sketch a graph of a function that satisfies all of the following conditions.

Question

1. Sketch a graph of a function that satisfies all of the following conditions:

1. f (3)=4
2. limx--->3 f (x)=-1
3. limx--->-2 f (x) does not exist.
4. limx--->-2- f (x)=4

2. Sketch a graph of a function that satisfies all of the following conditions:

1. limx---> -1 f (x)=3
2. f is discontinuous at -1
3. the domain of f is (- infinity, + infinity)
4. limx--->- infinity f (x) = 5
5. limx--->infinity f (x)= 0

3. Sketch a graph of a function that satisfies all of the following conditions:

1. limx--->2 f (x)= infinity
2. f has a removable discontinuity at 3.
3. f (3)=4
4. limx---> infinity f (x) =/(not equal to) +- infinity
5. f has no horizontal asymptotes

Answer 1

1)

 

Since the limit of f(x) does not exist as x approaches 2, we will have a vertical asymptote at x=-2.

A coordinate of f(x) is (3,4).

 

As x approaches 3 from the right, f(x) gets closer to -1.   Draw an open circle at (3, -1).

As x approaches 2 from the left, f(x) gets closer to 4.  Draw an open circle at (2, 4).

 

Draw a line that connects these points.  Note at x=3 has two values.  The include value is 4 and the excluded value is -1.

 

 

2)

 

The domain is all real numbers.  This means that the graph is a quadratic or linear type.

 

As x approaches -1 from the right, f(x) = 3.  Draw an open circle at (-1, 3).  This is also the discontinuity, so we are killing two birds with one stone on this part.  Use this point as your starting point.

 

Next is to analyze the limits.

As x approaches negative infinity from the right, f(x) is 5.  This is a horizontal asymptote at y=5.

As x approaches positive infinity from the right, f(x) is 0.  This should say as x approach positive infinity from the left.  This is a horizontal asymptote at y=5.This is a horizontal asymptote at y=0.

 

Now you can graph.  Try out the last one.  Sorry I cannot show the resulting graphs here.  I hope my instructions are helpful to you.