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Mathematics

1 answer:

liraira [26]3 years ago

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Answer:

Step-by-step explanation:

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Graph the following piecewise function on a separate piece of graph paper and upload your graph below.

Alecsey [184]

ANSWER

To graph the function

$f(x)=\left \{ {{x+4\:\:if\:\:-4\leq x$

follow the steps below.

1. Find y- intercept by plugging in $x=0$ .

$x=0$ is on the interval, $-4\leq x$ , so we substitute in to

$f(x)=x+4$

$\Rightarrow f(0)=0+4$

$\Rightarrow f(0)=4$

Hence the y-intercept is $(0,4)$

2. Find x-intercept by setting $f(x)=0$

This implies that

$x+4=0,$ on $-4\leq x$

or

$2x-1=0$ on $3\leq x$

We now solve for $x$ on each interval,

$x=-4,$ on $-4\leq x$

or

$x=\frac{1}{2}$ on $3\leq x$

But observe that

$x=\frac{1}{2}$ does not belong to $3\leq x$

This means it can never be an intercept for this piece-wise function.

Hence our x-intercept is $(-4,0)$

3. Plotting the boundaries of the interval.

For $f(x)=x+4$ on $-4\leq x$

$f(-4)=-4+4$

$\Rightarrow f(-4)=0$ .

This point $(-4,0)$ coincides with the x-intercept.

$f(3)=3+4$

$f(3)=7$

So we have the point $(3,7)$ . But note that $x=3$ does not belong to this interval so we plot this point as a hole.

For $f(x)=2x-1$ on $3\leq x$

$f(3)=2(3)-1$

$\Rightarrow f(3)=5$

So we plot $(3,5)$

$f(6)=2(6)-1$

$\Rightarrow f(6)=11$

So we plot $(6,11)$ also as a hole.

Plotting all these points we can now graph the function,

$f(x)=\left \{ {{x+4\:\:if\:\:-4\leq x$

See attachment for graph.