Example

Example: Graphing f(x)=2xf(x) = 2^x and g(x)=2x+1g(x) = 2^{x+1}

To graph the exponential functions f(x)=2xf(x) = 2^x and g(x)=2x+1g(x) = 2^{x+1} on the same coordinate system, we can utilize the point-plotting method. For the base function f(x)=2xf(x) = 2^x, plotting standard points yields (1,12)(-1, \frac{1}{2}), (0,1)(0, 1), and (1,2)(1, 2). When evaluating g(x)=2x+1g(x) = 2^{x+1} for the same xx-values, the outputs shift: at x=1x = -1, g(1)=20=1g(-1) = 2^0 = 1; at x=0x = 0, g(0)=21=2g(0) = 2^1 = 2; and at x=1x = 1, g(1)=22=4g(1) = 2^2 = 4. Comparing these two plotted curves clearly demonstrates that adding 11 in the exponent causes the entire graph of f(x)=2xf(x) = 2^x to undergo a horizontal translation of exactly one unit to the left.

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Updated 2026-05-25

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