When selecting the range of values for the rational function $$f(x)=\frac{mx+b}{1-x}$$    What value of x are we going to consider when selecting values from the left and right side range of values for the table?

When evaluating the rational function $$f\left(x\right)=\frac{2}{4-x^2}$$  , what is the value of the function at x = 2?

Which of the following Table of Values represents a function?

Which of the following Table of Values represents a function?

Which of the following Table of Values represents a function?

When using the Vertical Line Test determine which of the following Graph is a function?

When using the Vertical Line Test determine which of the following Graph is a function?

When using the Vertical Line Test determine which of the following Graph is a function?

Given the following Table of Values below, find the Limit of the function f(x)

By Method of Inspection, find the limit of the function f(x) as x approaches zero

Find the limit of the function f(x) as x Approaches 2 using the method of Inspection

Evaluate the $$\lim_{x\rightarrow2}=(1+3x)$$  and $$f(2)=(1+3x)$$  

What have you observed?

Evaluate the piecewise function given.

What have you observed?

Evaluate the piecewise function given.

What have you observed?

Evaluate $$\lim_{x\rightarrow2}\left[\left(x^2+x\right)+\left(x+1\right)\right]$$  

Evaluate $$\lim_{x\rightarrow2}\left(3x^2+3\right)$$  

Evaluate $$\lim_{x\rightarrow2}\left(x^2+2x+1\right)$$  

given f(x) = 2x - 2 and g(x) = 3x + 3

find ( g + f ) (3)

given f(x) = -x + 4 and g(x) = x + 3

find ( g - f ) (3)

given $$f(x)=x^3+3x^2$$   and $$g(x)=3x+1$$  

find f(2) * g(2)

Determine the limit of the Polynomial function $$f(x)=\lim_{x\rightarrow1}(2x+1)$$  

Determine the limit of the Rational function $$f(x)=\lim_{x\rightarrow2}\left(\frac{x}{x+1}\right)$$  

Determine the limit of the Rational function $$f(x)=\lim_{x\rightarrow2}\left(\frac{x^3-1}{\sqrt[]{x-1}}\right)$$  

Complete the table

Complete the table

Which of the graph below represents the expression  $$\log_2(x+5)$$  

Evaluate the $$\lim_{x\rightarrow\pi}4\sin\left(x+\pi\right)+3$$  

Evaluate the $$\lim_{x\rightarrow\pi}\cos\left(\frac{x}{2}+\frac{\pi}{4}\right)+\frac{1}{2}$$  

Evaluate the $$\lim_{x\rightarrow5}\log_3\left(3x^2+2x-4\right)$$  

Graph the function f(x) = 3x -1 at x =1

determine if the graph is Continuous or Discontinuous

Graph the function $$f\left(x\right)=\frac{3x^2-4x+1}{x-1}$$  at x=1

determine if the graph is Continuous or Discontinuous

Graph the function $$f\left(x\right)=\frac{1}{x}$$  at x=0

determine if the graph is Continuous or Discontinuous

Determine the 3 Step Continuity Test from the conditions given below

1.) $$f\left(c\right)$$   exist

2.) $$\lim_{x\rightarrow c}f\left(x\right)$$   exists.  where $$\lim_{x\rightarrow c^-}f\left(x\right)\ =\lim_{x\rightarrow c^{+-}}f\left(x\right)$$  

3.) $$\lim_{x\rightarrow c}f\left(x\right)=f\left(c\right)$$

4.) f(x) is a real number.  where $$\lim_{x\rightarrow c^-}f\left(x\right)\ =\lim_{x\rightarrow c^{+-}}f\left(x\right)$$

Determine which of the following are types of Discontinuity

1.) Limited Discontinuity

2.) Point / Removable Discontinuity

3.) Jump Discontinuity

4.) Asymptotic / Infinite Discontinuity

When using a graph what is the best description to determine that the graph of the function is continuous?

