The parent function y1 = log2 x is transformed to y2 = –2 log2 (x + 4) – 1. Determine the domain and y-intercept for y2 = –2 log2 (x + 4) – 1 symbolically.

Question

ganeshie8 · Answer

to determine domain of a function :
check for what inputs, the function becomes undefined.

ganeshie8 · Answer

another hint-
log(x) is not defined for input values x <= 0

anonymous · Answer

domain would be allreal numbers but how would you find the range?

ganeshie8 · Answer

nopes.
domain must be all numbers that make the thing inside log a +ve quantity

ganeshie8 · Answer

so... 

x+4 > 0

ganeshie8 · Answer

x > -4

this is the domain...
does this help/makes sense ?

anonymous · Answer

yes! thank you! how do you find the range?

ganeshie8 · Answer

is it range we need to find or y-intercept of transformed graph ?

anonymous · Answer

y-intercept sorry

ganeshie8 · Answer

to find y-intercept, put x = 0

ganeshie8 · Answer

y-intercept = –2 log2 (0 + 4) – 1

ganeshie8 · Answer

you can simplify ?

anonymous · Answer

so -5.661?

ganeshie8 · Answer

how ?

anonymous · Answer

thATS WHEN x= 0 right?

ganeshie8 · Answer

-2log2 (4) -1
-2 log2 (2^2) -1
-2*2log2 (2) -1
-4 . 1 - 1
-4-1
= ?

anonymous · Answer

so -5? when i looked at the calculator when x=0 it said -5.661? i dont know

ganeshie8 · Answer

should burn ur calculator then hehe...

ganeshie8 · Answer

jk... we solved it to -5, and it should be integer value, as log simplifies to integer value here. it cannot be a floatingpoint....

anonymous · Answer

so it cannot have a decimal?

ganeshie8 · Answer

thats right!

anonymous · Answer

okay thank you! can you help me with one more question?

ganeshie8 · Answer

sure post it in a new thread.. .il see if i can help.. if not other will :)

anonymous · Answer

okay thanks

ganeshie8 · Answer

np.. yw :D