Draw at least six different sized rectangles that have an area of 64 square units

Let

x------> the length of the rectangle

y------> the width of the rectangle

we know that

The area of a rectangle is equal to

so

--------> equation 1

let's assume different values of x to get the different values of y

case 1) For x=64 units

substitute in the equation 1

the dimensions of the rectangle are 64 units x 1 unit

see the draw in the attached figure N 1

case 2) For x=32 units

substitute in the equation 1

the dimensions of the rectangle are 32 units x 2 units

see the draw in the attached figure N 2

case 3) For x=16 units  

substitute in the equation 1

the dimensions of the rectangle are 16 units x 4 units

see the draw in the attached figure N 3

case 4) For x=30 units

substitute in the equation 1

the dimensions of the rectangle are 30 units x 2 (2/15) units

see the draw in the attached figure N 4

case 5) For x=40 units

substitute in the equation 1

the dimensions of the rectangle are 40 units x 1.60 units

see the draw in the attached figure N 5

case 6) For x=60 units

substitute in the equation 1

the dimensions of the rectangle are 60 units x 1 (1/15) units

see the draw in the attached figure N 6

answer: on graphs, the open and closed circles, or vertical asymptotes drawn as dashed lines us identify discontinuities.

as before, graphs and tables allow us to estimate at best.

when working with formulas, getting zero in the denominator indicates a point of discontinuity.

when working with piecewise-defined functions, check for discontinuities at the transition points where one piece ends and the next begins.

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