which of the following is the graph of this absolute value function?

\y = |x + 1|\

Question

which of the following is the graph of this absolute value function?

\y = |x + 1|\

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "tutor", "mastery_adaptive_brevity" ], "needs_drawing": true, "concepts_used": [ "Absolute Value Graphs", "Function Transformations" ], "new_concepts": [], "current_concepts": [ "Absolute Value Graphs", "Function Transformations" ] } ## Identify the parent function and vertex Using the *Absolute Value Graphs* and *Function Transformations* knowledge points $$ \begin{aligned} &y = |x - h| + k \ &\text{For } y = |x + 1|: \ &h = -1, \quad k = 0 \ &\text{Vertex } (h, k) = (-1, 0) \end{aligned} $$ ## Determine key points on the graph Using the *Absolute Value Graphs* knowledge point $$ \begin{aligned} &x = 0 \implies y = |0 + 1| = 1 \implies (0, 1) \ &x = -2 \implies y = |-2 + 1| = 1 \implies (-2, 1) \ &x = 1 \implies y = |1 + 1| = 2 \implies (1, 2) \end{aligned} $$ ## Match with the given options Using the *Absolute Value Graphs* knowledge point $$ \begin{aligned} &\text{First graph: Vertex at } (-1, 0), \text{ passes through } (0, 1) \text{ and } (-2, 1). \ &\text{Second graph: Vertex at } (1, 0). \ &\text{Third graph: Vertex at } (0, 1). \end{aligned} $$

(A) Graph with vertex at $(-1, 0)$ and y-intercept at $(0, 1)$

(B) Graph with vertex at $(1, 0)$ and y-intercept at $(0, 1)$

(C) Graph with vertex at $(0, 1)$ and y-intercept at $(0, 1)$

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QUESTION IMAGE

Question

Explanation:

Identify the parent function and vertex

Determine key points on the graph

Match with the given options

Answer: