Question

Identify which of the twelve basic functions listed below fit the description given

Answer 1

Choice A is correct

Explanation:

We perform direct substitution; substitute -infinity into each expression in the alternatives. Only the expressions in the first alternative will fit this criteria

Answer 2

A is correct.

i.e. the functions:

y=x , y= x^3 , y= int (x)

Explanation:

We have to find which of the choice is best such that it satisfy:

lim f(x) = -∞ when x→ -∞.

B)

[y=x, y=1/(1=e^{-x}) , y= int (x)

Now we consider the function y=1/(1+e^{-x}).

We know that when x → -∞

y=f(x)→ 0

since e^{-x} →∞ when x → -∞

and so 1+e^{-x} → ∞

and hence 1/(1+e^{-x}) → 0.

Hence, B option is incorrect.

D)

Similarly D option is also incorrect.( as done in part B)

C)

y=x^2, y=x^3 , y= int (x)

We know that y=x^2 always gives a positive value for any x.

The end behaviour of y=x^2 is that it reaches to ∞.

Hence when x → - ∞ y=x^2 → ∞

Hence, option C is incorrect.

So the options B,C, and D are discarded.

Hence, option: A is correct.

Also it can be observed by there graphs.