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use the graph to evaluate each expression. (a) \\((f+g)(0)\\) (b) \\((f…

Question

use the graph to evaluate each expression.
(a) \\((f+g)(0)\\)
(b) \\((f-g)(-1)\\)
(c) \\((fg)(1)\\)
(d) \\(\left(\frac{f}{g}\
ight)(3)\\)

\\((f+g)(0) = 3\\)
\\((f-g)(-1) = -3\\)
\\((fg)(1) = \square\\)

Explanation:

Response

<pre_analysis>
{
"quality": "clear",
"question_count": 1,
"skills_matched": [
"step_cot",
"blank_filling_formatter",
"explain_then_answer",
"quick"
],
"needs_drawing": false,
"concepts_used": [],
"new_concepts": [
"Function Operations",
"Graphical Evaluation"
],
"current_concepts": [
"Function Operations",
"Graphical Evaluation"
]
}
</pre_analysis>

<reasoning>

Find function values from the graph

\[

$$\begin{aligned} &f(1) = 4\\ &g(1) = -2 \end{aligned}$$

\]

Evaluate the product of the functions

\[

$$\begin{aligned} (fg)(1) &= f(1) \cdot g(1) \\ &= 4 \cdot (-2) \\ &= -8 \end{aligned}$$

\]
</reasoning>

<answer>
Use the graph to evaluate each expression.
\((fg)(1) =\) <blank>-8</blank>
</answer>

<post_analysis>
{
"subject": "Mathematics",
"question_type": "Fill-in-the-blank",
"knowledge_point": [
"Mathematics",
"Algebra",
"Function Operations"
]
}
</post_analysis>

Answer:

<pre_analysis>
{
"quality": "clear",
"question_count": 1,
"skills_matched": [
"step_cot",
"blank_filling_formatter",
"explain_then_answer",
"quick"
],
"needs_drawing": false,
"concepts_used": [],
"new_concepts": [
"Function Operations",
"Graphical Evaluation"
],
"current_concepts": [
"Function Operations",
"Graphical Evaluation"
]
}
</pre_analysis>

<reasoning>

Find function values from the graph

\[

$$\begin{aligned} &f(1) = 4\\ &g(1) = -2 \end{aligned}$$

\]

Evaluate the product of the functions

\[

$$\begin{aligned} (fg)(1) &= f(1) \cdot g(1) \\ &= 4 \cdot (-2) \\ &= -8 \end{aligned}$$

\]
</reasoning>

<answer>
Use the graph to evaluate each expression.
\((fg)(1) =\) <blank>-8</blank>
</answer>

<post_analysis>
{
"subject": "Mathematics",
"question_type": "Fill-in-the-blank",
"knowledge_point": [
"Mathematics",
"Algebra",
"Function Operations"
]
}
</post_analysis>