2.1.1 Exponential Functions

Exponential functions

• Exponential functions of the form y = a^x with a > 0 are considered at A level

Exponential graphs

• All graphs of the form y = a^x will pass through (0, 1) because a⁰ = 1
• The x-axis is an asymptote

a > 1

• Where x < 0 the higher value of a is the “lower” graph
• Where x > 0 the higher value of a is the “higher” graph
• a > 1 is exponential growth (see Exponential Growth & Decay)

0 < a < 1

• Where x < 0 the higher value of a is the “higher” graph
• Where x > 0 the higher value of a is the “lower” graph
• 0 < a < 1 is exponential decay

a = 1

• You may like to think about why a = 1 is not considered:

  If a = 1, y = 1^x = 1 for all values of x