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: Check y-intercept (x=0)

For any exponential function $f(x)=ab^x$, when $x=0$, $f(0)=a$. From the graph, when $x=0$, $y=2$. So $a=2$. This eliminates options A ($f(x)=3^x$, $a=1$) and B ($f(x)=4^x$, $a=1$).

Step2: Test remaining points

Now test $x=1$ on options C and D:

• Option C: $f(1)=2(3)^1=6$
• Option D: $f(1)=2(4)^1=8$

From the graph, when $x=1$, the y-value is 6, which matches option C.

Answer:

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