3e^2x = G
-3e^2x = G
-3e^-2x = D
1/8e^2x = G
-1/8e^-2x = D
Would that be correct? I just made these examples up in my head.
How can you tell if its growth or decay? I just look at the exponents. If is a negative then its decay? if its positive then its growth?
6 answers
The coefficient (which represents the original amount) can't be negative for growth or decay. Otherwise, you're correct.
Ahh thanks. I see. Hey would you happen to know how to graph log functions? and find the domain and range for them?
Since logs (which are just exponents) will never cause a number to be 0 or negative (you can't raise e, for example, to any exponent that will yield a value of 0 or below) the values of x that DO cause the number to be 0 or less will create an vertical asymptote.
EXAMPLE:
f(x)=log(6x+2)-3
You know that the part in the parenthesis must be greater than 0, so find the value of x that cause it to be 0, and say that the domain is all numbers greater than that value for x.
( DOMAIN: x > -1/3 )
The range is all real numbers, because y could be any positive or negative number (the log part will yield a negative number when there's a number that's less than 1 in the parenthesis and a positive value when the part in the parenthesis is greater than 1).
EXAMPLE:
f(x)=log(6x+2)-3
You know that the part in the parenthesis must be greater than 0, so find the value of x that cause it to be 0, and say that the domain is all numbers greater than that value for x.
( DOMAIN: x > -1/3 )
The range is all real numbers, because y could be any positive or negative number (the log part will yield a negative number when there's a number that's less than 1 in the parenthesis and a positive value when the part in the parenthesis is greater than 1).
By the way, at the vertical asymptote where x = -1/3, the value for y gets infinitely negative as you get closer and closer to that line (since the values in the parenthesis are getting smaller and smaller as you approach the minimum value for x, -1/3). Remember that it's FRACTIONS that cause logs to be negative (like getting from 2 to 1/2 requires an exponent [or log] of -1 and 2 to 1/4 requires an exponent [log] of -2). LOGS ARE EXPONENTS! Are you getting it now?
I remember my teacher saying that the Domain and Range are opposite, which did that apply to?
There's a constraint in the Domain with logarithms where the variable is in the parenthesis (which must be greater than 0). The Range is all reals with logarithms when the variable is in the parenthesis.
There's a constraint in the Range when the variable is in the exponent (the output will always be greater than 0). The Domain is all reals when the variable is the exponent.
There's a constraint in the Range when the variable is in the exponent (the output will always be greater than 0). The Domain is all reals when the variable is the exponent.