The parent function f(x) = log3x has been transformed by reflecting it over the x-axis, stretching it vertically by a factor of two and shifting it up three units. which function is representative of this transformation? g(x) = log3(2x) - 3 g(x) =log3(-2x) + 3 g(x) = 2log3(x) - 3 g(x) = -2log3(x) + 3

The transformation from f(x) to g(x) using

g(x)=a*f(x-h)+k

will stretch f(x) by a scale factor of a (>0), translates to the right by h, and translates upwards of k.

Similarly, the transformation from f(x) to g(x) using

g(x)=-a*f(x-h)+k

will stretch f(x) by a scale factor of a (>0) AND reflects over the x-axis, translates to the right by h, and finally translates upwards of k.

For the given problem,

f(x)=log_3(x)

a=-2  (dilates with scale factor of 2, AND with reflection over the x-axis)

h=0 (no horizontal translation)

k=3 (translates UPwards by 3 units)

Put into the above formula,

g(x)=-2f(x)+3=-2log_3(x)+3.

Note: in case you are not familiar with it, _ means subscript, and ^ means superscript, applicable to some text processing software.

step-by-step explanation: so we look at the formula un = a + (n-1)d

un is the amount of seats

n is the nth term aka row number

a is the original sequence/row number

d is the difference between each term

so in this a=22 d=6 and n can remain as n because we are simply formjng a rule

lets put these in the equation

un=22+(n-1)(6)

this is your answer to part a

however

lets double check that this is correct, we'll try putting it into the second term

un=a+(n-1)d

u2=22+(2-1)(6)

u2=22+6

u2=28

as the question said the second row has 28 seats so now we know the formula we made is correct.

as for part b

un=a+(n-1)

its asking us to find a row with 100 seats.

remember un was the amount of seata so all we do is substitute this in.

un=100 a=22 d=6

un=a+(n-1)d

100=22+(n-1)(6)

so now we simplify to find n which is the row number.

100-22=22+(n-1)(6)-22

78=(n-1)(6)

78/6=(n-1)(6)/6

13=n-1

13+1=n-1+1

14=n

so now we know that in the 14th row there is 100 seats.

hope this and that you understood! its my first time using the app or anyone out on here : p its also me to revise so a bunch! ask more questions if you dont understand ☺

easy its decreasing

step-by-step explanation:

because its top point is at the to of the graph on the left side (atleast from the veiw i see it) now if that top point wast in the lower part of the graph it would be increasing hope this have a nice day