We will use the solutions to the absolute value functions to determine the function's description as follows:
The two solutions to the absolute value function are given as follows:
We will investigate each description as follows:
A) The distance of x from -3 is 8.
We will use the number line and determine the distance from ( x = -3 ) to the other solution ( x = 5 ). The number of units along the x-axis from point ( x = -3 ) to ( x = 5 ) would be:
Hence, option A is correct!
B) This option describes the absolute value function as follows:
We will solve the above absolute value function as follows:
The above solution to the absolute value function is not equal to the solution presented in the number line. Hence, option B is incorrect!
C) The distance of x from 1 is 4
The above statement describes the center point of the two solutions represented on the number line. We will determine the distance of each solution given from point ( x = 1 ) as follows:
We see that the distance from each solution ( x = -3 ) AND ( x = 5 ) from point ( x = 1 ) is 4 units along the x axis. Hence, option C is correct!
D) The distance of x from 4 is 1
The above statement describes the center point of the two solutions represented on the number line. We will determine the distance of each solution given from point ( x = 4 ) as follows:
The above statement is true for the solution ( x = 5 ); however, incorrect for solution ( x = -3 ). Hence, we will reject this option D as it is not true in entirety!
E) This option describes the absolute value function as follows:
We will solve the above absolute value function as follows:
The above solution to the absolute value function is not equal to the solution presented in the number line. Hence, option E is incorrect!
F) This option describes the absolute value function as follows:
We will solve the above absolute value function as follows:
The above solution to the absolute value function is not equal to the solution presented in the number line. Hence, option F is incorrect!
G) The distance of x from -3 is 5
The above statement describes the center point of the two solutions represented on the number line. We will determine the distance of each solution given from point ( x = 4 ) as follows:
The above statement is not true for the solution ( x = 5 ). Hence, we will reject this option G as it is not true in entirety!
H) This option describes the absolute value function as follows:
We will solve the above absolute value function as follows:
The above solution to the absolute value function is equal to the solution presented in the number line. Hence, option H is correct!
The correct statements are:
The above statement describes the center point of the two solutions represented on the number line. We will determine the distance of each solution given from point ( x = 4 ) as follows: