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zhannawk [14.2K]
3 years ago
11

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

Mathematics
2 answers:
Alecsey [184]3 years ago
7 0
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.

Contact [7]3 years ago
6 0
For this case we have the following functions:
 For - 4  \leq x  \ \textless \  3 : 
 y = x + 4

 For 3  \leq x \ \textless \  6 :
 y = 2x - 1

 What we need to know for this case is:
 Both functions are one lines
 Both functions have a positive slope
 Both functions are in a certain interval
 Answer:
 See attached image to see functions

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