Describe the transformations required to obtain the graph of the function f(x) from the graph of the function g(x). f(x) = 4 cos x ; g(x) = cos x
select one:
a. vertical stretch by a factor of 4
b. horizontal stretch by a factor of 4
c. vertical shrink by a factor of 1/4
d. horizontal shrink by a factor of 1/4

Option a

Step-by-step explanation:

If the graph of the function  represents the transformations made to the graph of  then, by definition:

If   then the graph is compressed vertically by a factor c.

If   then the graph is stretched vertically by a factor c

If  then the graph is reflected on the x axis.

If the graph is stretched horizontally  by a factor

If the graph is compressed horizontally by a factor

In this problem we have the function and our parent function is

therefore it is true that     so and

Therefore the graph of is stretched vertically by a factor c = 4

The answer is "Vertical stretched by a factor of 4"

(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

step-by-step explanation: