Answered

Over which interval is the graph of the parent absolute value function decreasing?


(–∞, ∞)

(–∞, 0)

(–6, 0)

(0, ∞)

Verified Answer :

W0lf93

Answer: (-∞, 0)The graph of the parent absolute value function is decreasing over the interval (–∞, 0)
The graph drawn for the absolute value parent function is usually made up of two linear "pieces" which meet at a common vertex (the origin; 0, 0). The graph is symmetric around the y axis and generally takes a V shape or an inverted V shape. The absolute/relative minimum of the graph is 0 but there it has no absolute maximum; so the absolute maximum is usually represented by ‘∞’ (infinitive). Typically, the graph of the parent absolute value function is increasing over the interval (0, ∞), and is decreasing over the interval (-∞, 0).

The graph of the parent absolute value function decreases over (–∞, 0) interval.

Given

The graph of the parent absolute value function;

\(\rm f(x) = |x|\)

What is the parent absolute value function?

An absolute value function is a function that contains an algebraic expression within absolute value symbols.

Recall that the absolute value of a number is its distance from 0 on the number line.

The absolute value function is f(x) = |x| is defined as,

\(\rm f(x) = x \ if \ x>0\\\\f(x) = 0 \ if \ x=0\\\\f(x) =-x \ if \ x<0\)

Observe that the graph is V-shaped.

  • The vertex of the graph is (0,0).

  • The axis of symmetry (x =0 or y-axis) is the line that divides the graph into two congruent halves.

  • The domain is the set of all real numbers.

  • The range is the set of all real numbers greater than or equal to 0. That is y ≥0.

  • The x-intercept and the y-intercept are both 0.

Hence, the graph of the parent absolute value function decreases over (–∞, 0) interval.

To know more about the Absolute function click the link given below.

https://brainly.com/question/18599661

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