choose the correct number to finish the sentence.

the graph of (g) is a translation 3 units up of the graph of (f(x) = 4|x| - 2). the rate of change of (g) over the interval (5 \le x \le 8) is choose

Question

choose the correct number to finish the sentence.

the graph of (g) is a translation 3 units up of the graph of (f(x) = 4|x| - 2). the rate of change of (g) over the interval (5 \le x \le 8) is choose

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "blank_filling_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Function Transformations", "Average Rate of Change" ], "new_concepts": [], "current_concepts": [ "Function Transformations", "Average Rate of Change", "Absolute Value Transformations" ] } ## Define the function g(x) $$ \begin{aligned} f(x) &= 4|x| - 2 \ g(x) &= f(x) + 3 \ g(x) &= 4|x| - 2 + 3 \ g(x) &= 4|x| + 1 \end{aligned} $$ ## Evaluate g(x) at the interval endpoints $$ \begin{aligned} x_1 &= 5 \implies g(5) = 4|5| + 1 = 21 \ x_2 &= 8 \implies g(8) = 4|8| + 1 = 33 \end{aligned} $$ ## Calculate the average rate of change $$ \begin{aligned} \text{Rate of Change} &= \frac{g(8) - g(5)}{8 - 5} \ &= \frac{33 - 21}{3} \ &= \frac{12}{3} \ &= 4 \end{aligned} $$ Choose the correct number to finish the sentence. The graph of $g$ is a translation 3 units up of the graph of $f(x) = 4|x| - 2$. The rate of change of $g$ over the interval $5 \le x \le 8$ is 4. { "subject": "Mathematics", "question_type": "Fill-in-the-blank", "knowledge_point": [ "Mathematics", "Algebra", "Average Rate of Change" ] }

Sovi.AI - AI Math Tutor

QUESTION IMAGE

Question

Explanation:

Define the function g(x)

Evaluate g(x) at the interval endpoints

Calculate the average rate of change

Answer: