# manipulating a function

• May 2nd 2008, 03:28 PM
stones44
manipulating a function
f(x) = x^2 + x +1. Find the sum of all values of z for which f(3z) = 7

Is it 3x^2 +3x + 1 = 7 so z = 1 and -2....so the answer is -1

also, in general say you have f(x) ....how does the graph change (domain range, intercepts, max, min) if you make it, for example:
f(-2x)
.5f(x)
f(x-2)
f(x)+2
• May 2nd 2008, 11:04 PM
Isomorphism
Quote:

Originally Posted by stones44
f(x) = x^2 + x +1. Find the sum of all values of z for which f(3z) = 7

Is it 3x^2 +3x + 1 = 7 so z = 1 and -2....so the answer is -1
Isomorphism: It is not
3x^2 +3x + 1 = 7 but (3x)^2 + 3x + 1 = 7. So the equation reads 9x^2 + 3x - 6 = 0, which is 3x^2 + x - 2 = 0

also, in general say you have f(x) ....how does the graph change (domain range, intercepts, max, min) if you make it, for example:
f(-2x)
.5f(x)
f(x-2)
f(x)+2

Do you know what domain, range, intercepts, max,min means. If you know co-ordinate geometry, then express the quadratic as a parabola standard form. This will help you answer all questions easily.
• May 3rd 2008, 09:06 AM
stones44
thanks for the first part

but i am confused..why a quadratic....the function doesnt matter i just wanna know how manipulating inside and outside the perenticies with different operations affects the graph in the form of domain range, min, max and both intercepts
• May 4th 2008, 06:51 AM
stones44
someone please help with the 2nd part...how does each manipulation affect the parts of the equation on a graph? (int. min max, etc.)