A box contains 7 blue socks, 13 yellow socks and 5 green socks. What is the probability of choosing a green sock at random? Ques
1 answer:
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To solve the problem shown above you must apply the following proccedure:
1. You have the following function given in the problem:
<span> f(x)=x3–3x–2
2. When you give values to the x and plot each point obtained, you obtain the graph shown in the figure attached.
3. Based on the graph and analizing the alternate form:
f(x)=(x-2)(x+1)</span>²
As you can see, there is two roots x=-1, then, you can conclude that the correct answer is the option b, which is:
b) -1
<span>
</span>
1. You have the following function given in the problem:
<span> f(x)=x3–3x–2
2. When you give values to the x and plot each point obtained, you obtain the graph shown in the figure attached.
3. Based on the graph and analizing the alternate form:
f(x)=(x-2)(x+1)</span>²
As you can see, there is two roots x=-1, then, you can conclude that the correct answer is the option b, which is:
b) -1
<span>
</span>
Answer:
Step-by-step explanation:
Domain of f: "What values of x can we plug into this equation?" This makes sense for all real numbers so the domain is
Range of f: "What values of f(x) can we get out of the function?" From the graph we see we can get any real number greater than 0 out of the function by choosing a suitable x-value in the domain. The range is therefore .
Continuity: Since the graph is one, unbroken curve (i.e. a curve that can be drawn in one movement without taking your pen off the paper). We see that "roughly speaking" the function is continuous.
Increasing or decreasing behaviour: For all x in the domain, as x increases, f(x) decreases. This means the function exhibits decreasing behaviour.
Symmetry: It is clear to see the graph of f(x) has no symmetry.
Boundedness: Looking at the graph we see it is unbounded above as when we choose negative values, the graph of f(x) explodes upwards exponentially. Choose a value of x, plug it in, next choose (x-1), plug this in and we observe for all x in the domain.
The function is however bounded below by 0: no value of x in the domain exists which satisfies .
Extrema: As far as I can tell, there are no turning points on the curve. (Is this what you mean by extrema?)
Asymptotes: Contrary to the curve's appearance, there are no vertical asymtotes for this curve. The negative-x portion of the curve is just growing so quickly it appears to look like an asymptote. There is a value of f(x) for all x<0. There is however a horizontal asymtote: .
End behaviour: As . As
