The equation of the piecewise function is
On the graph, we have:
Hence, the piecewise function is:
This is the set of input values
In (a), we have:
x ≤ -1 and x > 2
Hence, the domain is (∞, 3] u (2, ∞)
<h3>The range of the function</h3>This is the set of output values
In (a), we have:
f(x) = 3 and f(x) -1
Hence, the range is [3] u (-1)
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Therefore the equation of the line in function-form is f(x)=-2x-1
An equation of a line on the cartesian plane is given by y=mx+c. Here m denotes the slope of the line and c denotes the y-intercept.
Slope of a line is defined as the inclination of the line along the positive x- axis . Slope is calculated by the formula where
and
are two points on the line.
y-intercept is defined as the point where the line passes through the y-axis.
From the graph we can see that the line passes through (0,-1)and (-1,1)
therefore slope of the line is
Now we know that the equation of a line passing through a point and with slope m is given by
Substituting the values in the equation we get
y-(-1)=-2(x-0)
or, y=-1-2x
Therefore the equation of the line in function-form is f(x)=-2x-1 .Hence the second option is correct.
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