Question

A graph of the exponential function f(x) is given.

The linear function f of x decreases through the ordered pairs negative 3,8 and negative 2,4 and negative 1,2 and 0,1 and 1,0.5
Write the equation to represent f(x).
a.f of x equals negative one half to the x power
b.f of x equals one half to the x power
c.f(x) = –2x
d.f(x) = 2x

Answer 1

The equation representing the exponential function f(x) that matches the given decreasing pattern through the ordered pairs is f(x) = (1/2)^x, which corresponds to answer choice b.

Step-by-step explanation:

The exponential function f(x) described in the question decreases through a series of ordered pairs. To find the equation representing f(x),

we can observe the pattern in the ordered pairs given: (-3, 8), (-2, 4), (-1, 2), (0, 1), and (1, 0.5). An exponential function with a base of one half (1/2) would decrease by a factor of 1/2 for each unit increase in x, matching the pattern provided.

Hence, the correct equation for the function is f(x) = (1/2)^x. This corresponds to answer choice b: f of x equals one half to the x power.