use the graphs of f and g to evaluate the composite function.
$(f \circ g)(-3)$

$(f \circ g)(-3) = \square$

Question

use the graphs of f and g to evaluate the composite function.
$(f \circ g)(-3)$

$(f \circ g)(-3) = \square$

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "blank_filling_formatter", "explain_then_answer", "tutor", "mastery_adaptive_brevity" ], "needs_drawing": false, "concepts_used": [ "Function Composition" ], "new_concepts": [], "current_concepts": [ "Function Composition", "Evaluating Composite Functions from Graphs" ] } ## Define the composite function Using the *Function Composition* knowledge point $$ (f \circ g)(-3) = f(g(-3)) $$ ## Evaluate the inner function from the graph Using the *Function Composition* knowledge point $$ \begin{aligned} &\text{Find } x = -3 \text{ on the graph of } y = g(x) \text{ (blue curve with vertex at } (5, 2)\text{).}\ &g(-3) = 10 \end{aligned} $$ ## Evaluate the outer function from the graph Using the *Function Composition* knowledge point $$ \begin{aligned} &\text{Substitute } g(-3) = 10 \text{ into } f(g(-3)) \text{ to get } f(10).\ &\text{Find } x = 10 \text{ on the graph of } y = f(x) \text{ (red line).}\ &f(10) = -9 \end{aligned} $$ Use the graphs of f and g to evaluate the composite function. $(f \circ g)(-3) =$ $-9$ { "subject": "Mathematics", "question_type": "Fill-in-the-blank", "knowledge_point": [ "Mathematics", "Algebra", "Function Composition" ] }

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Question

Explanation:

Define the composite function

Evaluate the inner function from the graph

Evaluate the outer function from the graph

Answer: