Question

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)

Answer 1

Solution (1)

For the function

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

The plot is shown below

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

Solution (2)

For the function

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

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

Solution (3)

For the function

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

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

Solution (4)

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

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