Select the correct answer. if f(x) = |x| and g(x) = |x| − 4, which transformation is applied to f(x) to get g(x)? a. a vertical transformation of f(x) four units upward b. a horizontal transformation of f(x) four units to the left c. a horizontal transformation of f(x) four units to the right d. a vertical transformation of f(x) four units downward

D. a vertical transformation of f(x) four units downward

Step-by-step explanation:

f(x) = |x|

In f(x), for every x value you input into x, you get a corresponding y value.

Now look at g(x) = |x| - 4

The part |x| of g(x) gives you the same y-value for each x value as you had in f(x). The part -4, makes each y-value 4 less than it was in f(x). Since every y-value is 4 lower than the corresponding y-value of f(x), the function g(x) is a vertical translation of f(x) four units downward.

Its D

Step-by-step explanation:

The - 4 moves the graph down 4 units.

the value of v.w= -12.

step-by-step explanation:

we are given three vector r,v and w as:

r = < 5, -5, -2> ; v = < 2, -8, -8> ; w = < -2, 6, -5>

we know that r,v and w could also be represented as:

r=5i-5j-2k

v=2i-8j-8k

and w= -2i+6j-5k

where i,j and k are the unit vectors of x,y and z-axis respectively.

also we know that it has the following property:

i.i=1 ; j.j=1; k.k=1

and i.=j.i=i.k=k.i=j.k=k.j=0

i.e. when we multiply two vectors or we find it's dot product we need to only multiply the components of x coordinates with each other; y with each other and z with each other.

hence, v.w= (2i-8j- -2i+6j-5k)

                  = 2×(-2)+(-8)×(6)+(-8)×(-5)

                  = -4-48+40

                  = -12

hence, v.w= -12

mk./km: lm

step-by-step explanation:

,mlmlm

; mk

lk