1. ## Transformation of graphs

If f(x) = $\displaystyle e^x$ and g(x) = $\displaystyle 2f(x) - 3$ of the original function,

for g(x) would the graph of $\displaystyle e^x$ have an asymptote at -3 and pass through y=1 when x is zero, and then reach infinity twice as fast as the original function?

2. Hello, db5vry!

You have a typo . . . or you made a silly error.

If $\displaystyle f(x) \,=\,e^x\:\text{ and }\:g(x) \:=\:2f(x) - 3$

Would the graph of $\displaystyle g(x)$ have an asymptote at -3
and pass through $\displaystyle y= {\color{red}-}1$ when $\displaystyle x = 0$
and then reach infinity twice as fast as the original function?
YES to the corrected statements.

The graph of: .$\displaystyle g(x) \;=\;2e^x - 3$ is the graph of $\displaystyle f(x) \,=\,e^x$
. . which rises twice as fast and has been lowered 3 units.

3. Originally Posted by Soroban
Hello, db5vry!

You have a typo . . . or you made a silly error.

YES to the corrected statements.

The graph of: .$\displaystyle g(x) \;=\;2e^x - 3$ is the graph of $\displaystyle f(x) \,=\,e^x$
. . which rises twice as fast and has been lowered 3 units.

It was a silly error there thank you very much for clarifying this for me though