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A piecewise function is defined as shown.

[tex]\[ f(x)=\left\{\begin{array}{cc}
-x, & x \leq -1 \\
1, & x = 0 \\
x + 1, & x \geq 1
\end{array}\right.
\][/tex]

What is the value of [tex]\( f(x) \)[/tex] when [tex]\( x = 3 \)[/tex]?

A. [tex]\(-3\)[/tex]

B. [tex]\(-2\)[/tex]

C. [tex]\(1\)[/tex]

D. [tex]\(4\)[/tex]



Answer :

GinnyAnswer
To find the value of the piecewise function [tex]\( f(x) \)[/tex] when [tex]\( x = 3 \)[/tex], let's analyze the conditions given in the definition of the piecewise function:

[tex]\[ f(x) = \begin{cases} -x, & \text{if } x \leq -1 \\ 1, & \text{if } x = 0 \\ x + 1, & \text{if } x \geq 1 \end{cases} \][/tex]

We are tasked with finding [tex]\( f(3) \)[/tex]. Let's match [tex]\( x = 3 \)[/tex] with the appropriate condition from the piecewise function definition:

1. For [tex]\( x \leq -1 \)[/tex]:
[tex]\[ f(x) = -x \][/tex]
This condition does not apply because [tex]\( 3 \)[/tex] is not less than or equal to [tex]\(-1\)[/tex].

2. For [tex]\( x = 0 \)[/tex]:
[tex]\[ f(x) = 1 \][/tex]
This condition does not apply because [tex]\( 3 \)[/tex] is not equal to [tex]\( 0 \)[/tex].

3. For [tex]\( x \geq 1 \)[/tex]:
[tex]\[ f(x) = x + 1 \][/tex]
This condition applies because [tex]\( 3 \)[/tex] is greater than or equal to [tex]\( 1 \)[/tex].

Since [tex]\( x = 3 \)[/tex] satisfies the third condition, we use the formula [tex]\( f(x) = x + 1 \)[/tex]:

[tex]\[ f(3) = 3 + 1 = 4 \][/tex]

Therefore, the value of [tex]\( f(3) \)[/tex] is [tex]\( 4 \)[/tex]. The corresponding answer is:

[tex]\[ \boxed{4} \][/tex]

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