Question

Graph the function.

\[g(x)=\dfrac{3}4\cdot2^x\]

Answer 1

To graph g(x) = (3/4)·2^x:

Key features
- Domain: (−∞, ∞)
- Range: (0, ∞)
- Horizontal asymptote: y = 0
- y-intercept: g(0) = 3/4, so the point (0, 3/4)
- No x-intercepts (the curve never crosses y = 0)
- Increasing function (since base 2 > 1)
- Vertical scaling: it is the parent 2^x compressed by a factor 3/4

Points you can plot
- x = −2: g(−2) = (3/4)·2^(−2) = 3/16 = 0.1875
- x = −1: g(−1) = 3/8 = 0.375
- x = 0: g(0) = 3/4 = 0.75
- x = 1: g(1) = 3/2 = 1.5
- x = 2: g(2) = 3

Plot the horizontal line y = 0 as the asymptote, then plot the points above and draw a smooth curve through them that approaches y = 0 on the left and rises rapidly to the right. On a graphing calculator enter y = (3/4)*2^x.