Which of the following describes the function -x3+5?

[tex]Which of the following describes the function -x3+5?[/tex]

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Which of the following describes the function -x3+5?

[tex]Which of the following describes the function -x3+5?[/tex]

Answer with explanation:

Graph Drawn by Pauley

When Pauley graph the change in temperature of a glass of hot tea over time. He sees that the function appears to decrease quickly at first, then decrease more slowly as time passes.

Suppose , Change in Temperature = X - Axis

Time =Y-Axis

Since, Rate of Decrease or Increase is not Constant throughout.That is if you will try to find out the slope at any point on the curve, it will not be same.So, it can't be a Linear function.

Also, Linear function is either Increasing or Decreasing.

Option D:

It is nonlinear because linear functions increase or decrease at the same rate.

A is the correct answer

Answer with explanation:

Graph drawn by Pauley ,for the change in temperature of hot tea:

→Function Decreases Quickly first, and then decreases more slowly as time passes

If the equation of the function has been linear, there must have been constant rate of decrease of temperature.

Here,when we compose the function,that is , f(x)=y, where,[tex]x=t,t_{1},t_{2},t_{3},...[/tex]

that is , y(temperature), decreases,when time increases.

Suppose this function is linear,represented as

→ y=k x, where k is the slope of line , a fixed real umber, it shows that,y and x are directly proportional to each other,that is when time increases ,temperature increases or vice versa.

→But , here the situation is different,that is with increase in one variable(time),other variable (temperature), decreases .

So,we can conclude that, the given function can't be linear.

Option D: It is nonlinear because linear functions increase or decrease at the same rate. is description about the situation Described.

Answer :- It is nonlinear because linear functions increase or decrease at the same rate.

Explanation:-

Given: Pauley graphs the change in temperature of a glass of hot tea over time.

The function appears to decrease quickly at first, then decrease more slowly as time passes.

But a linear function has a constant rate of change i.e.it increase or decrease at the same rate.

Thus the function appears is not linear as it was first decreased fastly and then slowly.

Thus fourth option is the correct option.

It is nonlinear because linear functions increase or decrease at the same rate.

Step-by-step explanation:

A linear function is a function with a constant rate of change. This means it increases or decreases at the same rate.

Since this function decreases quickly and then more slowly, it does not have a constant rate of change; it is not linear.

A is the correct answer

"It is nonlinear because linear functions increase or decrease at the same rate."

Step-by-step explanation:

Linear function decrease/increase at a constant rate.

If we need variables increase/decrease, then we choose a non-linear function.

According to Pauley, the function [temperature] decreases at a higher rate at first and then decreases at a lower rate eventually. So there is change in rate. So, we can describe this graph as non-linear. Because linear functions increase or decrease at the same rate, which here is non-applicable.

Thus, the 4th option is right, "It is nonlinear because linear functions increase or decrease at the same rate."

It is nonlinear because linear functions increase or decrease at the same rate.

Step-by-step explanation:

Because the water's temperature is continuously decreasing, the graphed line would curve downwards, then slowly straighten out horizontally, as the water reaches an official stop in temperature change.

Based from the graph, I think the answer is D. a piece-wise function with separate pieces of linear and step-functions. This is because as you can see from the graph, for intervals [0,1], [5,6], and [10,11] the function is linear. On the other hand, for the remaining intervals, it has a constant value which can be described as a step function.

D

Step-by-step explanation: