INTERMEDIATE VALUE THEOREM

Authored by Greg Snelick

Mathematics

10th Grade - University

CCSS covered

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18 questions

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FILL IN THE BLANKS QUESTION

45 sec • 2 pts

INTERMEDIATE VALUE THEOREM
$g\left(x\right)$ is continuous on $\left[\ a,b\ \right]$
No $word1,word2,word3\ word4$
Submit $word1,word2,word3,word4$ (small letters) (alphabetical order) (3 plurals) (no spaces)

(a)

FILL IN THE BLANKS QUESTION

45 sec • 2 pts

INTERMEDIATE VALUE THEOREM
$g\left(x\right)$ is continuous on $\left[\ a,b\ \right]$
$\left[\ a,b\ \right]$ is a $word$ interval
Submit $word$ (small letters)

(a)

MULTIPLE CHOICE QUESTION

45 sec • 2 pts

INTERMEDIATE VALUE THEOREM
$g\left(x\right)$ is continuous on $\left[\ a,b\ \right]$
Relationship between $a$ and $b$
if $a\ne b$

$a>b$

$a=b$

$a<b$

INTERMEDIATE VALUE THEOREM
$g\left(x\right)$ is continuous on $\left[\ a,b\ \right]$
Point on the graph of $g\left(x\right)\ @\ x=a$
Submit CALCULUS notation (no spaces)

(a)

FILL IN THE BLANKS QUESTION

45 sec • 2 pts

INTERMEDIATE VALUE THEOREM
$g\left(x\right)$ is continuous on $\left[\ a,b\ \right]$
Point on the graph of $g\left(x\right)\ @\ x=b$
Submit CALCULUS notation (no spaces)

(a)

MULTIPLE SELECT QUESTION

45 sec • 2 pts

INTERMEDIATE VALUE THEOREM
$g\left(x\right)$ is continuous on $\left[\ a,b\ \right]$
Points $\left[a,g\left(a\right)\right]$ and $\left[b,g\left(b\right)\right]$
Relationship between $g\left(a\right)$ and $g\left(b\right)$
(check all that apply)

$g\left(a\right)<g\left(b\right)$

$g\left(a\right)=g\left(b\right)$

$g\left(a\right)>g\left(b\right)$

MULTIPLE SELECT QUESTION

45 sec • 2 pts

INTERMEDIATE VALUE THEOREM
$g\left(x\right)$ is continuous on $\left[\ a,b\ \right]$
$k$ is between $g\left(a\right)$ and $g\left(b\right)$
(check all that apply)

$k$ is a y-value

$g\left(a\right)\ ,\ g\left(b\right)$ are x-values

$k\ ,\ g\left(a\right)\ ,\ g\left(b\right)$ are x-values

$k$ is an x-value

$g\left(a\right)\ ,\ g\left(b\right)$ are y-values

$k\ ,\ g\left(a\right)\ ,\ g\left(b\right)$ are y values

INTERMEDIATE VALUE THEOREM
$g\left(x\right)$ is continuous on $\left[\ a,b\ \right]$
There exists at least one number $c$ on $\left[\ a,b\ \right]$
Point at $x=c$
Submit CALCULUS notation (no spaces)

(a)

FILL IN THE BLANKS QUESTION

45 sec • 2 pts

INTERMEDIATE VALUE THEOREM
$g\left(x\right)$ is continuous on $\left[\ a,b\ \right]$
There exists at least one number
$c$ on $\left[\ a,b\ \right]$ such that $M\left(N\right)=P$
Submit $M,N,P$ (no spaces) (small letters)

(a)

10.

FILL IN THE BLANKS QUESTION

45 sec • 2 pts

Apply IVT if $k=5$
Window $\left[\ -\ 2,6,1\ \right]\ x\ \left[\ -\ 30,50,5\ \right]$
How many points $\left[\ c,g\left(c\right)\ \right]$ exist ?
Submit $N$

(a)

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INTERMEDIATE VALUE THEOREM

INTERMEDIATE VALUE THEOREM g(x)g\left(x\right)g(x) is continuous on [ a,b ]\left[\ a,b\ \right][ a,b ] [ a,b ]\left[\ a,b\ \right][ a,b ] is a wordwordword interval Submit wordwordword (small letters) (a)

