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posledela
3 years ago
5

Sines/cosines please help!!!!

Mathematics
1 answer:
AleksandrR [38]3 years ago
8 0
I can help explain it if you PM me.
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Express the function graphed on the axes below as a piecewise function.
adoni [48]

Answer:

  f(x) = {x-3 for x ≤ -1; -3x+14 for x > 5}

Step-by-step explanation:

To write the piecewise function, we can consider the pieces one at a time. For each, we need to define the domain, and the functional relation.

__

<h3>Left Piece</h3>

The domain is the horizontal extent. It is shown as -∞ to -1, with -1 included.

The relation has a slope (rise/run) of +1, and would intersect the y-axis at -3 if it were extended.

The first piece can be written ...

  f(x) = x-3 for x ≤ -1

__

<h3>Right Piece</h3>

The domain is shown as 5 to ∞, with 5<em> not included</em>.

The relation is shown as having a slope (rise/run) of (-3)/(1) = -3. If extended, it would intersect the point (5, -1), so we can write the point-slope equation as ...

  y -(-1) = -3(x -5)

  y = -3x +15 -1 = -3x +14

The second piece can be written ...

  f(x) = -3x +14 for x > 5

__

<h3>Whole function</h3>

Putting these pieces together, we have ...

  \boxed{f(x)=\begin{cases}x-3&\text{for }x\le-1\\-3x+14&\text{for }5 < x\end{cases}}

_____

<em>Additional comment</em>

Sometimes it is convenient to write inequalities in number-line order (using < or ≤ symbols). This gives a visual indication of where the variable stands in relation to the limit(s). Perhaps a more conventional way to write the domain for the second piece is, <em>x > 5</em>.

3 0
2 years ago
A square has a perimeter of 12x+52 units which expression represents the side length of the square in units
saw5 [17]
The side of the square is (12x+52)/4=3x+13.
3 0
3 years ago
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Find the exact area of a circle having the given circumference.
BaLLatris [955]
Circumference is given by
C=2\pi r
Area is given by
A=\pi r^2

figure out the radius of the circle, then use it to find area
5 0
3 years ago
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Laura works at a coffee shop. Her boss has asked that she write down how many minutes each of the next 10 orders take to make. H
ASHA 777 [7]

Answer:

4

Step-by-step explanation:

6+2+4+2+2+7+5+6+3+3=40

40/10=4

Therefore the mean is 4

8 0
2 years ago
What is the sum and classification of <img src="https://tex.z-dn.net/?f=%5Cfrac%7B2%7D%7B5%7D%20%2B%20%5Csqrt%7B88%7D" id="TexFo
aleksandrvk [35]

Answer:

The answer is def. A.

8 0
2 years ago
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