the graph of $h(x) = |x - 10| + 6$ is shown. on what interval is this graph increasing?

$(-\infty, 6)$
$(-\infty, 10)$
$(6, \infty)$
$(10, \infty)$

Question

the graph of $h(x) = |x - 10| + 6$ is shown. on what interval is this graph increasing?

$(-\infty, 6)$
$(-\infty, 10)$
$(6, \infty)$
$(10, \infty)$

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "tutor", "mastery_adaptive_brevity" ], "needs_drawing": false, "concepts_used": [ "Increasing Decreasing Intervals", "Vertex of Absolute Value Function" ], "new_concepts": [], "current_concepts": [ "Absolute Value Functions", "Increasing Decreasing Intervals", "Vertex of Absolute Value Function" ] } ## Identify the vertex of the function Using the *Vertex of Absolute Value Function* knowledge point $$ \begin{aligned} &h(x) = |x - 10| + 6\ &\text{Vertex } (h, k) = (10, 6) \end{aligned} $$ ## Determine the increasing interval Using the *Increasing Decreasing Intervals* knowledge point $$ \begin{aligned} &\text{For } x > 10,\quad h(x) = (x - 10) + 6 = x - 4\ &\text{Slope } m = 1 > 0 \implies \text{increasing on } (10, \infty) \end{aligned} $$

(A) $(-\infty, 6)$

(B) $(-\infty, 10)$

(C) $(6, \infty)$

(D) $(10, \infty)$

{ "subject": "Mathematics", "question_type": "Multiple Choice", "knowledge_point": [ "Mathematics", "Algebra", "Increasing Decreasing Intervals" ] }

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QUESTION IMAGE

Question

Explanation:

Identify the vertex of the function

Determine the increasing interval

Answer: