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Unit 2 Corrective Assignment – Functions and Limits, Lecture notes of Pre-Calculus

2) Your GPA is a function of the grades you earn in each class. Identify the independent and dependent variables. 3) Use the graph to the right to approximate ...

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Name:_________________________________Date:_________________Period:________ID:2
PreCalculus
Unit2
Unit2CorrectiveAssignmentFunctionsandLimits
PreCalculus
1)Dothefollowingpairsofinputandoutput
valuesrepresentafunction:󰇛3, 2󰇜,󰇛2,3󰇜,
󰇛0, 4󰇜,󰇛4,4󰇜,and󰇛2,3󰇜?Iftheydon’t,givea
specificreasonwhynot.
2)YourGPAisafunctionofthegradesyouearn
ineachclass.Identifytheindependentand
dependentvariables.
3)Usethegraphtotherighttoapproximatethe
followingvaluestothenearesttenth.
a.󰇛3󰇜
b.󰇛0󰇜
c.If󰇛󰇜2,then
d.If󰇛󰇜0,thenthepossiblevalue(s)of
are:
4)Ifthedependentvariableistheheightfromthegroundinfeetandtheindependentvariableisthe
amountoftimeinsecondsthatyouhavespentonaFerrisWheel,writeasentenceexplainingthe
meaningof󰇛105󰇜62.

5)Tellifeachgraphbelowrepresentsafunction.
a.

b.
   



   



x
y
pf3
pf4

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Download Unit 2 Corrective Assignment – Functions and Limits and more Lecture notes Pre-Calculus in PDF only on Docsity!

Name: _________________________________ Date:_________________ Period: ________ ID: 2

Pre‐Calculus – Unit 2

Unit 2 Corrective Assignment – Functions and Limits

Pre‐Calculus

  1. Do the following pairs of input and output

values represent a function:

ሺ0, 4ሻ, ሺ4,4ሻ, and ሺെ2,3ሻ? If they don’t, give a

specific reason why not.

  1. Your GPA is a function of the grades you earn

in each class. Identify the independent and

dependent variables.

  1. Use the graph to the right to approximate the

following values to the nearest tenth.

a. ݂

b. ݂ ሺ0ሻ ൌ

c. If ݂ ሺݔሻ ൌ െ2, then ൌ ݔ

d. If ݂

, then the possible value(s) of ݔ

are:

  1. If the dependent variable is the height from the ground in feet and the independent variable is the

amount of time in seconds that you have spent on a Ferris Wheel, write a sentence explaining the

meaning of ܪሺ105ሻ ൌ 62.

  1. Tell if each graph below represents a function.

a. b.

      







       







x

y

         











x

y

         











x

y

         











x

y

         







x

y

For 6 ‐9, name the basic function shown and write the equation****.

  1. Function
  1. Function
  1. Function
  1. Function

For 10 ‐11, identify the domain intervals where each function is increasing, decreasing, and constant. Use interval

notation.

  1. Inc: Dec: 11) Inc: Dec:

Constant: Constant:

For 12 ‐15, identify the domain and range of each function. Use both interval notation and inequality notation.

Domain:

Interval: ______________

Inequality: ____________

Range:

Interval: ______________

Inequality: ____________

Domain:

Interval: ______________

Inequality: ____________

Range:

Interval: ______________

Inequality: ____________

Domain:

Interval: ______________

Inequality: ____________

Range:

Interval: ______________

Inequality: ____________

Domain:

Interval: ______________

Inequality: ____________

Range:

Interval: ______________

Inequality: ____________

   





x

y

      







x

y

      







x

y

         





x

y

x

y

x

y

Answer Key to PC Unit 2 Corrective Assignment

  1. Function. 2) Independent: grades you earn in each class.

Dependent: GPA

  1. a) 1 b) 1 c) 0.5 d) -2.8, -1.5, or 0.

  2. After 105 seconds on the Ferris Wheel, your height from the ground is 62 feet.

a) Function

b) Not a function

  1. Greatest Integer;

݂ ሺݔሻ ൌ intሺݔሻ

  1. Logarithm; ݂

log ݔ

  1. Linear; ݂
  1. Sine; ݂

ሺݔሻ ൌ sin ݔ

  1. Inc: ሺെ4, െ3ሻ ∪ ሺെ2, 3ሻ

Dec: ሺെ3, െ2ሻ

Const: ሺെ∞, െ4ሻ ∪ ሺ3, ∞ሻ

  1. Inc: ሺെ4, െ3ሻ ∪ ሺ2, 3ሻ

Dec: ሺെ∞, െ4ሻ ∪ ሺെ3, െ1ሻ ∪ ሺ3, െ∞ሻ

Const: ሺെ1, 2ሻ

  1. Domain: ሺ0, ∞ሻ; ݔ൒ 0

Range: ሾ0, 3ሻ; 0 ൑ ݕ൏ 3

  1. Domain: ሾെ2, 5ሻ; െ2 ൑ ݔ൏ 5

Range: ሾെ2, 3ሿ; െ2 ൑ ݕ൑ 3

  1. Domain: ሺെ5, െ1ሿ ∪ ሺ2, ∞ሻ; െ5 ൏ ݔ൑ െ

Range: ሺെ3, െ1ሿ; െ3 ൏ ݕ൑ െ

  1. Domain: ሺെ5, െ3ሿ ∪ ሺെ2, ∞ሻ; െ5 ൏ ݔ൑ െ

and ݔ൐ െ

Range: ሾെ2, ∞ሻ; ݕ൒ െ

  1. Nonremovable infinite discontinuity at ݔൌ െ3.

Removable discontinuity at ݔൌ െ2.

Nonremovable jump discontinuity at ݔൌ 3.

  1. a. 3 b. Does not exist c. 1 d. 2 e. െ2 f. െ

18) HA:

lim

௫→ିஶ݂

ሺݔሻ ൌ െ

lim

݂௫→ஶ

ሺݔሻ ൌ െ

VA:

lim

௫→ିଶ

݂ష

ሺݔሻ ൌ െ∞

lim

௫→ିଶ

݂శ

ሺݔሻ ൌ ∞

19) HA:

lim

௫→ିஶ݂

ሺݔሻ ൌ 3

lim

݂௫→ஶ

ሺݔሻ ൌ 3

VA:

lim

௫→ଵ

݂ష

ሺݔሻ ൌ ∞

lim

௫→ଵ

݂శ

ሺݔሻ ൌ െ∞

x -2.1 -2.01 -2.001 -2 -1.999 -1.99 -1.

f(x) -11.3 -110.3 -1100.3 Error 1099.7 109.7 10.

HA:

lim

௫→ିஶ݂

ሺݔሻ ൌ െ0.

lim

݂௫→ஶ

ሺݔሻ ൌ െ0.

VA:

lim

௫→ିଶ

݂ష

ሺݔሻ ൌ െ∞

lim

௫→ିଶ

݂శ

ሺݔሻ ൌ ∞