choose the correct number to finish the sentence.

for the function $f(x) = \sqrt{x + 3}$, the average rate of change to the nearest hundredth over the interval $1 \le x \le 5$ is

options:
0.21
0.18
0.20
0.19

Question

choose the correct number to finish the sentence.

for the function $f(x) = \sqrt{x + 3}$, the average rate of change to the nearest hundredth over the interval $1 \le x \le 5$ is

options:
0.21
0.18
0.20
0.19

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Average Rate of Change", "Square Root Functions" ], "new_concepts": [], "current_concepts": [ "Average Rate of Change", "Square Root Functions" ] } ## Evaluate the function at the interval endpoints $$ \begin{aligned} f(1) &= \sqrt{1 + 3} = \sqrt{4} = 2 \ f(5) &= \sqrt{5 + 3} = \sqrt{8} \approx 2.8284 \end{aligned} $$ ## Calculate the average rate of change $$ \begin{aligned} \text{Average Rate of Change} &= \frac{f(5) - f(1)}{5 - 1} \ &= \frac{\sqrt{8} - 2}{4} \ &\approx \frac{2.8284 - 2}{4} \ &= \frac{0.8284}{4} \ &\approx 0.2071 \end{aligned} $$ ## Round to the nearest hundredth $$ 0.2071 \approx 0.21 $$

(A) 0.21

(B) 0.18

(C) 0.20

(D) 0.19

{ "subject": "Mathematics", "question_type": "Multiple Choice", "knowledge_point": [ "Mathematics", "Algebra", "Average Rate of Change" ] }

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QUESTION IMAGE

Question

Explanation:

Evaluate the function at the interval endpoints

Calculate the average rate of change

Round to the nearest hundredth

Answer: