Drawing exponential graphs

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Learning objective overview

Master Teaching Guide coverage for this objective.

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Build a table of values and draw the graph of a simple exponential growth curve y = b^x (e.g. y=2^x, y=3^x, y=4^x).
Draw exponential growth curves with a vertical shift, y = b^x + c (e.g. y=2^x+1, y=3^x+2).
Draw exponential decay curves y=(1/b)^x, including with a leading coefficient (e.g. y=(1/2)^x, y=5(1/2)^x).
Draw exponential graphs with a leading coefficient a in y=a.b^x, for both growth and decay bases, with and without a vertical shift.
Draw exponential graphs with a horizontal shift in the exponent, y=b^(x-h) or y=b^(x+h), combined with a coefficient and/or vertical shift.
Draw exponential graphs combining a coefficient, horizontal shift, and vertical shift, and mark the horizontal asymptote.
Draw exponential graphs with combined transformations, marking the horizontal asymptote and/or y-intercept, and state whether the graph shows growth or decay.

Students build a table of values for an exponential rule y = ab^x by substitution, then plot the points and draw the smooth curve.
Students should be able to identify the asymptote -- the horizontal line the curve approaches but never reaches (for y = ab^x with no vertical shift, this is y = 0).
Distinguish from T4_LO12 (parabolas): an exponential curve does not have symmetry or a vertex/turning point; it grows (or decays) continuously in one direction while flattening toward the asymptote in the other.