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

3977

Step-by-step explanation:

The range of the sine and cosine functions is .

This means that the maximum value the basic sine and cone functions is 1 and the minimum value is -1.

This means that the two functions are bounded above and below.

The correct answer is B.

A is correct.

i.e. the functions:

y=x  , y= x^3 , y= int (x)

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.

Choice A is correct

Step-by-step explanation:

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

The correct option is;

b. y = x²,

Step-by-step explanation:

The equations are

1) y = x

2) y = x²

3) y = x³

4)

5) y = 1/x

6) y = eˣ

7) y = √x

8) y = ㏑x

9) y = sin x

undefined

10) y = cos x

undefined

11) y int (x)

12)

Therefore, the correct options are y = x² and

The Sine function:  

f

(

x

)

=

sin

(

x

)

The Cosine function:  

f

(

x

)

=

cos

(

x

)

and

The Logistic function:  

f

(

x

)

=

1

1

−

e

−

x

are the only function of the "Basic Twelve Functions" which are bounded above.

Step-by-step explanation:

working on it.

Step-by-step explanation: