select the correct answer.

consider this absolute value function.

$f(x) = |x + 3|$

if function $f$ is written as a piecewise function, which piece will it include?

$\bigcirc -x - 3, x

Question

select the correct answer.

consider this absolute value function.

$f(x) = |x + 3|$

if function $f$ is written as a piecewise function, which piece will it include?

$\bigcirc -x - 3, x < 3$
$\bigcirc x + 3, x \ge -3$
$\bigcirc -x + 3, x < -3$
$\bigcirc x + 3, x \ge 3$

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Absolute Value Functions", "Piecewise Functions" ], "new_concepts": [], "current_concepts": [ "Absolute Value Functions", "Piecewise Functions" ] } ## Apply the definition of absolute value $$ |x + 3| = \begin{cases} x + 3, & \text{if } x + 3 \ge 0 \ -(x + 3), & \text{if } x + 3 < 0 \end{cases} $$ ## Simplify the inequalities $$ \begin{aligned} x + 3 \ge 0 &\implies x \ge -3 \ x + 3 < 0 &\implies x < -3 \end{aligned} $$ ## Write the piecewise function and match options $$ f(x) = \begin{cases} x + 3, & x \ge -3 \ -x - 3, & x < -3 \end{cases} $$ Comparing with the given choices, the piece $x + 3, \text{ for } x \ge -3$ is listed.

(A) $-x - 3, \quad x < 3$

(B) $x + 3, \quad x \ge -3$

(C) $-x + 3, \quad x < -3$

(D) $x + 3, \quad x \ge 3$

{ "subject": "Mathematics", "question_type": "Multiple Choice", "knowledge_point": [ "Mathematics", "Algebra", "Piecewise Functions" ] }

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QUESTION IMAGE

Question

Explanation:

Apply the definition of absolute value

Simplify the inequalities

Write the piecewise function and match options

Answer: