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Kaylis [27]
3 years ago
14

Can someone help me with #9 & 10.

Mathematics
1 answer:
kap26 [50]3 years ago
6 0
First find the slope
which is y2-y1/x2-x1
= 3/5
and equation of line in point form is
y-5=3/5(x+3)
intercept from here we get 34/5
so equation in slope intercept form is
y= 3/5x+34/5
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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

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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.

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