Question

How do you make a table to graph $f(x) = {\left( {\dfrac{1}{2}} \right)^x}$ ?

Answer 1

Hint: As given in the question $f(x) = {\left( {\dfrac{1}{2}} \right)^x}$ , this function represent the relationship between the input variable that is $x$ and the output variable that is $y$ . Here we have exactly one output for every input. We can get the table by assuming an input variable then find the output variables corresponding to that input variable. Input variable is also known as independent variable as well as domain of the function. Output variable is also known as dependent variable as well as range of the function.

Complete step by step answer:
We have $f(x) = {\left( {\dfrac{1}{2}} \right)^x}$
Now, for finding the value of dependent variable ,
Setting independent variable, $x = 0,1,2,3,4.....$
$f(x) = {\left( {\dfrac{1}{2}} \right)^0} = 1$ (for $x = 0$ )
We have $(0,1)$
$f(x) = {\left( {\dfrac{1}{2}} \right)^1} = 0.5$ (for $x = 1$ )
We have $(1,0.5)$
$f(x) = {\left( {\dfrac{1}{2}} \right)^2} = 0.25$ (for $x = 2$ )
We have $(2,0.25)$
Similarly, we can find further…
Therefore , the required table is ,

x	y = F(x)
0	1
1	0.5
2	0.25

So, the graph will be given as

Note: Functions are usually represented by a function rule where you express the variable, y, in terms of the variable, x. Here y is dependent on x .A pair of an input value and its corresponding output value is named an ordered pair and may be written as (a, b). In an ordered pair the primary number, the input a, corresponds to the horizontal axis and also the second number, the output b, corresponds to the vertical axis.
A pairing of any set of inputs with their corresponding outputs is termed a relation. Every function may be a relation, but not all relations are functions.