consider $f(x) = 2x^2 + 1$ and $g(x) = 3x - 3$. which statement about $f + g$ is true?

a. it is a linear function.
b. it is a quadratic function.
c. the domain is $x \ge -3$.
d. the range is $y \ge -3$.

Question

consider $f(x) = 2x^2 + 1$ and $g(x) = 3x - 3$. which statement about $f + g$ is true?

a. it is a linear function.
b. it is a quadratic function.
c. the domain is $x \ge -3$.
d. the range is $y \ge -3$.

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [], "new_concepts": [ "Function Addition", "Classifying Functions" ], "current_concepts": [ "Function Addition", "Classifying Functions", "Quadratic Functions" ] } ## Find the sum function $f + g$ $$ \begin{aligned} (f+g)(x) &= f(x) + g(x) \ &= (2x^2 + 1) + (3x - 3) \ &= 2x^2 + 3x - 2 \end{aligned} $$ ## Determine the type of function $$ \text{Degree of } (f+g)(x) = 2 \implies \text{Quadratic function} $$ ## Evaluate the options $$ \begin{aligned} &\text{A. Linear function} \implies \text{False} \ &\text{B. Quadratic function} \implies \text{True} \ &\text{C. Domain is } x \ge -3 \implies \text{False (Domain is } \mathbb{R}\text{)} \ &\text{D. Range is } y \ge -3 \implies \text{False (Vertex } y\text{-value is } -\frac{25}{8} = -3.125\text{)} \end{aligned} $$

A. It is a linear function.

B. It is a quadratic function.

C. The domain is x \ge -3.

D. The range is y \ge -3.

{ "subject": "Mathematics", "question_type": "Multiple Choice", "knowledge_point": [ "Mathematics", "Algebra", "Function Operations" ] }

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QUESTION IMAGE

Question

Explanation:

Find the sum function \(f + g\)

Determine the type of function

Evaluate the options

Answer: