Jason Farmer
2021-05-14
Answered

Determine whether each of the given sets is a real linear space, if addition and multiplication by real scalars are defined in the usual way. For those that are not, tell which axioms fail to hold. The function are real-valued. All rational functions f/g, with the degree off ≤≤ the degree ofg (including f = 0).

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AGRFTr

Answered 2021-05-15
Author has **95** answers

The degree restriction for f and g has no effect on satisfaction of any axioms. As that condition will be satisfied even if we add two rational functions of same type or if we multiply some real number to a rational function of that type. And inclusion of f=0 implies that axiom 5 and axiom 6 hold.

2 Therefore all axioms are satisfied similar to exercise 1(refer previous solution).

2 Therefore all axioms are satisfied similar to exercise 1(refer previous solution).

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Determine

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g is related to one of the parent functions. Describe the sequence of transformations from f to g. g(x) = -2|x - 1| - 4

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What transformations of the parent graph of

$f\left(x\right)=\sqrt{x}$

produce the graphs of the following functions?

a)$m\left(x\right)=\sqrt{7x\text{}-\text{}3.5}\text{}-\text{}10$

b)$j\left(x\right)=-2\sqrt{12x}\text{}+\text{}4$

produce the graphs of the following functions?

a)

b)

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For the function f whose graph is given, state the following.

(a)$\underset{x\to \mathrm{\infty}}{lim}f(x)$

b)$\underset{x\to -\mathrm{\infty}}{lim}f(x)$

(c)$\underset{x\to 1}{lim}f(x)$

(d)$\underset{x\to 3}{lim}f(x)$

(e) the equations of the asymptotes

Vertical:- ?

Horizontal:-?

(a)

b)

(c)

(d)

(e) the equations of the asymptotes

Vertical:- ?

Horizontal:-?