The second graph is the correct match for the piecewise defined function .
Further explanation:
Given:
The given piecewise-defined function is .
Calculation:
The given function is defined as for , for and for .
Therefore, the function is defined over the interval.
In the interval function is a line , over the interval function gives a parabola and over the interval function gives another line as .
Choose the values of which lies in the interval and draw a graph for .
Choose the values of which lies in the interval and draw a graph for .
Again choose the values of which lies in the interval and draw a graph for .
The table for the values of and the corresponding values the function is shown below in Table 1.
The table for the values of and the corresponding values the function is shown below in Table 2.
The table for the values of and the corresponding values the function is shown below in Table 3.
Now the graph of piecewise-defined function is sketched in Figure 1.
Thus, the second graph is the correct match for the piecewise defined function .
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: SeniorSchool .
Subject: Mathematics .
Chapter: Function.
Keywords:
lines, parabola, straight lines, g(x),function, piecewise defined function, graph, domain, intervals, intercepts, function value, intercepts of lines, slope, slope intercept form, continuous, range, point, y=-2x,y=x,y=x^2.