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WINSTONCH [101]
3 years ago
11

what is a linear function and a nonlinear fuction and how can you tell if the ordered pairs go to them

Mathematics
1 answer:
vfiekz [6]3 years ago
4 0

9514 1404 393

Answer:

  • linear: slope between any two points is the same
  • non-linear: slope between two points may differ

Step-by-step explanation:

A function is a linear function if the slope between any two ordered pairs is the same as it is between any other two. That is, the ordered pairs of a linear function will all fall on the same line when they are graphed.

__

A nonlinear function is one that is not linear. That is, its points do not all fall on the same line when graphed. Slopes between different pairs of points may differ.

_____

<em>Detailed Example</em>

If you are given two tables to compare, it is easiest if the x-values (inputs) are separated by a constant amount. For example, x = -2, 0, 2, 4. These all differ by 2. Then the y-values (outputs) of a linear function will all differ by the same quantity. For example, outputs 10, 15, 20, 25 for the above inputs would correspond to a linear function. This one is y = 2.5x +15.

If the output values for that same set of inputs do not have constant differences, then the function is nonlinear. For example, outputs 10, 15, 21, 27 have differences of 5, 6, 7, so correspond to a nonlinear function. This one happens to be y = (x^2 +22x +120)/8.

__

If the input values are not uniformly spaced, then you can check to see if the slope between one pair of points is the same as the slope for the next pair, and so on. The slope formula is ...

  m = (y2 -y1)/(x2 -x1)

For our first table, the first pair of points (-2, 10) and (0, 15) are on a line with slope ...

  m = (15 -10)/(0 -(-2)) = 5/2

Of course, when the calculations are repetitive, it is convenient to use a spreadsheet or calculator to do them. See the attachment for the calculations for this example.

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Step-by-step explanation:

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Step-by-step explanation:

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Suppose a family drives at an average rate of 60 mi/h on their way to visit relatives and then an average rate of 40 mi/h on the
hammer [34]

Answer:

Part A) 2 hours

Part B) d/60 hours

Part C) 48 miles/hour

Step-by-step explanation:

Part A) Let "d" be the distance in miles the family traveled to visit their relatives. How many hours did it take to drive there?

we know that

Let

x ----> the time it take on their way to visit relatives in hours

y ---> the time it take on the way back in hours

we know that

The distance of the way to visit is equal to the distance of the way back

The speed multiplied by the time is equal to the distance

so

60x=40y -----> equation A

y=x+1 -----> equation B

substitute equation B in equation A and solve for x

60x=40(x+1)

60x=40x+40

20x=40

x=2 hours

Find the value of y

y=2+1=3 hours

d=60x

The time it take on their way to visit relatives is 2 hours

The time it take on the way back is 3 hours

Part B) In terms of "d," how many hours did it take to drive there?

we have that

The distance is equal to the speed multiplied by the time

d=60x

Solve for x

x=d/60 hours

Part C) Write and solve an equation to determine the distance the family drove to see their relatives. What was the average rate for the entire trip?

To find the average rate for the whole trip we will need the total distance and the total time

The distance of the way to visit is

d=60x

substitute the value of x

d=60(2)=120 miles

so

The total distance is

120(2)=240 miles

we know that the total time is

2 + 3 =5 hours

The average rate for the complete trip is

240/5=48 miles/hour

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