Math

QuestionDefine a piecewise function for letter weight xx (0<x3.50<x \leq 3.5) and sketch its graph. P(x)=xP(x)=x for all intervals.

Studdy Solution

STEP 1

Assumptions1. The function (x)(x) is a piecewise-defined function of the weight xx of a letter, with 0<x3.50<x \leq3.5. . The function is defined as (x)=x(x) = x for all 0<x3.50<x \leq3.5.

STEP 2

Since the function (x)=x(x) = x is the same for all 0<x.50<x \leq.5, it means that the function is a straight line passing through the origin with a slope of1.

STEP 3

To sketch the graph, we need to plot the points that satisfy the function. Since the function is the same for all 0<x3.50<x \leq3.5, we can select any two points in this interval to plot the graph.

STEP 4

Let's choose two points, say x=1x =1 and x=3.x =3..Substitute these values into the function (x)=x(x) = x to get the corresponding yy values.
For x=1x =1, (1)=1(1) =1 and for x=3.x =3., (3.)=3.(3.) =3..

STEP 5

Now, plot these points on a graph. The point (1,1)(1,1) and the point (3.5,3.5)(3.5,3.5).

STEP 6

Draw a straight line passing through these points. This line is the graph of the function (x)=x(x) = x for 0<x3.50<x \leq3.5.

STEP 7

Since the function is defined only for 0<x3.50<x \leq3.5, we need to indicate this on the graph. We do this by putting a small circle at the point (0,0)(0,0) to show that this point is not included in the graph, and a filled circle at the point (3.5,3.5)(3.5,3.5) to show that this point is included in the graph.
The graph of the function (x)=x(x) = x for 0<x3.50<x \leq3.5 is a straight line passing through the points (1,1)(1,1) and (3.5,3.5)(3.5,3.5), with a small circle at the point (0,0)(0,0) and a filled circle at the point (3.5,3.5)(3.5,3.5).

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