An absolute role is a duty which constantly gives a confident for any real worth of domain.

Absolute value of a number is street from 0 on the number line.

You are watching: Which statement holds true for absolute value functions?

Example:

The absolute value duty is expressed as presented below.

*

Concept used:

If a constant is added to the absolute worth function, the graph of the function shifts vertically upwards if the constant is positive and also it shifts vertically bottom if the consistent is negative.

The graph that

*
is shifted vertically upwards and also the graph of
*
change vertically downwards by units.

Here, is a constant.

Consider that pure value duty is in the form as

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.

If the value of is hopeful then the curve of the function open upwards and also if the value of is an unfavorable then the curve of the function open downwards.

If the value of greater than

*
or much less than
*
then the graph becomes narrower.

The graph of is narrower.

If the coefficient the the absolute value function is in portion then the graph of the duty becomes wider.

The graph that the role is wider.

Calculation:

The very first option is incorrect due to the fact that the pure value duty cannot determine the direction in i m sorry graph opens up it is chose by the authorize of the function.

The graph the the duty is open up downward and graph of the function opens up upward.

The 2nd option is incorrect because the coefficient cannot identify the the opposite of the graph.

The graph the the role is symmetric about -axis and also the graph that the duty is likewise symmetric around -axis.

The third option is incorrect because the distance between right arm and also left arm depends upon the coefficient the the absolute value duty and if the is fraction then the graph becomes broader and if that is integer and greater than one 보다 the graph i do not care narrower.

The graph the is broader and graph of is narrower 보다 graph the .

The fourth option is correct. From number 1 (attached in the end) that is observed the the vertex coordinates and also the absolute worth determines the an ar of the graph top top the plane.

This indicates that correct alternative is alternative (D).

Therefore, the correct choice is .

Learn more:

1. Coordinate of the suggest :

2. Equation:

Answer details:

Grade: High school

Subject: Mathematics

Chapter: Function

Keywords: coordinate geometry, x-axis, y-axis, x-coordinate, y-coordinate, Absolute value function, graph , region, coefficient, vertically opens, horizontally downs.

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*

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The correct alternative is

*
.

Further explanation:

Absolute worth function:

An absolute function is a duty which always gives a confident for any kind of real value of domain.