Exponential Functions & Graphs (DP IB Applications & Interpretation (AI)): Revision Note

Exponential Functions & Graphs

What are the key features of exponential graphs?

• An exponential graph is of the form

  • or where 

  • 

    • Where e is the mathematical constant 2.718…

• The y-intercept is at the point (0, k + c)

• There is a horizontal asymptote at y = c

• The value of k determines whether the graph is above or below the asymptote

  • If k is positive the graph is  above the asymptote

    • So the range is 

  • If k is negative the graph is below the asymptote

    • So the range is 

• The coefficient of x and the constant k determine whether the graph is increasing or decreasing

  • If the coefficient of x and k have the same sign then graph is increasing

  • If the coefficient of x and k have different signs then the graph is decreasing

• There is at most 1 root

  • It can be found using your GDC