DiffCalculus Week 3

1. Opener.

Answer the following

Week 3

viernes, 24 de agosto de 12

2. What is a logarithm?

Remember that

means “to what power should I rise a to get b”.


2. Logarithmic Equations.

Solve the equations



Solve the equations

x = 8



Solve the equations

x = 8

x = 11/2



Solve the equations

x = 8

x = 11/2

x = e-1/2


3. Exponential Equations.

Solve the equations



Solve the equations

x = 4



Solve the equations

x = 4

x = -1



Solve the equations

x = 4

x = -1

x = 3


4. Basic Graphs of Functions.

Sketch the graph of the following functions.

1. y = x2. y = x2

3. y = x3

4. y = x4

5. y = 1x6. y = x

7. y = x3

8. y = x9. y = ax

10. y = loga x


1. Exercise.

Sketch the following functions. Find the domain, range and asymptotes (if any).


2. Transformation of Functions.

If we have a function f(x), what happens if we have

1. f(x) + a

2. f(x) - a

3. f(x + a)

4. f(x - a)

5. - f(x)

6. f(-x)




1. f(x) + a

2. f(x) - a

3. f(x + a)

4. f(x - a)

5. - f(x)

6. f(-x)

Shifted upward a units




1. f(x) + a

2. f(x) - a

3. f(x + a)

4. f(x - a)

5. - f(x)

6. f(-x)


Shifted downward a units




1. f(x) + a

2. f(x) - a

3. f(x + a)

4. f(x - a)

5. - f(x)

6. f(-x)



Shifted left a units




1. f(x) + a

2. f(x) - a

3. f(x + a)

4. f(x - a)

5. - f(x)

6. f(-x)




Shifted right a units




1. f(x) + a

2. f(x) - a

3. f(x + a)

4. f(x - a)

5. - f(x)

6. f(-x)





Reflected about the x-axis




1. f(x) + a

2. f(x) - a

3. f(x + a)

4. f(x - a)

5. - f(x)

6. f(-x)





Reflected about the x-axis

Reflected about the y-axis


3. Homework 3

Blackboard -> Assignments


Practice with Graphical Analysis

Domain



Domain = R



Domain = R

Range



Domain = R

Range =



Evaluate f(0)Evaluate f(0) - f(1)Evaluate f(f(0))



Evaluate f(0) = 3

Evaluate f(0) - f(1)Evaluate f(f(0))



Evaluate f(0) = 3

Evaluate f(0) - f(1) = 3 - 2 = 1

Evaluate f(f(0))



Evaluate f(0) = 3

Evaluate f(0) - f(1) = 3 - 2 = 1

Evaluate f(f(0)) = f(3) = -6



Solve for x: f(x) < -4



Solve for x: f(x) < -4 (2, 4)



Solve for x: f(x) < -4 (2, 4)

Solve for x: f(x) 2



Solve for x: f(x) < -4 (2, 4)

Solve for x: f(x) 2 [-1, 1]


Homework 4Blackboard -> Assignments


DiffCalculus Week 3

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