Using the Pencil to trace the graph above, illustrate and determine the continuity of the function between the interval (-∞,2)

Using the Pencil to trace the graph above, illustrate and determine the continuity of the function between the interval (2,+∞)

Using the Pencil to trace the graph above, illustrate and determine the continuity of the function between the interval (3,4)

Determine whether the function on the following interval is continuous or not

$$f\left(x\right)=\sqrt[]{4-x^2}$$   for the interval (-2, 2)

Determine whether the function on the following interval is continuous or not

$$f\left(x\right)=3x^2-x+5$$   for the interval (-∞,+∞)

Determine whether the function on the following interval is continuous or not

$$f\left(x\right)=\frac{x-2}{x^2-x-2}$$   for the interval (-3,+1)

Which of the following definition best describes Jump Discontinuities

1.) This type of discontinuity occurs when the graph has a break in it and the values of the function to either side of the break are finite (The Function does not go to infinity)

2.) In this Type of discontinuity, at least one of the two limits is infinite

3.) Occurs when no general limits exists at the given x value (where the left and right hand limits exist but are not equal

4.) Are discontinuities which is represented by a hole in the graph

Which of the following definition describes Hole Discontinuities

1.) This type of discontinuity occurs when the graph has a break in it and the values of the function to either side of the break are finite (The Function does not go to infinity)

2.) In this Type of discontinuity, at least one of the two limits is infinite

3.) Occurs when no general limits exists at the given x value (where the left and right hand limits exist but are not equal

4.) Are discontinuities which is represented by a hole in the graph

Which of the following definition describes Asymptotic Discontinuities

1.) This type of discontinuity occurs when the graph has a break in it and the values of the function to either side of the break are finite (The Function does not go to infinity)

2.) In this Type of discontinuity, at least one of the two limits is infinite

3.) Occurs when no general limits exists at the given x value (where the left and right hand limits exist but are not equal

4.) Are discontinuities which is represented by a hole in the graph

Which of the following statements are true about Intermediate Value and Extreme Value theorems

1.) Intermediate Value Theorem (IVT) is only applicable for closed loop

2.) The Extremum is either the Minimum or Maximum value of the function

3.) Intermediate Value Theorem (IVT) is only applicable for open loops

4.) The Extremum is neither the Minimum or Maximum value of the function

Consider $$f(x)=x^2$$  on the closed interval [-4,2],

what are the minimum and maximum values of the function?

Consider f(x) = 2x - 5 on the closed interval [1,5],

what are the values of m when evaluating IVT?

Evaluate the function $$f\left(x\right)=x^3-x^2-2$$  

and determine if the f(x) is continuous at x = 1

Evaluate the function $$f\left(x\right)=\frac{x^2-x-2}{x-2}$$  

and determine if the f(x) is continuous at x = 0

Evaluate the function $$f\left(x\right)=\frac{\sqrt[]{x+1}}{\sqrt[]{x-1}}$$  

and determine if the f(x) is continuous at x = 0

Which of the following is not a property of a Tangent Function ?

Which of the following table of values represents the Graph of a Tangent Function ?

Which of the following is a Graph of a Function of a Tangent?

Find the equation of the Tangent line to

y = x2 at (2,4)

Find the slope intercept form of the Tangent line to

f(x) = 2x + 1 at x = 4

Find the slope of the Tangent line to the graph 

$$y=\sqrt[]{x-1}$$   at point (5,2)

Find the derivative of the function

$$f(x)=3x^2-5x$$   at x = 1

Find the derivative of the function

$$f(x)=x^2-5x+6$$  at x=2

Find the derivative of the function

$$f(x)=3x^2-5x$$  at x=1

using the alternative definition of derivatives

Find the slope of the tangent line to the curve

$$y=x^2$$   at x = 2

Find the slope of the tangent line to the curve

$$f\left(x\right)=\sqrt[]{x}$$   at x = 4

Find the slope of the tangent line to the curve

$$y=x^2-4x+5$$   at x = 1

Which of the following is another way of writing the derivative of y = f(x)

Which of the following statements are true about Differentiability and Continuity?

1.) if a function is differentiable x = c, then it is continuous at x = c, so differentiability implies continuity

2.) it is possible for a function to be continuous at x = c and not differentiable at x = c. So continuity does not imply differentiability

3.) Differentiation must always be continuous and Continuous Functions can always be differentiated

4.) 1,2 and 3 statements are all incorrect