evaluate the function for the given values of $x$.

\f(x) = \begin{cases} -3|x| + 7 & \text{for } x \le -2 \\ 5x + 3 & \text{for } -2

Question

evaluate the function for the given values of $x$.

\f(x) = \begin{cases} -3|x| + 7 & \text{for } x \le -2 \\ 5x + 3 & \text{for } -2 < x < 3 \\ 4 & \text{for } x \ge 3 \end{cases}\

part 1 of 5
$f(-3) = $

part 2 of 5
$f(3) = $

part 3 of 5
$f(-2) = $

part 4 of 5
$f(0) = $

part 5 of 5
$f(4) = $

Accepted Answer

{ "quality": "clear", "question_count": 5, "skills_matched": [ "step_cot", "table_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Piecewise Functions", "Function Evaluation", "Absolute Value Properties" ], "new_concepts": [], "current_concepts": [ "Piecewise Functions", "Function Evaluation", "Absolute Value Properties" ] } ## Determine the interval for each input value $$ \begin{aligned} x = -3 &\implies x \le -2 \implies f(x) = -3|x| + 7 \ x = 3 &\implies x \ge 3 \implies f(x) = 4 \ x = -2 &\implies x \le -2 \implies f(x) = -3|x| + 7 \ x = 0 &\implies -2 < x < 3 \implies f(x) = 5x + 3 \ x = 4 &\implies x \ge 3 \implies f(x) = 4 \end{aligned} $$ ## Evaluate the function for each part $$ \begin{aligned} f(-3) &= -3|-3| + 7 = -3(3) + 7 = -2 \ f(3) &= 4 \ f(-2) &= -3|-2| + 7 = -3(2) + 7 = 1 \ f(0) &= 5(0) + 3 = 3 \ f(4) &= 4 \end{aligned} $$ | No. | Answer | |---|---| | Part 1 of 5 | $f(-3) = -2$ | | Part 2 of 5 | $f(3) = 4$ | | Part 3 of 5 | $f(-2) = 1$ | | Part 4 of 5 | $f(0) = 3$ | | Part 5 of 5 | $f(4) = 4$ | { "subject": "Mathematics", "question_type": "Multi-part", "knowledge_point": [ "Mathematics", "Algebra", "Piecewise Functions" ] }

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QUESTION IMAGE

Question

Explanation:

Determine the interval for each input value

Evaluate the function for each part

Answer:

No.	Answer
Part 2 of 5	\(f(3) = 4\)
Part 3 of 5	\(f(-2) = 1\)
Part 4 of 5	\(f(0) = 3\)
Part 5 of 5	\(f(4) = 4\)