Answer:
Option 1 and 2.
Step-by-step explanation:
Given : Function [tex]f(x)= |4(x-8)|-1[/tex]
To find : Which of the following are attributes of the function?
Solution :
We find the domain, range , x-intercept and symmetry of the given function to match from given attributes.
Function [tex]f(x)= |4(x-8)|-1[/tex]
1) Domain is defined as the set of values in which function is defined.
Since, The given function for value x is under the absolute function so it is defined for all real numbers.
i.e. [tex]D=[(-\infty,\infty), x|x\in \mathbb R][/tex]
2) The range is defined as the set of values that correspond with the domain.
i.e. [tex]R=[(-1,\infty), y|y\geq -1][/tex]
3) x - intercept is defined as the value of x when y=0.
So, [tex]|4(x-8)|-1=0[/tex]
[tex]|4(x-8)|=1[/tex]
The values of x are [tex](\frac{33}{4},0), (\frac{31}{4},0)[/tex]
So, x-intercept exist.
4) Symmetry about x-axis
We show it by graphically as the vertex of equation is (8,0)
And if we construct a line x=8 the graph divides into two equal parts which means it is symmetrical at x=8.
Refer the attached figure below.
Therefore, From the following options, Option 1 and 2 are correct.
