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Ulleksa [173]
3 years ago
10

Tell whether each function is linear or non-linear.

Mathematics
1 answer:
MrMuchimi3 years ago
3 0

Answer:

Function A is non-linear and Function B is linear.

Step-by-step explanation:

Linear function:

Has the following format:

y = mx + b

In which m is the slope and b is the y-intercept.

In a linear function, when x changes by 1, y will always changes by the same amount.

Function A:

When x changes by 1, y can change by various amounts. So function A is non-linear.

Function B:

y = -x + 5

In the format of a linear function, so linear

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Answer:

Option a)

Step-by-step explanation:

To get the vertical asymptotes of the function f(x) you must find the limit when x tends k of f(x). If this limit tends to infinity then x = k is a vertical asymptote of the function.

\lim_{x\to\\2}\frac{x^3}{(x-2)^4} \\\\\\lim_{x\to\\2}\frac{2^3}{(2-2)^4}\\\\\lim_{x\to\\2}\frac{2^3}{(0)^4} = \infty

Then. x = 2 it's a vertical asintota.

To obtain the horizontal asymptote of the function take the following limit:

\lim_{x \to \infty}\frac{x^3}{(x-2)^4}

if \lim_{x \to \infty}\frac{x^3}{(x-2)^4} = b then y = b is horizontal asymptote

Then:

\lim_{x \to \infty}\frac{x^3}{(x-2)^4} \\\\\\lim_{x \to \infty}\frac{1}{(\infty)} = 0

Therefore y = 0 is a horizontal asymptote of f(x).

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