Suppose that the function g is defined, for all real numbers, as follows.

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Explanation:

The piecewise function g(x) is defined based on what the input is.

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In the case of g(-1), we have x = -1 which makes true.

So we'll use the second piece

g(x) = -(x-1)^2+3

g(-1) = -(-1-1)^2+3

g(-1) = -(-2)^2+3

g(-1) = -4+3

g(-1) = -1

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For g(1), we have x = 1 which makes true

We'll use the third piece

g(x) = (-1/2)x-1

g(1) = (-1/2)*1 - 1

g(1) = -1/2 - 1

g(1) = -1/2 - 2/2

g(1) = -3/2

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For g(5), we have x = 5 which makes true

g(x) = (-1/2)x-1

g(5) = (-1/2)*5-1

g(5) = -5/2 - 1

g(5) = -5/2 - 2/2

g(5) = -7/2

(x3 + 6x2 + 2x - 6) • (x - 1)

step-by-step explanation:

polynomial long division :

3.2     polynomial long division

dividing :   x4+5x3-4x2-8x+6

                              ("dividend")

by         :     x-1     ("divisor")

dividend     x4   +   5x3   -   4x2   -   8x   +   6

- divisor   * x3     x4   -   x3            

remainder         6x3   -   4x2   -   8x   +   6

- divisor   * 6x2         6x3   -   6x2        

remainder             2x2   -   8x   +   6

- divisor   * 2x1             2x2   -   2x    

remainder               -   6x   +   6

- divisor   * -6x0               -   6x   +   6

remainder                     0

quotient :   x3+6x2+2x-6   remainder:   0

when rotating a figure 180 degrees, imagine that you are able to take the figure and turn it clockwise or counterclockwise around a center point. to rotate a figure 180 degrees, you will need to apply the rule (x, y) → (-x, -y). start by using a coordinate grid with coordinates for each vertex of the figure. the center point of the coordinate grid is located at (0, 0), which is what you will rotate the figure around. write down the original coordinates of the shape you are going to rotate. then, apply the rule. for example, coordinate (1, 2) becomes (-1, -2). another example would be, coordinate (-4, -2) becoming (4, 2). after you change each original coordinate to the rotated coordinate, you will draw your new figure.

step-by-step explanation: