Graphing y = 2ˣ

Pre-Calculus · Axiom Academy

Build a table, plot the points, and read off the key features of an exponential growth curve. Graph the exponential function y = 2^x and identify all of its key features: the table of values, the y -intercept, the horizontal asymptote, the behavior, the domain, and the range. The six table points lie on a single smooth curve that rises steeply to the right and presses down toward y = 0 on the left without ever touching it. Nice work — you graphed y = 2^x end to end: a table of values, the plotted points, the smooth curve, and every key feature. Make a table: at x = -2,-1,0,1,2,3 the outputs are — each step right doubles the previous y . Anchor point: the y -intercept is (0, 1) because 2^0 = 1 (true for any base). Asymptote: y = 0 is a horizontal asymptote — as the curve approaches the x-axis but never reaches it. Shape: base means the curve is increasing (growth), with domain and range . Every exponential y = b^x with has this same skeleton — pass through (0,1) , hug y = 0 on the left, and climb without bound on the right.

This is the written version of the interactive lesson above. See the full Pre-Calculus course.