Question

Given the functions f(x) = 3(0.56)^x and g(x) = 6(4)^x
Part A: is f(x) increasing or decreasing ? Is g(x) increasing or decreasing ? Explain your reasoning .
Part B: what is the y intercept of each function?
Part C: what is the value of each function when x = 4?

Answer 1

A)  f(x) is decreasing because the base is less than 1.
      0.56 is close to 0.5, so its like saying that you are taking half each time, therefore the value is getting smaller.

g(x) is increasing because the base is greater than 1.
you are multiplying by 4 each time, making the value bigger.


B )  The y-intercept is where x=0.
      Anything to the '0' power is 1. Therefore the y-intercept is equal to the coefficient in front of each function.
    f(x) = 3 ,   g(x) = 6


C)  Just plug in x=4 to each function in a calculator.
 f(4) = 0.295
g(4) = 1536