INTERMEDIATE VALUE THEOREM g(x)g\left(x\right)g(x) is continuous on [ a,b ]\left[\ a,b\ \right][ a,b ] Relationship between aaa and bbb if a≠ba\ne ba=b

INTERMEDIATE VALUE THEOREM g(x)g\left(x\right)g(x) is continuous on [ a,b ]\left[\ a,b\ \right][ a,b ] Point on the graph of g(x) @ x=ag\left(x\right)\ @\ x=ag(x) @ x=a Submit CALCULUS notation (no spaces) (a)

INTERMEDIATE VALUE THEOREM g(x)g\left(x\right)g(x) is continuous on [ a,b ]\left[\ a,b\ \right][ a,b ] Point on the graph of g(x) @ x=bg\left(x\right)\ @\ x=bg(x) @ x=b Submit CALCULUS notation (no spaces) (a)

INTERMEDIATE VALUE THEOREM g(x)g\left(x\right)g(x) is continuous on [ a,b ]\left[\ a,b\ \right][ a,b ] kkk is between g(a)g\left(a\right)g(a) and g(b)g\left(b\right)g(b) (check all that apply)

INTERMEDIATE VALUE THEOREM g(x)g\left(x\right)g(x) is continuous on [ a,b ]\left[\ a,b\ \right][ a,b ] There exists at least one number ccc on [ a,b ]\left[\ a,b\ \right][ a,b ] Point at x=cx=cx=c Submit CALCULUS notation (no spaces) (a)

INTERMEDIATE VALUE THEOREM g(x)g\left(x\right)g(x) is continuous on [ a,b ]\left[\ a,b\ \right][ a,b ] There exists at least one number ccc on [ a,b ]\left[\ a,b\ \right][ a,b ] such that M(N)=PM\left(N\right)=PM(N)=P Submit M,N,PM,N,PM,N,P (no spaces) (small letters) (a)

Apply IVT if k=5k=5k=5 Window [ − 2,6,1 ] x [ − 30,50,5 ]\left[\ -\ 2,6,1\ \right]\ x\ \left[\ -\ 30,50,5\ \right][ − 2,6,1 ] x [ − 30,50,5 ] How many points [ c,g(c) ]\left[\ c,g\left(c\right)\ \right][ c,g(c) ] exist ?Submit NNN (a)

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INTERMEDIATE VALUE THEOREM
$g\left(x\right)$ is continuous on $\left[\ a,b\ \right]$
$\left[\ a,b\ \right]$ is a $word$ interval
Submit $word$ (small letters)

(a)

INTERMEDIATE VALUE THEOREM
$g\left(x\right)$ is continuous on $\left[\ a,b\ \right]$
Relationship between $a$ and $b$
if $a\ne b$

INTERMEDIATE VALUE THEOREM
$g\left(x\right)$ is continuous on $\left[\ a,b\ \right]$
Point on the graph of $g\left(x\right)\ @\ x=a$
Submit CALCULUS notation (no spaces)

(a)

INTERMEDIATE VALUE THEOREM
$g\left(x\right)$ is continuous on $\left[\ a,b\ \right]$
Point on the graph of $g\left(x\right)\ @\ x=b$
Submit CALCULUS notation (no spaces)

(a)

INTERMEDIATE VALUE THEOREM
$g\left(x\right)$ is continuous on $\left[\ a,b\ \right]$
$k$ is between $g\left(a\right)$ and $g\left(b\right)$
(check all that apply)

INTERMEDIATE VALUE THEOREM
$g\left(x\right)$ is continuous on $\left[\ a,b\ \right]$
There exists at least one number $c$ on $\left[\ a,b\ \right]$
Point at $x=c$
Submit CALCULUS notation (no spaces)

(a)

INTERMEDIATE VALUE THEOREM
$g\left(x\right)$ is continuous on $\left[\ a,b\ \right]$
There exists at least one number
$c$ on $\left[\ a,b\ \right]$ such that $M\left(N\right)=P$
Submit $M,N,P$ (no spaces) (small letters)

(a)

Apply IVT if $k=5$
Window $\left[\ -\ 2,6,1\ \right]\ x\ \left[\ -\ 30,50,5\ \right]$
How many points $\left[\ c,g\left(c\right)\ \right]$ exist ?
Submit $N$

(a)