Question

1. an exponential function is graphed on the grid. which function is best represented by the graph?

a ( f(x) = 10(0.5)^x )
b ( f(x) = 10(2)^x )
c ( f(x) = 5(10)^x )
d ( f(x) = 5(0.5)^x )

Explanation:

Step1: Identify y-intercept

The graph crosses the y-axis at $(0, 10)$. For exponential functions $f(x)=a(b)^x$, when $x=0$, $f(0)=a$. So $a=10$. This eliminates options C and D.

Step2: Test a second point

Pick a point on the graph, e.g., $(2, 2.5)$. Substitute $x=2$, $f(x)=2.5$ into remaining options.
For option A: $f(2)=10(0.5)^2=10\times0.25=2.5$, which matches.
For option B: $f(2)=10(2)^2=10\times4=40$, which does not match.

Answer:

A. $f(x) = 10(0.5)^x$