consider the absolute value functions $c$ and $d$.

$\begin{array}{c|ccccc}
x & -5 & -4 & -3 & -2 & -1 \\
\hline
c(x) & -4 & -3 & -4 & -5 & -6
\end{array}$

which statement correctly describes these functions?

- the minimum value of $d$ is 5 more than the maximum value of $c$.
- the minimum value of $d$ is 3 more than the maximum value of $c$.
- the maximum value of $d$ is 3 less than the minimum value of $c$.

Question

consider the absolute value functions $c$ and $d$.

$\begin{array}{c|ccccc}
x & -5 & -4 & -3 & -2 & -1 \\
\hline
c(x) & -4 & -3 & -4 & -5 & -6
\end{array}$

which statement correctly describes these functions?

- the minimum value of $d$ is 5 more than the maximum value of $c$.
- the minimum value of $d$ is 3 more than the maximum value of $c$.
- the maximum value of $d$ is 3 less than the minimum value of $c$.

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Absolute Value Functions" ], "new_concepts": [], "current_concepts": [ "Absolute Value Functions", "Parabola Key Features" ] } ## Determine key features of function c $$ \begin{aligned} &\text{Table values for } c(x):\ &c(-5) = -4\ &c(-4) = -3\ &c(-3) = -4\ &c(-2) = -5\ &c(-1) = -6\ &\text{The vertex of } c(x) \text{ is at } (-4, -3).\ &\text{Since the values decrease on both sides of } x = -4,\ &\text{the maximum value of } c \text{ is } -3. \end{aligned} $$ ## Determine key features of function d $$ \begin{aligned} &\text{Graph of } d(x):\ &\text{The vertex (lowest point) of the absolute value graph is at } (-1, 2).\ &\text{Since the graph opens upwards,}\ &\text{the minimum value of } d \text{ is } 2. \end{aligned} $$ ## Compare the extremum values $$ \begin{aligned} &\text{Minimum value of } d = 2\ &\text{Maximum value of } c = -3\ &\text{Difference: } 2 - (-3) = 5\ &\text{Thus, the minimum value of } d \text{ is } 5 \text{ more than the maximum value of } c. \end{aligned} $$

(A) The minimum value of d is 5 more than the maximum value of c.

(B) The minimum value of d is 3 more than the maximum value of c.

(C) The maximum value of d is 3 less than the minimum value of c.

{ "subject": "Mathematics", "question_type": "Multiple Choice", "knowledge_point": [ "Mathematics", "Algebra", "Absolute Value Functions" ] }

Sovi.AI - AI Math Tutor

QUESTION IMAGE

Question

Explanation:

Determine key features of function c

Determine key features of function d

Compare the extremum values

Answer: