The correct option is .
Further explanation:
Absolute value function:
An absolute function is a function which always gives a positive for any real value of domain.
Absolute value of a number is distance from 0 on the number line.
Example:
The absolute value function is expressed as shown below.
Concept used:
If a constant is added to the absolute value function, the graph of the function shifts vertically upwards if the constant is positive and it shifts vertically downward if the constant is negative.
The graph of is shifted vertically upwards and the graph of shift vertically downwards by units.
Here, is a constant.
Consider that absolute value function is in the form as .
If the value of is positive then the curve of the function open upwards and if the value of is negative then the curve of the function open downwards.
If the value of greater than or less than then the graph becomes narrower.
The graph of is narrower.
If the coefficient of the absolute value function is in fraction then the graph of the function becomes wider.
The graph of the function is wider.
Calculation:
The first option is incorrect because the absolute value function cannot determine the direction in which graph opens it is decided by the sign of the function.
The graph of the function is open downward and graph of the function opens upward.
The second option is incorrect because the coefficient cannot determine the symmetry of the graph.
The graph of the function is symmetric about -axis and the graph of the function is also symmetric about -axis.
The third option is incorrect because the distance between right arm and left arm depends upon the coefficient of the absolute value function and if it is fraction then the graph becomes wider and if it is integer and greater than one than the graph becomes narrower.
The graph of is wider and graph of is narrower than graph of .
The fourth option is correct. From figure 1 (attached in the end) it is observed that the vertex coordinates and the absolute value determines the region of the graph on the plane.
This implies that correct option is option (D).
Therefore, the correct option is .
Learn more:
1. Coordinate of the point : brainly.com/question/1286775
2. Equation: brainly.com/question/1473992
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.