Question

Given the function f(x)=x^3+2x^2-3x-5, what is the resulting function when f(x) is shifted to the right 1 unit?

Answer 1

'Shifting to the right one unit' means 'subtracting 1 from x'.
f(x) becomes (x-1)^3 + 2(x-1)^2 - 3(x-1) - 5
After multiplying out and simplifying, f(x) becomes x^3 - x^2 - 4x - 1

Answer 2

can you help me with a coupe more please??

Answer 3

calculate the average rate of change for the function f(x)= -x^4+4x^3-2x^2+x+1, from x=0 to x=1

Answer 4

I think I'm right about how to do this question. Have you done derivatives yet? Rate of change sounds like a derivative question but I think you can just calculate the slope of line made by those two points instead.

f(0) = 1 (At x=0 the function is 1). I got this be substituting 0 for all the x's.
So (0,1) is your first point.
At x=1 the function is -4+4-2+1+1 = 0
So (1,0) is your second point.
slope = (0-1) / (1-0) = -1
So the average rate of change for the function between x = 0 and x = 1 is -1