Question

The graphs of the exponential functions $y=2^x,y=4^x$and $y=4^x$are shown in the figure at the left. Use your knowledge of transformations to determine which graph is which without using a graphing calculator.

$y=2^x,y=4^x,y=2\left(2^x\right)y=e^x,y=e^{3x},y=e^{-2x}$

Short answer

The graph is determined without using a graphing calculator.

Step-by-step solution

Step 1. Given information

We have to determine that which graph is without using a graphing calculator.

Step 2. Determine

The graph of $y=2^x,y=4^x,y=2\left(2^x\right)$is:

The graph passing through (0,2) Is $2\left(2^x\right)$.The graph passing through (0,1) and (1.4) is $4^x$ The graph passing through (2,4) Is 2^x

Step 3. Determine the second graph

The graph of $y=e^x,y=e^{3x},y=e^{-2x}$is :

The graph passing through (0.1) is e^x The graph passing through (0.1) is e^3x The graph passing through (0.1) is e^-2x