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Use the piecewise-defined function to find the following values for [tex]\( f(x) \)[/tex]:

[tex]\[ f(x) = \begin{cases}
3 - 5x & \text{if } x \leq 1 \\
3x & \text{if } 1 \ \textless \ x \ \textless \ 6 \\
5x + 2 & \text{if } x \geq 6
\end{cases} \][/tex]

Find [tex]\( f(-4), f(0), f(3), f(4) \)[/tex], and [tex]\( f(8) \)[/tex].

[tex]\[ f(-4) = \quad \square \][/tex]



Answer :

GinnyAnswer
Alright! Let's determine the values for the piecewise-defined function [tex]\( f(x) \)[/tex] at the given points.

The piecewise function [tex]\( f(x) \)[/tex] is defined as follows:
[tex]\[ f(x) = \begin{cases} 3 - 5x & \text{if } x \leq 1 \\ 3x & \text{if } 1 < x < 6 \\ 5x + 2 & \text{if } x \geq 6 \end{cases} \][/tex]

### Finding [tex]\( f(-4) \)[/tex]:
Since [tex]\( -4 \leq 1 \)[/tex], we use the first case of the function:
[tex]\[ f(-4) = 3 - 5(-4) \][/tex]
[tex]\[ f(-4) = 3 + 20 \][/tex]
[tex]\[ f(-4) = 23 \][/tex]

### Finding [tex]\( f(0) \)[/tex]:
Since [tex]\( 0 \leq 1 \)[/tex], we use the first case of the function:
[tex]\[ f(0) = 3 - 5(0) \][/tex]
[tex]\[ f(0) = 3 \][/tex]

### Finding [tex]\( f(3) \)[/tex]:
Since [tex]\( 1 < 3 < 6 \)[/tex], we use the second case of the function:
[tex]\[ f(3) = 3(3) \][/tex]
[tex]\[ f(3) = 9 \][/tex]

### Finding [tex]\( f(4) \)[/tex]:
Since [tex]\( 1 < 4 < 6 \)[/tex], we use the second case of the function:
[tex]\[ f(4) = 3(4) \][/tex]
[tex]\[ f(4) = 12 \][/tex]

### Finding [tex]\( f(8) \)[/tex]:
Since [tex]\( 8 \geq 6 \)[/tex], we use the third case of the function:
[tex]\[ f(8) = 5(8) + 2 \][/tex]
[tex]\[ f(8) = 40 + 2 \][/tex]
[tex]\[ f(8) = 42 \][/tex]

Thus, the values are:
[tex]\[ \begin{aligned} f(-4) & = 23 \\ f(0) & = 3 \\ f(3) & = 9 \\ f(4) & = 12 \\ f(8) & = 42 \\ \end{aligned} \][/tex]

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