Answer:
Option D: Absolute value function
Step-by-step explanation:
The absolute value of a number is the distance of the number from 0 to the left or right on the number line.
We are given the function;
f(x) = |2x³ - 3x| + 5
This function contains an absolute value symbol which is |2x³ - 3x|.
This function is thus illustrated by an an absolute value function because an absolute value function will be one that contains algebraic expressions within absolute value symbols.
Given a coordinate point (x, y), the first value of the point represents the value on the x-axis while the second value represent the value on the y-axis.
1.) To express the values (-4, -1), (-1, 2), (1, -4), (2, -3), (4, 3) as a table, we have:
x y
-4 -1
-1 2
1 -4
2 -3
4 3
The values (-4, -1), (-1, 2), (1, -4), (2, -3), (4, 3) expressed as a graph have been attached as graph_1
To express the values (-4, -1), (-1, 2), (1, -4), (2, -3), (4, 3) as a mapping, we have two circles with one labelled x and the other one labelled y.
Inside the circle labelled x are the numbers -4, -1, 1, 2, 4 written vertically and inside the circle labelled y are the numbers -4, -3, -1, 2, 3 written vertically.
There are lines joining from the circle labelled x to the circle labelled y with line joining -4 in circle x to -1 in circle y, -1 in circle x to 2 in circle y, 1 in circle x to -4 in circle y, 2 in circle x to -3 in circle y, 4 in circle x to 3 in circle y.
The domain of the relation is the set of the x-values of the relation, i.e. domain is {-4, -1, 1, 2, 4}.
The range of the relation is the set of the y-values of the relation, i.e. range is {-4, -3, -1, 2, 3}
2.) To express the values (-2, 1), (-1, 0), (1, 2), (2, -4), (4, 3) as a table, we have:
x y
-2 1
-1 0
1 2
2 -4
4 3
The values (-2, 1), (-1, 0), (1, 2), (2, -4), (4, 3) expressed as a graph have been attached as graph_2
To express the values (-2, 1), (-1, 0), (1, 2), (2, -4), (4, 3) as a mapping, we have two circles with one labelled x and the other one labelled y.
Inside
the circle labelled x are the numbers -2, -1, 1, 2, 4 written
vertically and inside the circle labelled y are the numbers -4, 0, 1, 2, 3 written vertically.
There are lines joining from the circle labelled x to the circle labelled y with a line joining -2 in circle x to 1 in circle y, -1 in circle x to 0 in circle y, 1 in circle x to 2 in circle y, 2 in circle x to -4 in circle y, 4 in circle x to 3 in circle y.
The domain of the relation is the set of the x-values of the relation, i.e. domain is {-2, -1, 1, 2, 4}.
The range of the relation is the set of the y-values of the relation, i.e. range is {-4, 0, 1, 2, 3}
