Thread: 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

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.

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

someone please help with the 2nd part...how does each manipulation affect the parts of the equation on a graph? (int. min max, etc.)