What transformation has changed the parent function f(x) = log2x to its new appearance shown in the graph below?

logarithmic graph passing through point 2, negative 2.

−2 • f(x)
2 • f(x)
f(x) − 2
f(x) + 2

First Option

−2 • f(x)

Step-by-step explanation:

The function passes through point (2,1) since the exponential function when .

Then, if the transformed function passes through the point (2, -2) then this means that f(x) was multiplied by a factor of -2. So if an ordered pair belonged to f(x), then belongs to the transformed function. Therefore, if passed through point (2, 1) then the transformed function passes through point (2, -2)

The transformation that multiplies to f(x) by a factor of -2 is:

and the transformed function is:

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

lockers 1, 4, 9, 16, 25, 40, and 49 are open

i ran through it by the other answer is wrong