Let's work through the problem step by step.
First, let's think about the function [tex]\( f(x) = 3 - 2x \)[/tex].
The notation [tex]\( f(0) \)[/tex] signifies the value of the function [tex]\( f(x) \)[/tex] when [tex]\( x \)[/tex] is equal to 0.
To find [tex]\( f(0) \)[/tex], we substitute [tex]\( x = 0 \)[/tex] into the function:
[tex]\[ f(0) = 3 - 2 \cdot 0 \][/tex]
[tex]\[ f(0) = 3 \][/tex]
So,
[tex]\[ f(0) = 3 \][/tex]
The special name for [tex]\( f(0) \)[/tex] is the y-intercept of the function. The y-intercept is the point where the graph of the function intersects the y-axis, which occurs when [tex]\( x = 0 \)[/tex].
So, the special name of [tex]\( f(0) \)[/tex] is the y-intercept.
Thus, the detailed solution to the problem is:
[tex]\[ f(0) = 3 \][/tex]
and
[tex]\[ f(0) \][/tex] is called the y-intercept.
