draw the graph of f(x)=1-2x and find the range
Answers
Answer:
Clearly the function f is defined for all real numbers and so its domain is R.
Also note that f(x) >/=0 for all x, and given any non-negative real number y, taking x =y+1 we see that f(x)=||y+1|-1| =|y+1–1|=|y|=y, because |y+1|=y+1, as (y+1)>0, as y>/=0, and for the same reason |y|=y. Hence every real number y>/=0 is f(y+1). Therefore the range of f is {y € R : y>/=0}.
As for drawing the graph of the function f, for x>/=1, f(x)=x-1. For 0 </=x<1, f(x)=1-x. Observe that the function is an even function of x, as f(-x)=f(x) for all x. Hence for negative values of x, the graph can be obtained by reflecting it about the y-axis. So for -1 < x < 0,
f(x) =f(-x)=1-(-x) (as 0<(-x)<1) = 1+x, and finally for x</=(-1), f(x) = f(-x) =-(-x)-1 (since (-x)>/=1)
= -(x+1). Thus the graph looks like a gigantic W, being given by
1: x </=(-1) : f(x)=-(x+1)
2:(-1) < x </= 0 : f(x)=(x+1)
3: 0 < x < 1 : f(x)= (1-x)
4: x >/= 1 : f(x) = (x-1). The angular points of this giant W are at (-1,0), (0,1) and (1,0).
Answer:
The range of f(x) = 1 - 2x is set of all real numbers.
Step-by-step explanation:
Consider the given function as follows:
f(x) = 1 - 2x . . . . . (1)
Substitute the value 1 for x, we get
f(1) = 1 - 2(1)
= 1 - 2
= -1
Substitute the value 0 for x, we get
f(0) = 1 - 2(0)
= 1 - 0
= 1
Substitute the value 1/2 for x, we get
f(1/2) = 1 - 2(1/2)
= 1 - 1
= 0
Substitute the value -1 for x, we get
f(-1) = 1 - 2(-1)
= 1 + 2
= 3
The points (x, f(x)) is listed in the table as follows:
x 1 0 1/2 -1
f(x) -1 1 0 3
Plot all the points on the graph.
From the graph,
Notice that the function f(x) = 1 - 2x is defined on each and every point of real number.
Thus, the range of f(x) is the set of all real numbers, .
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