The prize is C. ) The distance in between the left and also the ideal arm is based on the works with of the vertex.

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



The correct option is .

Further explanation:

Absolute worth function:

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

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

Example:

The absolute value role is to express as shown below.

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Concept used:

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

The graph of

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is change vertically upwards and also the graph that
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change vertically downwards by units.

Here, is a constant.

Consider that absolute value role is in the kind as

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.

If the value of is optimistic then the curve that the duty open upwards and also if the worth of is negative then the curve the the role open downwards.

If the worth of higher than

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or much less than
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climate the graph becomes narrower.

The graph the is narrower.

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

The graph of the duty is wider.

Calculation:

The first option is incorrect since the pure value duty cannot recognize the direction in which graph opens up it is chose by the authorize of the function.

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

The 2nd option is incorrect since the coefficient cannot determine the the opposite of the graph.

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

The 3rd option is incorrect due to the fact that the distance between right arm and left arm relies upon the coefficient the the absolute value role and if the is fraction then the graph becomes wider and if it is integer and also greater than one than the graph i do not care narrower.

The graph that is more comprehensive and graph the is narrower 보다 graph the .

The 4th option is correct. From figure 1 (attached in the end) that is observed the the peak coordinates and also the absolute value 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. Name: coordinates of the allude :

2. Equation:

Answer details:

Grade: High school

Subject: Mathematics

Chapter: Function

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

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The correct option is

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.

Further explanation:

Absolute value function:

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

Absolute worth of a number is street from 0 ~ above the number line.

Example:

The pure value role is express as displayed below.

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The correct answer is:D) the peak coordinates and the absolute value recognize the an ar of the graph ~ above the plane.Explanation:The vertex works with of an absolute value duty determine how far the graph is shifted vertically and horizontally native the origin, together the crest of the parental graph y=|x| is the beginning (0, 0).The coefficient in front of the absolute worth bars identify which direction the graph opens up in and also how vast or narrow the bars space (the distance in between the arms). If the coefficient is positive, the graph opens upward; if the coefficient is negative, the graph opens up downward. If the coefficient is one integer higher than 1 or much less than -1, climate the graph will be an ext narrow 보다 the parental graph; if the coefficient is a fraction, climate the graph will be broader than the parent graph.Since the peak affects the position and the coefficient identify the direction it opens up, these determine the an ar of the graph ~ above the plane.