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Fofino [41]
3 years ago
8

" title="y = \frac{3}{{ \times }^{2} - 1} " alt="y = \frac{3}{{ \times }^{2} - 1} " align="absmiddle" class="latex-formula">
​
Mathematics
2 answers:
xxTIMURxx [149]3 years ago
7 0

Answer:

ep-by-step explanation:

nataly862011 [7]3 years ago
7 0
The correct answer would be (TRAY WAY)
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Segment MN has endpoints at M(-5, 4) and N(7, -5). What is the midpoint of MN???? PLZ HELP
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Theres a formula to find the midpoint it’s... (x1+x2)/2, (y1+y2)/2. You fill in the x’s and y’s to get (-5+7)/2 for x, which equals 1 and (4-5)/2 to get -0.5. (1, -0.5) is your answer

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3 years ago
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
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