Exponential Functions:     y = a(bx)

Prof. Battaly, College Algebra

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The blue curve shown on the graph has the equation y = a bx. For this equation the variable x is in the exponent. 
The base, b > 0 and b ≠ 1
The sliders represent values for the coefficient a and the base b.
What happens to the curve when you move the sliders (change the values of a and b)?

1.  If a is positive, then y is ______________________
  
     Why does this make sense? _______________________________

2.  If a is negative, then y is _______________________

3.  Can y ever be 0? ______

4.  Can x ever be 0? ______

5.  When a is positive and b > 1, the curve is ____________________________

     When a is positive and 0 < b < 1, the curve is ____________________________

6.  When a is positive, the Range is ______________________________

     When a is negative, the Range is ______________________________

Gertrude Battaly, 27 March 2013, Created with GeoGebra

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Answers
1. Positive.   Since exponents indicate the number of times the base is used as a factor in multiplication and the base is positive, the resulting product will be positive.
2. Negative
3. No. Although y approaches the x-axis as an asymptote, it never crosses the axis.
4. Yes.
5. increasing, decreasing
6.  y > 0,        y < 0