Marcel collects soccer cards. He has 24 cards in his collection. Four-sixths of his cards have been canceled. How many of the ca
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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.
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<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
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<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
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<h3>Whole function</h3>Putting these pieces together, we have ...
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<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>.
Answer: Restaurant: $34.50; Toy Company: $4.50
Step-by-step explanation:
Let's represent the situation mathematically. I will use "r" for the restaurant stock price and "t" for the toy company stock price.
represents the value of their stock portfolio.
represents that the restaurant stock was worth $30 more than the toy company stock.
We need to multiply the second equation by 60 to balance the terms out. This gets us .
Now, you can combine the like terms in these equations to get , which can be simplified further to
.
Now you need to divide both sides by 102 to remove the coefficient, getting you . This means that the price of the restaurant stock was $34.50.
To find the toy company stock price, subtract $30 from the restaurant stock price, because the restaurant stock is worth $30 more than the toy company stock. This gets you $4.50.