Graphing y = 2·3ˣ

Algebra 1 · Axiom Academy

EXAMPLE Graphing an Exponential Function Build a table of values for , then plot the points and trace its growth curve. Graph the exponential function . We'll read off its parts, build a table of values, find the y -intercept, and plot the points to see the shape of exponential growth. Plotting the table points and connecting them gives the J-shaped curve of exponential growth: it crosses the y -axis at (0, 2) and climbs ever more steeply to the right. The curve crosses the y -axis at (0, 2) , because y = a when x = 0 . Each step right multiplies y by the base 3 : . All real numbers — x can be any value. y > 0 — always positive, so it never touches the x -axis. Nice work. You graphed an exponential function from scratch — here's what carries over to any : The form : a is the coefficient (the y -intercept), and b is the base (the growth factor). Y-intercept: at x = 0 every exponential gives y = a , since b^0 = 1 — here y = 2 . Growth factor: each time x increases by 1 , y is multiplied by b — here . The shape: a positive base > 1 gives a J-shaped curve that climbs faster and faster. Always positive: with a, b > 0 stays above the x -axis — its range is y > 0 . This multiplicative pattern shows up everywhere exponential growth does — compound interest, populations, and viral spread all follow the same shape.

This is the written version of the interactive lesson above. See the full Algebra 1 course.