Drawing exponential graphs

Task goals

• 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.