Let f f f be a function that is defined for all real numbers x . x. x . Of the following, which is the best interpretation of the statement lim ⁡ x → 2 f ( x ) = 7 ? \lim_{x\rightarrow2}f\left(x\right)=7? x → 2 lim f ( x ) = 7 ?

As x x approaches 2, 2 , the values of f\left(x\right) f ( x ) approach 7. 7 .

The value of the function f f f at x = 2 x=2 x = 2 is 7. 7. 7 .

The value of the function f f at x = 7 x=7 x = 7 is 2. 2. 2 .

As x x approaches 7 , 7, 7 , the values of f\left(x\right) f ( x ) approach 2. 2. 2 .

Let f f f be a function that is defined for all real numbers x . x. x . Of the following, which is the best interpretation of the statement lim ⁡ x → 3 f ( x ) = 5 ? \lim_{x\rightarrow3}f\left(x\right)=5? x → 3 lim f ( x ) = 5 ?

As x x approaches 3 , 3, 3 , the values of f\left(x\right) f ( x ) approach 5. 5. 5 .

The value of the function f f f at x = 3 x=3 x = 3 is 5. 5. 5 .

The value of the function f f at x = 5 x=5 x = 5 is 2. 2. 2 .

As x x approaches 5 , 5, 5 , the values of f\left(x\right) f ( x ) approach 3. 3. 3 .

1.2 Defining Limits

Authored by JAMIE BETH MCLEOD

Mathematics

9th - 12th Grade

CCSS covered

Used 17+ times

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FILL IN THE BLANK QUESTION

1 min • 1 pt

$\lim_{x\rightarrow-2}f\left(x\right)=$

If the limit does not exist, write "DNE."

FILL IN THE BLANK QUESTION

1 min • 1 pt

$f\left(4\right)=$

If the function value is undefined, write "UND."

Tags

CCSS.HSF.IF.A.2

FILL IN THE BLANK QUESTION

1 min • 1 pt

$f\left(-2\right)=$

If the function value is undefined, write "UND."

Tags

CCSS.HSF.IF.A.2

FILL IN THE BLANK QUESTION

1 min • 1 pt

$\lim_{x\rightarrow-1}f\left(x\right)=$

If the limit does not exist, write "DNE."

FILL IN THE BLANK QUESTION

1 min • 1 pt

$\lim_{x\rightarrow4}f\left(x\right)=$

If the limit does not exist, write "DNE."

FILL IN THE BLANK QUESTION

1 min • 1 pt

$\lim_{x\rightarrow0}f\left(x\right)=$

If the limit does not exist, write "DNE."

FILL IN THE BLANK QUESTION

1 min • 1 pt

$\lim_{x\rightarrow1}f\left(x\right)=$

If the limit does not exist, write "DNE."

Tags

CCSS.HSF.IF.A.2

FILL IN THE BLANK QUESTION

1 min • 1 pt

$f\left(1\right)=$

If the function value is undefined, write "UND."

Tags

CCSS.HSF.IF.A.2

FILL IN THE BLANK QUESTION

1 min • 1 pt

$\lim_{x\rightarrow2}f\left(x\right)=$

If the limit does not exist, write "DNE."

10.

FILL IN THE BLANK QUESTION

1 min • 1 pt

$f\left(-2\right)=$

If the function value is undefined, write "UND."

Tags

CCSS.HSF.IF.A.2

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1.2 Defining Limits

lim⁡x→−2f(x)=\lim_{x\rightarrow-2}f\left(x\right)=x→−2lim​f(x)= If the limit does not exist, write "DNE."

f(4)=f\left(4\right)=f(4)= If the function value is undefined, write "UND."

f(−2)=f\left(-2\right)=f(−2)= If the function value is undefined, write "UND."

lim⁡x→−1f(x)=\lim_{x\rightarrow-1}f\left(x\right)=x→−1lim​f(x)= If the limit does not exist, write "DNE."

lim⁡x→4f(x)=\lim_{x\rightarrow4}f\left(x\right)=x→4lim​f(x)= If the limit does not exist, write "DNE."

lim⁡x→0f(x)=\lim_{x\rightarrow0}f\left(x\right)=x→0lim​f(x)= If the limit does not exist, write "DNE."

lim⁡x→1f(x)=\lim_{x\rightarrow1}f\left(x\right)=x→1lim​f(x)= If the limit does not exist, write "DNE."

f(1)=f\left(1\right)=f(1)= If the function value is undefined, write "UND."

lim⁡x→2f(x)=\lim_{x\rightarrow2}f\left(x\right)=x→2lim​f(x)= If the limit does not exist, write "DNE."

f(−2)=f\left(-2\right)=f(−2)= If the function value is undefined, write "UND."

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$\lim_{x\rightarrow-2}f\left(x\right)=$

If the limit does not exist, write "DNE."

$f\left(4\right)=$

If the function value is undefined, write "UND."

$f\left(-2\right)=$

If the function value is undefined, write "UND."

$\lim_{x\rightarrow-1}f\left(x\right)=$

If the limit does not exist, write "DNE."

$\lim_{x\rightarrow4}f\left(x\right)=$

If the limit does not exist, write "DNE."

$\lim_{x\rightarrow0}f\left(x\right)=$

If the limit does not exist, write "DNE."

$\lim_{x\rightarrow1}f\left(x\right)=$

If the limit does not exist, write "DNE."

$f\left(1\right)=$

If the function value is undefined, write "UND."

$\lim_{x\rightarrow2}f\left(x\right)=$

If the limit does not exist, write "DNE."

$f\left(-2\right)=$

If the function value is undefined, write "UND."