Which graph represents the function f(x) = ()–x

On a coordinate plane, an exponential function approaches y = 0 in quadrant 2 and increases into quadrant 1. It goes through points (0, 1), (1, 1.5), (3, 3.5).

On a coordinate plane, an exponential function approaches y = 0 in quadrant 1 and increases into quadrant 2. It goes through points (0, 1), (1.5, 0.5).

On a coordinate plane, an exponential function approaches y = 0 in quadrant 2 and increases into quadrant 1. It goes through points (0, 1.5) and (2, 3.5).

On a coordinate plane, an exponential function approaches y = 0 in quadrant 1 and increases into quadrant 2. It goes through points (0, 1.5), and (2.5, 0.5).

On a coordinate plane, an exponential function approaches y = 0 in quadrant 1 and increases into quadrant 2. It goes through points (0, 1), (1.5, 0.5).

How is the graph of the exponential function found?

Given:

The possible (exponential) function in the question is presented as follows;

[tex]f(x) = \left(\dfrac{3}{2} \right)^{-x}[/tex]

Required:

Description of the graph which represents the function

Solution:

Exponential functions; The function [tex]f(x) = \left(\dfrac{3}{2} \right)^{-x}[/tex] is in the form f(x) = aˣ,

where the variable x, which is the input variable is a power of a constant

term a, is an exponential function.

By evaluating the function for different x-values gives the following, x, and f(x) table showing points on the graph of function, [tex]f(x) = \left(\dfrac{3}{2} \right)^{-x}[/tex]

Table of values for the function:

[tex]\begin{array}{|c|c|}x&f(x)\\0&1\\1.5&0.54\\2&0.44\end{array}\right][/tex]

By comparison of the values in the table with the options given, the

closest option that represents the graph is therefore;

On a coordinate plane, an exponential function approaches y = 0 in quadrant 1 and increases into quadrant 2. It goes through points (0, 1), (1.5, 0.5)

Learn more about exponential functions here:

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