Consider the line y = x . if the line is dilated by a factor of 2, what is the equation of the resulting line? if the resulting line is translated 3 units up, what is the equation of the resulting line?

Remember, if f(x) is a function, then

1. We can move up or down f(x) adding a constant c to the whole function, that is, f(x)+c is the function f(x) translated c units up if c is positive or c units down if c is negative.

2. We can compress or dilate f(x) multiplying the whole function by a factor c, that is, cf(x) is the function dilated by a factor of c if or cf(x) is he function compress by a factor of c if .

Then, if y=f(x)=x

1. The equation of f(x) dilated by a factor of 2 is

2. The equation of f(x) translated 3 units up is

b. 24 mm

step-by-step explanation:

use the pythagorean theorem.

a^2 + b^2 = c^2

a^2 + 7^2 = 25^2

a^2 + 49 = 625

a^2 = 576

a = 24

answer: b. 24 mm

(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