Rational Functions and Their Graphs

The Graphs of Rational Functions

By Melodie Hunt

Graphs of​ Rationals

Partner Review Activity​ DRAFT

By Melodie Hunt

Remember: CONTINUOUS FUNCTIONS ARE TRACEABLE IN ONE STROKE

Remember: CONTINUOUS FUNCTIONS ARE TRACEABLE IN ONE STROKE

Remember: RATIONAL FUNCTIONS DO NOT HAVE A DOMAIN OF ALL REAL NUMBERS

REMEMBER: IF THE FACTOR CANCELS IT CAUSES A HOLE, IF IT DOESN'T CANCEL IT CAUSES A VERTICAL ASYMPTOTE​

The interval over which the function is continuous on is also called the DOMAIN​

​Choose one problem from this page to do in your notes.

​Solutions

Multiple Choice

Determine the value the would cause the denominator to equal zero.
x²-2x-8
__________
3x-2

• y=2/3
• x=3/2
• x= 2/3
• x=1/3

Multiple Choice

Where is the function discontinuous?

x =

• 3

• -3

• 6

• -6

Multiple Choice

Where is the expression undefined?

*Don't pay any attention to the answer choices in the image.

• x = 8, -4

• x = 0

• x = 4 only

• x = -8, 4

Multiple Choice

For which values of x is the denominator equal to zero?

• -3 , 0
• -2, 1 
• 2, -1
• -1 only

Multiple Choice

State the value for which f(x) is undefined:  f(x)=(x-2)/(x+5).

• x = -2/5
• x = -5/2
• x = -5
• x = 2

Multiple Choice

Simplify and state the excluded values.

• 6/(5x),
  x≠0
• (x-4)/(x-2),
  x≠-2
• (x+3)/(x+2),
  x≠-2, 4
• (x+3)/(x-4),
  x≠-2, 4

​On the next slide you will see 5 questions. Turn and talk to your partner about the answers to each of these questions. Then each of you will write your agreed upon answers down on paper. Turn them into the bin when you have finished this entire quizizz.​​

​Take out your notes on graphing rationals - REHEARSE GRADE.

On the left side of you paper, answer these questions in complete sentences. On the right side of your paper find everything for the example problem.

​

1. How d​o you find points of discontinuity for a rational function?

2. How do you determine if the points of discontinuities are holes or ​vertical asymptotes?

3. If the discontinuity is a hole, how do you find the x and y coordinate of the hole.

4. What are the three cases of the horizontal asymptote.

5. ​Explain to a student how they would find the horizontal asymptote.

Multiple Choice

What are the asymptotes?

• x = -3        y = 1  
• x = 3         y = 1
• x = -3        y = -1
• x = 3         y = -1

Multiple Choice

What is the Vertical Asymptotes? 

• x= -5
• x= 5
• x= 6
• x= -6

Multiple Choice

What are the Vertical Asymptotes of...

• x = 0, -5
• x=0, 5
• x = 2, -7
• x = -2, 7

Multiple Choice

What is/are the vertical asymptote(s)?

• There are no vertical asymptotes
• x=5
• x=-5
• x=-1/2

Multiple Choice

What creates a hole in the graph of a rational function?

• Crossing the x-axis

• An absence of dirt.

• Crossing a vertical asymptote.

• A factor that cancels out.

Multiple Choice

How do you find the y-coordinate of a hole? Read carefully!

• Set the denominator equal to zero.

• Evaluate f(0)

• Substitute the x-coordinate of the hole into the original function.

• Substitute the x-coordinate of the hole into the simplified function.

Multiple Choice

What is the hole?

• x= 4
• x= -4
• x= 5
• x= -5

Multiple Choice

What is the y-coordinate of the hole?

• 0

• 8

• 1/2

• 2

Multiple Choice

What is the y-coordinate of the hole?

• 10/9

• 0

• 9/10

• -1/9

Multiple Choice

Find the horizontal asymptote.

• None
• y = 0
• y = -1/3
• y = -3

Multiple Choice

What is the horizontal asymptote?

• y = 1

• y = 2

• y = 0

• There isn't one.

Multiple Choice

Determine the horizontal asymptote.

• y = 1

• y = 1/2

• y = 0

• There isn't one.

Multiple Choice

Find the domain of i(x):

• (-∞, +∞)
• (-∞, 0) U (0, ∞)
• (-∞, 3) U (3, ∞)
• [0, ∞)

Multiple Choice

State the domain:

• (-oo, 7) U (7, oo)

• (-oo, -7) U (7, oo)

• (7, oo)

• [7, oo)

Multiple Choice

State the domain:

• (-oo, 1) U (1, oo)

• (-oo, -1) U (-1, 1) U (1, oo)

• (-oo, oo)

• (-oo, -1] U [-1, 1] U [1, oo)

Multiple Choice

State the domain:

• (-oo, oo)

• (-oo, 6) U (-2, oo)

• (-oo, -2) U (-2, 6) U (6, oo)

• (-oo, -2) U (-2, 0) U (0, 6) U (6, oo)

Multiple Choice

State the domain:

• (-oo, oo)

• [3, oo)

• (3, oo)

• (-oo, 3) U (3, oo)