Function f ( x) = 3( x − 5)2 + 9 is transformed as follows.
1. f(x) is shifted 6 units to right to obtain function g(x). What is the equation of g(x) in terms of f(x)?
2. What is the equation of g(x) in terms of x?
3. Then, g(x) is shifted 7 units down to obtain function j( x) . What is the equation of j(x) in terms of
f(x)?
4. What is the equation of j(x) in terms of x?
+130085 f(x) = 3 (x - 5)^2 + 9
1. f(x) is shifted 6 units to right to obtain function g(x). What is the equation of g(x) in terms of f(x)?
g(x) = f(x - 6)
2. What is the equation of g(x) in terms of x?
g(x) = 3 (x - 11)^2 + 9
3. Then, g(x) is shifted 7 units down to obtain function j( x) . What is the equation of j(x) in terms of
f(x)?
j(x) = f(x - 6) - 7
4. What is the equation of j(x) in terms of x?
j(x) = 3 (x - 11)^2 + 2
EDIT to correct a previious omission....
+2446 The steps are not too long-winded luckily. Unfortunately for Cphill, the 3 that precedes the argument is missing from Cphill's answer.
1) As Cphill mentioned, if \(f(x)\) is the original function, then \(f(x-6)\) translates the function 6 units rightward. The instructions specificially request for the answer with an equation of \(g(x)\) in terms of \(f(x)\), \(g(x)=f(x-6)\)
2) In the previous answer, we determined that \(g(x)=f(x-6)\), so we can use this information to solve for the current problem:
| \(g(x)=f(x-6)\\ f(x)=3(x-5)^2+9\) | \(f(x)=3(x-5)^2+9\) |
| \(f(x-6)=3[(x-6)-5]^2+9\) | |
| \(f(x-6)=3(x-11)^2+9\) | |
| \(g(x)=f(x-6)=3(x-11)^2+9\\ g(x)=3(x-11)^2+9\) |
3) If \(g(x)\) is translated 7 units downward to obtain \(j(x)\), then \(g(x)-7=j(x)\). Of course, the question asks for the equation to be in terms of f(x):
| \(j(x)=g(x)-7\) | Now, substitute g(x)=f(x-6). |
| \(j(x)=f(x-6)-7\) | |
4) Find j(x) in terms of x:
| \(j(x)=g(x)-7\) | We have determined previously that \(g(x)=3(x-11)^2+9\), so substitute that in. |
| \(j(x)=[3(x-11)^2+9]-7\) | Now, simplify. There is not much to do. |
| \(j(x)=3(x-11)^2+2\) | |
