Question

identify the graph for the given exponential function.

1. an exponential function is graphed on the grid.

which function is best represented by the graph?
a. $f(x)=3^x$
b. $f(x)=4^x$
c. $f(x)=2(3)^x$
d. $f(x)=2(4)^x$
○ a
○ b
○ c
○ d

Explanation:

Step1: Test x=0 for all functions

For $f(x)=3^x$: $f(0)=3^0=1$
For $f(x)=4^x$: $f(0)=4^0=1$
For $f(x)=2(3)^x$: $f(0)=2(3)^0=2$
For $f(x)=2(4)^x$: $f(0)=2(4)^0=2$
The graph passes through $(0,2)$, so eliminate A and B.

Step2: Test x=1 for remaining functions

For $f(x)=2(3)^x$: $f(1)=2(3)^1=6$
For $f(x)=2(4)^x$: $f(1)=2(4)^1=8$
The graph passes through $(1,6)$, so eliminate D.

Answer:

C. $f(x) = 2(3)^x$