A:
The function d(x) = |x| -4 would be graphed on the number line with the point (0, -4) as the starting point. The function would then continue in either direction from that point, depending on the value of x.
B:
To graph this function, start by finding the points where x = 0 and x = -4. These will be your y-intercepts. So, plot those points on a graph first. Then, for every other value of x, determine whether it is positive or negative. For positive values of x, plot a point above the y-axis; for negative values of x, plot a point below the y-axis. Connect all these points with a smooth curve to get your final graph!
The graph of | x | - 4 , this function will be similar to | x | but will shift 4 units down along the y-axis.
We know the absolute value function of the modulus function always outputs a positive value irrespective of the sign of the input.
In piecewise terms | x | = x for x ≥ 0 and | x | = - x for x < 0.
Given, d(x) = | x | - 4.
So, at x = 0 d(x) = - 4.
So, the coordinate points are (0, - 4).
Now, to graph, this function will be similar to | x | but will shift 4 units down along the y-axis.
learn more about the modulus function here :
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