How do you graph y=-2(2.5)^x?

Mar 5, 2018

If the standard exponential $f \left(x\right) = {2.5}^{x}$ is the "parent" graph, then the graph of $y$ is the graph of $f \left(x\right)$ scaled by 2 and reflected in the $x -$axis.

Explanation:

Consider the standard exponential graph $f \left(x\right) = {\left(2.5\right)}^{x}$ below.

graph{2.5^x [-5.71, 5.39, -1.244, 4.306]}

If we take $f \left(x\right)$ above as the "parent" graph, then the graph of $y$ is the graph of $f \left(x\right)$ scaled by 2 and reflected in the $x -$axis.

The graph of $y$ is shown below.

graph{-2(2.5)^x [-5.757, 5.343, -4.107, 1.443]}