Graphs of Exponential and Logarithmic Functions

Graph of Exponential Function f ( x ) = bx Domain: ( −∞, ∞ ) or x ∊ ℝ Range: ( 0, ∞ ) or y > 0 Intercept: ( 0, 1 ) y -intercept Asymptote: y = 0 Horizontal

Graph of Exponential Function f ( x ) = 2x Domain: ( −∞, ∞ ) or x ∊ ℝ Range: ( 0, ∞ ) or y > 0 Intercept: ( 0, 1 ) Asymptote: y = 0 Now, graph: g ( x ) = 2(x – 3) + 4 Domain: ( −∞, ∞ ) or x ∊ ℝ No change Range: ( 4, ∞ ) or y > 4 Up by 4 Intercept: ( 0, 4.125 ) Let x = 0 Asymptote: y = 4 Up by 4

Graph of Logarithmic Function f ( x ) = logbx Domain: ( 0, ∞ ) or x > 0 Range: ( – ∞, ∞ ) or y ∊ ℝ Intercept: ( 1, 0 ) x -intercept Asymptote: x = 0 Vertical