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nata0808 [166]
3 years ago
5

A corporate team-building event costs $1, plus an additional $1 per attendee. Write an equation that shows the relationship betw

een the attendees x and the cost y.Write your answer as an equation with y first, followed by an equals sign.
Mathematics
1 answer:
Elis [28]3 years ago
6 0

The equation is y=x+1

Here's an explanation:

The equation starts out with y since that's what we're told to do. Since the even costs $1, then the total cost would be the total number of attendees +1. The variable for attendees is x, and since the additional cost is $1 per attendee, you don't have to multiply x with anything. So, the answer would be y=x+1. (Everything's in dollars)

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1. As you can tell from the function definition and plot, there's a discontinuity at x = -2. But in the limit from either side of x = -2, f(x) is approaching the value at the empty circle:

\displaystyle \lim_{x\to-2}f(x) = \lim_{x\to-2}(x-2) = -2-2 = \boxed{-4}

Basically, since x is approaching -2, we are talking about values of x such x ≠ 2. Then we can compute the limit by taking the expression from the definition of f(x) using that x ≠ 2.

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4. Your answer is correct; the limit doesn't exist because there is a jump discontinuity. f(x) approaches two different values depending on which direction x is approaching 2.

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For 7-8, divide through each term by the largest power of x in the expression:

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\displaystyle \lim_{x\to\infty}\frac{x^2+x-12}{2x^2-5x-3} = \lim_{x\to\infty}\frac{1+\frac1x-\frac{12}{x^2}}{2-\frac5x-\frac3{x^2}}=\boxed{\frac12}

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\displaystyle \lim_{x\to\infty} \frac{-2x^2+2}{x+1} = \lim_{x\to\infty} (-2x+2) = \boxed{-\infty}

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