The vertex of the function [tex]g\left(x\right)=\left|{x-8}\right|+6[/tex] is [tex]\boxed{\bf \left( {8,6} \right)}[/tex].
Further explanation:
Concept used:
The function [tex]g\left(x\right)=\left|x\right|[/tex] is defined as follows:
[tex]g\left(x\right)=\left\{\begin{aligned}-x,\,\,\,\,\,x\leq0\hfill\\x,\,\,\,\,\,\,\,\,\,x\geq0\hfill\\ \end{aligned}\right[/tex]
The vertex is defined as the common end point of the two lines.
The graph of the function [tex]g\left(x\right)=\left|{x-8}\right|+6[/tex] is obtained from the graph of [tex]g\left(x\right)=\left|x\right|[/tex] in following two steps.
(a). Shift the graph of the function [tex]g\left(x\right)=\left|x\right|[/tex] to 8 units in right direction to obtain the graph of function [tex]g\left(x\right)=\left|{x-8}\right|[/tex].
(b). Now, shift the obtained graph of function [tex]g\left(x\right)=\left|{x-8}\right|[/tex] to 6 units in upward direction to obtain the graph of function [tex]g\left(x\right)=\left|{x-8}\right|+6[/tex].
From figure 1, it is observed that the vertex of the function [tex]g\left(x\right)=\left|{x-8}\right|+6[/tex] is [tex]\boxed{\bf \left( {8,6} \right)}[/tex].
Learn more:
1. Which function has an inverse that is also a function? {(–1, –2), (0, 4), (1, 3), (5, 14), (7, 4)} {(–1, 2), (0, 4), (1, 5), (5, 4), (7, 2)} {(–1, 3), (0, 4), (1, 14), (5, 6), (7, 2)} {(–1, 4), (0, 4), (1, 2), (5, 3), (7, 1)}
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2. A given line has the equation 10x + 2y = −2. what is the equation, in slope-intercept form, of the line that is parallel to the given line and passes through the point (0, 12)? y = ( )x + 12
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3. what are the domain and range of the function f(x) = 3x + 5?
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Answer Details :
Grade: Junior high School.
Subject: Mathematics.
Chapter: Coordinate geometry.
Keywords:
Mode, modulus, g(x)=|x-8|+6, lines, straight lines, (8,6), shifting, function, point slope, equation of line passing, perpendicular line, graph, domain, intervals, intercepts, function value, intercepts of lines, slope, slope intercept form, continuous, range, point, line segment.
