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3 years ago

$9.60 for 4 pounds as a unit rate

Mathematics

1 answer:

Reika [66]3 years ago

4 0

You would divide 9.60 by 4 and you would get 2.40 each pound which would be your unit rate

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3 years ago

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3 years ago

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See below

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2 years ago

Sketch the graph of f(x)=((x^(3)-1)/(x^(2)-1))

Verdich [7]

It's easier to sketch if you simplify $f(x)$ . Factorize the numerator and denominator - simple to do with a difference of cubes or squares.

$\dfrac{x^3 - 1}{x^2 - 1} = \dfrac{(x - 1)(x^2 + x + 1)}{(x - 1) (x + 1)}$

If $x\neq1$ , we can cancel the factors of $x-1$ . Note that $f(1)$ itself is undefined. For all intents and purposes, aside from the singularity at $x=1$ , the graph of $f(x)$ will look exactly like the graph of

$\dfrac{x^2 + x + 1}{x + 1}$

Now, rewrite this as

$\dfrac{x(x + 1) + 1}{x + 1}$

Then when $x\neq-1$ (note that $f(-1)$ is also undefined), we can cancel $x+1$ to reduce this to

$x + \dfrac1{x+1}$

On its own, the graph of $x$ is a line through the origin. When $x$ is a large number $\frac1{x+1}$ is small. But as $x$ gets closer to -1, the rational term blows up. Effectively, this means the graph of $f(x)$ looks like $\frac1{x+1}$ around $x=-1$ , and far enough away it looks like $x$ .