An exponential function g(x) is shown in the figure above. What is the exact value of g(-4)?

Answer

A

Explanation

Difficult:Hard
Category: Passport to Advanced Math/ Functions
Strategic Advice: When you're told that a functions is exponential, start with the form `g(x)=a*b^(x)` (with a=1) to write an equation that represents the graph.
Getting to the Answer: The notation g(-4) means that you are looking for the y-value when x is -4. Because you cannot tell what the exact value is from the graph, you need to find the equation of the function. To find the base, b, which is being raised to a power, make a list of sereval point on the graph and look for a pattern: `(0, 1), (1, 3), and (2, 9)`. The y-values are all powers of 3, so try b=3. Notice that `3^(0)=1,3^(1)=3, and 3^(2)=9`. The equation of the function is `g(x)=3^(x)`, so substitute -4 for x and simplify:
`g(-4)=3^(-4)=(1)/(3^(4))=(1)/(3times3times3times3)=(1)/(81)`
Grib in 1/81.