Exponential Functions Part 1
 y = abx - h + k

Enter a = 1, b = 2, h = 0, and k = 0  
gives y = 1×2x-0 + 0  or  y = 2x
Click Graph, then Click Store.
Use this graph to compare 

1 . Enter a = 1, b = 2, h = 0, and k = 1   
Predict which way the graph will SHIFT?
Up None
Down

Now click Graph.

2. Enter  a = 1, b = 2, h = 0, and k = -2   
Predict which way the graph will SHIFT?
Up None
Down

Now click Graph.

3. Enter a = 1, b = 2, h = 0, and k = 5/2    
Predict which way the graph will SHIFT?
Up None
Down

Now click Graph.
Exponential Part 2
 y = abx - h + k

Enter a = 1, b = 2, h = 0, and k = 0  
gives y = 1×2x-0 + 0  or  y = 2x
Click Graph, then Click Store.
Use this graph to compare 

1 . Enter a = 1, b = 2, h = 3, and k = 0   
Predict which way the graph will SHIFT?
Left None
Right

Now click Graph.

2. Enter a = 1, b = 2, h = -6, and k = 0 (change window to fit)
Predict which way the graph will SHIFT?
Left None
Right

Now click Graph.

3. Enter a = 1, b = 2, h = 4, and k = 0 
Predict which way the graph will SHIFT?
Left None
Right

Now click Graph.
Exponential Part 3
 y = abx - h + k

Enter a = 1, b = 2, h = 0, and k = 0  
gives y = 1×2x-0 + 0  or  y = 2x
Click Graph, then Click Store.
Use this graph to compare 
  • Increasing means the line rises from left to right (positive slope)
  • Decreasing means the line falls from left to right (negative slope)

 1 . Enter a = 1, b = 1/2, h = 0, and k = 0   
Predict which way the graph will go?
  Increasing
  Decreasing
Verify with grapher

 2. Enter a = 1, b = 2.7, h = 0, and k = 0
Predict which way the graph will SHIFT?
Increasing
Decreasing
Verify with grapher

 3. Enter a = 1, b = 3/5, h = 0, and k = 0
Predict which way the graph will SHIFT?
Increasing
Decreasing
Verify with grapher

 4. Enter a = 1, b = -4, h = 0, and k = 0
Predict which way the graph will SHIFT?
Increasing Undefined
Decreasing

Verify with grapher
Exponential Part 4
 y = abx - h + k

Enter a = 1, b = 2, h = 0, and k = 0  
gives y = 1×2x-0 + 0  or  y = 2x
Click Graph, then Click Store.
Use this graph to compare 
  • Look how the steepness of the graph changes.

1. Enter a = 3, b = 2, h = 0, and k = 0
Predict which way the graph will CHANGE?
y - intercept (0,3)  Increasing None
y - intercept (0,3)  Decreasing 
y - intercept (0,-3) Increasing
y - intercept (0,-3) Decreasing 
Now click Graph.

2. Enter a = -4, b = 2, h = 0, and k = 0 

Predict which way the graph will CHANGE?
y - intercept (0,4)  Increasing 
y - intercept (0,4)  Decreasing 
y - intercept (0,-4) Increasing
y - intercept (0,-4) Decreasing
Now click Graph.

3. Enter a = -2, b = 1/2, h = 0, and k = 0 
Predict which way the graph will CHANGE?
y - intercept (0,2)  Increasing 
y - intercept (0,2)  Decreasing 
y - intercept (0,-2) Increasing
y - intercept (0,-2) Decreasing
Now click Graph.
Lines Altogether
Predict the following shifting, then verify using grapher.
 y = 3x - 2 + 1
 y = 2(3x) -  4
 y = -(2x) +  2
 y = (1/3)x + 2 -  4
 

Tutorials and Applets by
Joe McDonald
Community College of Southern Nevada