Graphing Exponential Functions

This tutorial will illustrate some graphs of the exponential form. It will enable you to compare graphs with various values of coefficients (A) and exponents (k) in the general exponential equation.

\(y = Ae^{kx}\)

Comparing Coefficients    

Differing positive coefficients

On the same axis are two graphs with different positive coefficients. In the example the coefficients are 1 and 5. The blue curve is everywhere 5 times higher than the red curve.
On the same axis are two graphs with different positive coefficients. In the example the coefficients are 1 and 5. The blue curve is everywhere 5 times higher than the red curve.

Differing negative coefficients

On the same axis are two graphs with different negative coefficients.In the example the coefficients are -1 and -5. The green curve is everywhere 5 times deeper than the red curve.
On the same axis are two graphs with different negative coefficients.In the example the coefficients are -1 and -5. The green curve is everywhere 5 times deeper than the red curve.

Positive and negative coefficients

On the same axis are two graphs. The curve with the positive coefficient curves upward , and the curve with the negative coefficient curves down.
On the same axis are two graphs. The curve with the positive coefficient curves upward, and the curve with the negative coefficient curves down.

 

Comparing Exponents

Differing positive exponents

On the same axis are two graphs with different exponents. Note that the larger the exponent, the more sharply the graph curves (the blue-green graph).
On the same axis are two graphs with different exponents. Note that the larger the exponent, the more sharply the graph curves (the blue-green graph). 

Differing negative exponents

On the same axis are two graphs with different negative exponents. As the blue dashed curve shows, the more negative the exponent, the steeper the graph.
On the same axis are two graphs with different negative exponents. As the blue dashed curve shows, the more negative the exponent, the steeper the graph.

Positive and negative exponents

On the same axis are two graphs. The curve with the positive exponent curves upward (red), while the graph with the negative exponent slopes downward and approaches zero asymptotically.
On the same axis are two graphs. The curve with the positive exponent curves upward (red), while the graph with the negative exponent slopes downward and approaches zero asymptotically.