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This is "vertical translation." "k" represents the number of units by which the original graph is shifted up or down. You might try graphing g(x)=f(x)-k for a couple of values of k, such as 1, 2, 3.
I still don't quite understand...........
"If g(x) is obtained by shifting f(x) down by 2 units" this written down mathematically is saying g(x)=f(x)-2
I think the value of k is 2, but I'm not really sure.
Oh, wait I just saw that you put that. Thx
yes exactly but lets be sure :)q
g(x)=f(x)-2 lets see what we are given g(x)= (0.5)^x -k f(x)= (0.5)^x sub these into the main equation : g(x)=f(x)-2 (0.5)^x -k = (0.5)^x - 2 so what is k? or solve for k
what value of k makes this equality true
Do you think you could help me with one more?
The present value of a house is $242,000. The value of the house increases at the rate of 4% per year. A function is shown below: f(x)= 242,000(1.04)^x (The x is an exponent, just in case you didn't know) What does f(x) represent? A) The original value of the house. B) The future value of the house after x years. C) The increase in the value of the house each year. D) The increase in the value of the house after x years. I'm torn between B & D, but I'm leaning towards D.
What do you think?
the future value of hte house after x years
think about 1 year what happens the house will be worth 242,000 + 0.04*242,000 if u factor 242000 u get 242,000(1+0.04)
now for the 2nd year this price of the house is once again increased by 0.04 percent price after 1st year 242,000(1+0.04) price after 2nd year 242,000(1+0.04) + 0.04*(242,000(1+0.04)) factor again 242,000(1+0.04)(1+0.04) simplify 242,000(1+0.04)^2 this way the price after x years must be 242,000(1+0.04)^x
Oh, so the answer is B because it's talking about the future not just a normal increase?
the answer is B and not D because B is talking about the total price of the house currently and D just wants the increase of the house price after x years to get just the increase in price it is 242,000(1+0.04)^x - 242,000
Oh, ok. Thx!!!
I fanned and gave you a medal :D