Using the given absolute value function, we have that:
1. The x-intercepts are (5.75,0) and (6.25).
2. The y-intercept is (0, 138).
3. The vertex is (6,-6).
4. The range is [-6, ∞).
5. The negative range of values of x is 5.75 < x < 6.25 = (5.75, 6.25). (I think there is a mistake in the formulation of this item).
6. x -> ∞, y -> ∞.
What is the absolute value function?
The absolute function is defined by:
It measures the distance of a point x to the origin.
For this problem, the function is defined as follows:
f(x) = 8(|3x - 18|) - 6
The x-intercepts are the values of x when f(x) = 0, hence:
8(|3x - 18|) - 6 = 0
|3x - 18| = 3/4
|3x - 18| = 0.75.
Two solutions, as follows:
3x - 18 = -0.75
3x = 17.25
x = 17.25/3
x = 5.75.
3x - 18 = 0.75
3x = 18.75
x = 18.75/3
x = 6.25.
The x-intercepts are (5.75,0) and (6.25). The function is negative between the intercepts, hence the negative range of values of x is 5.75 < x < 6.25 = (5.75, 6.25).
The y-intercept is the value of f(x) when x = 0, hence:
f(0) = 8(|3(0) - 18|) - 6 = 8 x 18 - 6 = 138.
The y-intercept is (0, 138).
The vertex is between the roots(5.75 and 6.25) at the shifted down position(down 6 units), hence (6, -6).
The range is from the y-value of the vertex to infinity, hence the range is [-6, ∞).
The function was not reflected(multiplied by -1), hence it goes to infinity to the right, that is, as x -> ∞, y -> ∞.
More can be learned about the absolute value function at https://brainly.com/question/28396388
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