Name: ____________________________________________________ Date: _________________ Per: ______
LC Math 1 Adv – Exploring the Graph of Exponential Functions (Pt 2)
Use the general exponential function y  ab x , where a  0 , b  0 and b  1 to answer the questions below.
Part 1 – y-intercept
1. As you manipulate the sliders, what generalization can you make about the value of the y-intercept of an
exponential function of the form y  ab x ? Be precise.
2. By definition, the y-intercept of any function is the value of the dependent variable when the value of the
independent variable is _______.
In y  ab x , _______ is the independent variable, and the value of the dependent variable when _______ equals
_______ is _______. Explain this statement you created and how it relates to your answer to #1.
3. Now use y  ab x  k as your function and utilize a new slider for k. Choose any particular values for a and b
while you manipulate the value of k to answer the following questions.
4. As you manipulate the sliders, what generalization can you make about the value of the y-intercept of an
exponential function of the form y  ab x  k ? Be precise.
5. By definition, the y-intercept of any function is the value of the dependent variable when the value of the
independent variable is _______.
In y  ab x  k , _______ is the independent variable, and the value of the dependent variable when _______
equals _______ is _______. Explain this statement you created and how it relates to your answer to #4.
Use the general exponential function y  ab x , where a  0 , b  0 and b  1 to answer the questions below.
Part 2 – End Behavior
6. Complete the table to describe what happens “as x approaches infinity” or “as x approaches negative infinity”.
0  b 1
a0
a0
b 1
As x  
As x  
As x  
As x  
y
y
y
y
As x  
As x  
As x  
As x  
y
y
y
y
7. Sketch the two cases of exponential functions for which 0  b  1. What generalization can you make about
the end behavior of this class of exponential functions? Be precise.
8. Sketch the two cases of exponential functions for which b  1 . What generalization can you make about the
end behavior of this class of exponential functions? Be precise.
9. Now use y  ab x  k as your function and utilize a new slider for k. Choose any particular values for a and b
while you manipulate the value of k to answer the following questions.
10. Complete the table to describe what happens “as x approaches infinity” or “as x approaches negative infinity”.
0  b 1
a0
a0
b 1
As x  
As x  
As x  
As x  
y
y
y
y
As x  
As x  
As x  
As x  
y
y
y
y
11. Sketch the two cases of exponential functions for which 0  b  1. What generalization can you make about
the end behavior of this class of exponential functions? Be precise.
12. Sketch the two cases of exponential functions for which b  1 . What generalization can you make about the
end behavior of this class of exponential functions? Be precise.
13. Generalize the effect that k has on the graph of y  ab x  k . Be precise.