } } F ( x ) , \lim _ { x \rightarrow 5 ^ { - } } F ( x ) limx→5+​F(x) ,limx→5−​F(x)

Correct AnswerverifiedShow Answer

Find the range of the function. y=2+cos⁡xy = 2 + \cos xy=2+cosx

Correct AnswerverifiedShow Answer

Correct AnswerverifiedShow Answer

Find a function $g$ that agrees with $f$ for $x \neq 25$ and is continuous on $\Re$ . $f ( x ) = \frac { 5 - \sqrt { x } } { 25 - x }$

Correct Answer
verified

Find the range of the function. $y = 2 + \cos x$ Select the correct answer.

Correct Answer
verified

Correct Answer
verified

Find $a$ , such that the function $f ( x ) = 4 x + \sqrt { a - x ^ { 2 } }$ has the domain $( - 4,4 )$ .

Correct Answer
verified

Find the value of $\lim _ { x \rightarrow 0 ^ { + } } f ( x )$ $f ( x ) = \frac { 1 } { 1 + 6 ^ { 1 / x } }$

Correct Answer
verified

How would you define $f ( 7 )$ in order to make $f$ continuous at 7 ? $f ( x ) = \frac { x ^ { 2 } - 2 x - 3 } { x - 7 }$

Correct Answer
verified

Find the limit. $\lim _ { x \rightarrow 2 } \frac { x ^ { 2 } + 2 x - 12 } { x - 2 }$

Correct Answer
verified
6

Determine whether $f$ is even, odd, or neither. $f ( x ) = \frac { 4 x ^ { 2 } } { x ^ { 4 } + 5 }$

Correct Answer
verified

Correct Answer
verified
\[f ( x ) = \left\{ \begin{arr...
View Answer

Correct Answer
verified

Find the domain of the function. $f ( x ) = \frac { 7 x + 1 } { x ^ { 2 } }$

Correct Answer
verified

Correct Answer
verified

Correct Answer
verified

Determine whether $f$ is even, odd, or neither. $f ( x ) = \frac { 8 x ^ { 2 } } { x ^ { 4 } + 1 }$

Correct Answer
verified
even

Graph the function by hand, not by plotting points, but by starting with the graph of one of the standard functions and then applying the appropriate transformations. $y = 4 + 2 x - x ^ { 2 }$

Correct Answer
verified
11eb9093_a3c0_b6bd_bccc_0115fe2dbf8d_TB8681_00

The graph of the function $f ( x ) = x ^ { 2 } - 11 x + 7$ has been stretched horizontally by a factor of 2 . Find the function for the transformed graph.

Correct Answer
verified

Evaluate the limit. $\lim _ { x \rightarrow 9 } \frac { 3 - \sqrt { x } } { x - 9 }$

Correct Answer
verified

Let $F ( x ) = \frac { x - 5 } { | x - 5 | }$ . Find the following limits. $\lim _ { x \rightarrow 5 ^ { + } } F ( x ) , \lim _ { x \rightarrow 5 ^ { - } } F ( x )$

Correct Answer
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Find the range of the function. $y = 2 + \cos x$

Correct Answer
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Correct Answer
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