Cal 1 Boot Camp: Student PacketParent Functions

Parent Function Graph Parent Function Graph

Lineary=x

Domain: (-∞,∞)Range: (-∞,∞)

Symmetry: Odd Origin

Absolute Valuey=IxI

Domain: (-∞,∞)Range: [0,∞)

Symmetry: Even Y-axis

Quadraticy=x2

Domain: (-∞,∞)Range: [0,∞)

Symmetry: Even Y-axis

Radicaly=√ x

Domain: [0,∞)Range: [0,∞)

Symmetry: Neither

Cubicy=x3

Domain: (-∞,∞)Range: (-∞,∞)

Symmetry: Odd Origin

Cube Rooty=3√ x

Domain: (-∞,∞)Range: (-∞,∞)

Symmetry: Odd Origin

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Exponentialy=bx, b>1

Domain: (-∞,∞)Range: (0,∞)

Symmetry: Neither

Logy=log b x , b>1, x>0

Domain: (0,∞)Range: (-∞,∞)

Symmetry: Neither

Rational(Inverse)y=1/x

Domain: (-∞,0)U(0,∞)

Range: (-∞,0)U(0,∞)

Symmetry: Odd Origin

Rational(InverseSquared)

y=1/x2

Domain: (-∞,0)U(0,∞)

Range: (0,∞)

Symmetry: Even Y-axis

Greatest Integery=int(x)=[x]

Domain: (-∞,∞)Range:{y:yεZ}

(integers)

Symmetry: Neither

Constanty=C (in this graph

y=2)

Domain: (-∞,∞)Range: {y: y=C}

Symmetry: Even Y-axis

Tips and Tricks - Transformations of Functions

y=mx+v

y=a ( x−h )2+v

y=a√x−h+v

y=a ( x−h )3+v

y=a 3√x−h+v

y=a|x−h|+v

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y=aⅇ( x−h)+v

y=a 2( x−h )+v

y=a log10 ( x−h )+v

y= ax−h

+v

y= a( x−h)2 +v

Tips and Tricks – Vertical Asymptotes and Horizontal Asymptotes

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f ( x )=1x

f ( x )= 1x−1 f ( x )= x2

x−1

Tips and Tricks – For x and y Intercepts, Vertical Asymptotes, and Horizontal Asymptotes

1. y=x+1

2. y=x2+3

3. y=x3+6

4. y=√x

5. y=√x−9

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6. y= 3√x

7. y= 3√x+10

8. y=1x

9. y= 1x−1

10. y= 1x2

11. y= 1( x+4 )2

12. y= 1√ x

13. y= 1√ x−8

Tips and Tricks – Determining the Following for GraphsUse the graph of f to determine each of the following. Where applicable, use interval notation:

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a. The domain of fb. The range of fc. The x-interceptsd. The y-intercepte. Intervals on which f is increasingf. Intervals on which f is decreasingg. Intervals on which f is constanth. The number at which f has a relative minimumi. The relative minimum of fj. f(-3)k. the values of x for which f(x)=-2l. Is f even, odd, or neither?

Understanding Graphs and Limits

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1.limx →1

1

( x−1 )2

2.lim

x→ 1−¿−1

x−1¿

¿

3.lim

x→ 1+¿−1

x−1 ¿

¿

4.lim

x→−2−¿ x2+2 x−8x2− 4

¿

¿

5.lim

x→−2+¿ x2+2 x−8x2−4

¿

¿

Understanding Cal 1 Graphs

Where is the graph undefined, continuous, or discontinuous?

a) f (−2 )=¿

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b) f (−1 )=¿c) f (1 )=¿d) f (2 )=¿e) x→1−¿¿=f) x→ 1+¿¿=g) x→−4+¿=¿¿

h) x→ ∞−¿=¿¿

a) f (−2 )=¿

b) limx→−2

f ( x )=¿ c) f (0 )=¿

d) limx →0

f ( x )

e) f (2 )=¿

f) limx →2

f ( x )=¿

g) f ( 4 )=¿

h) limx→ 4−¿ f ( x )=¿¿

¿

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i) limx→ 4+¿ f ( x )=¿¿

¿

j) limx→ 4

f ( x )=¿

a) f (1 )=¿b) limx →1

f ( x )=c) f ( 4 )=¿d) limx→ 4

f ( x )=

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Definition of a DerivativeDefinition of a Derivative of a function:

The derivative of f at x is given by

f ’(x) = lim

Δx →0f ( x+ Δx )− f ( x )

Δx

provided the limit exists. For all x for which this limit exists, f ’ is a function of x.

Find the limit by the limit process.

1. f ( x )=4 x

2. f ( x )=x2−4 x+7

3. f ( x )=7

4. f ( x )=x3

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Tips and Tricks – Difference QuotientDefinition of a Difference Quotient:

The expression

f ( x+h )− f ( x )h

For h ≠ 0 is called the difference quotient.

1. For f ( x )=4 x , find f ( x+h )−f ( x )

h

2. For f ( x )=x2−4 x+7 , find f ( x+h )−f ( x )

h

3. For f ( x )=1x−2 , find

f ( x+h )−f ( x )h

4. For f (x)=√x +8, find f ( x+h )−f ( x )

h

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Tips and Tricks -For Deriving Pythagorean Identities

sin2 (θ )+cos2 (θ )=1

tan2 (θ )=sec 2 (θ )−1

cot2 (θ )=csc2 (θ )−1

Where did π come from?

1. π=Cd

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Trigonometric Parent Functions

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Blank Unit Circle

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Tips and Tricks – Do’s and Don’ts of Calculator:

The Do’s:

Texas Instruments TI - 84 Plus CE: Casio FX-115 ES Plus:

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Best Software Calculator!!!TI SmartView CE for the TI – 84 Plus Family:

The Don’ts:Texas Instruments TI-83 series calculators

Texas Instruments TI-30 series calculators

Texas Instruments TI-nSpire calculators

Casio FX-9750 GII calculator

Casio G series calculators

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Basic Differential Rules

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Basica Integration Formulas

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Formula Trig Sheet

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