Answer :
To find the axis of symmetry for the given function [tex]\( f(x) = 4|x-5| - 8 \)[/tex], we need to understand the form of the absolute value function.
The function [tex]\( f(x) = a|x-h| + k \)[/tex] is in the vertex form of an absolute value function. In this form, [tex]\( h \)[/tex] represents the x-coordinate of the vertex of the V-shaped graph, and the graph is symmetric around the line [tex]\( x = h \)[/tex]. Therefore, the equation of the axis of symmetry is [tex]\( x = h \)[/tex].
Looking at the given function [tex]\( f(x) = 4|x-5| - 8 \)[/tex], we can identify that:
- The value of [tex]\( h \)[/tex] is 5 based on the expression [tex]\( |x-5| \)[/tex].
Thus, the axis of symmetry for this function is the line [tex]\( x = 5 \)[/tex].
Therefore, the correct answer is:
B. [tex]\( x = 5 \)[/tex]
The function [tex]\( f(x) = a|x-h| + k \)[/tex] is in the vertex form of an absolute value function. In this form, [tex]\( h \)[/tex] represents the x-coordinate of the vertex of the V-shaped graph, and the graph is symmetric around the line [tex]\( x = h \)[/tex]. Therefore, the equation of the axis of symmetry is [tex]\( x = h \)[/tex].
Looking at the given function [tex]\( f(x) = 4|x-5| - 8 \)[/tex], we can identify that:
- The value of [tex]\( h \)[/tex] is 5 based on the expression [tex]\( |x-5| \)[/tex].
Thus, the axis of symmetry for this function is the line [tex]\( x = 5 \)[/tex].
Therefore, the correct answer is:
B. [tex]\( x = 5 \)[/tex]