Question #310194

Show the graph and determine if the given function is continuous on each of the given intervals.




1. f(x)=4x²-x+6; (-infinite, 0)



2.f(x)=4/x-5;(-5,5)



3.f(x)=√x-1;(1,+infinite)



4.f(x)=-|-5x|;(-1,+infinite)

1
Expert's answer
2022-03-17T13:38:31-0400

Solution (1)


For the function

f(x)=4x2x+6f(x)=4x²-x+6 over the interva(,0](-\infty, 0]


The plot is shown below





From the plot, we can see that f(x)=4x2x+6;f(x)=4x²-x+6; is continouse over the interval (,0](-\infty, 0]


Solution (2)


For the function

f(x)=4xf(x)=\frac{4}{x} over the interval (5,5)(-5,5) the plot is shown below





From the plot we can see that the function f(x)=4xf(x)=\frac{4}{x} is not continous at x=0x=0


Solution (3)


For the function

f(x)=x1f(x)=\sqrt{x-1} over the interval (1,)(1,\infty) the plot is shown below





From the plot we can see that the function f(x)=x1f(x)=\sqrt{x-1} over the interval (1,)(1,\infty) is continous


Solution (4)


For the function f(x)=5xf(x)=-|-5x| over the interva(1,)(-1, \infty)the plot is shown below





From the plot we can see that the function f(x)=5xf(x)=-|-5x| over the interval (1,)(-1,\infty) is continous


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