Answer :
To determine the [tex]$y$[/tex]-intercept of the function [tex]\( f(x) = 4 - 5x \)[/tex], we need to find the value of [tex]$y$[/tex] when [tex]$x = 0$[/tex]. This is because the [tex]$y$[/tex]-intercept is the point where the graph of the function crosses the [tex]$y$[/tex]-axis, and on the [tex]$y$[/tex]-axis, the value of [tex]$x$[/tex] is always 0.
Here are the steps to find the [tex]$y$[/tex]-intercept:
1. Start with the given function: [tex]\( f(x) = 4 - 5x \)[/tex].
2. Substitute [tex]$x = 0$[/tex] into the function:
[tex]\[ f(0) = 4 - 5(0) \][/tex]
3. Simplify the expression:
[tex]\[ f(0) = 4 - 0 \][/tex]
4. The simplified expression results in:
[tex]\[ f(0) = 4 \][/tex]
Therefore, the [tex]$y$[/tex]-intercept of the function [tex]\( f(x) = 4 - 5x \)[/tex] is [tex]\( 4 \)[/tex].
So, the correct answer is [tex]\( \boxed{4} \)[/tex].
Here are the steps to find the [tex]$y$[/tex]-intercept:
1. Start with the given function: [tex]\( f(x) = 4 - 5x \)[/tex].
2. Substitute [tex]$x = 0$[/tex] into the function:
[tex]\[ f(0) = 4 - 5(0) \][/tex]
3. Simplify the expression:
[tex]\[ f(0) = 4 - 0 \][/tex]
4. The simplified expression results in:
[tex]\[ f(0) = 4 \][/tex]
Therefore, the [tex]$y$[/tex]-intercept of the function [tex]\( f(x) = 4 - 5x \)[/tex] is [tex]\( 4 \)[/tex].
So, the correct answer is [tex]\( \boxed{4} \)[/tex].
