Question

a)predict th erelationship between the graph of y=x^4+x^3 and the graph of y=[(x+3)^4+(x+3)^3]-1
b)determine the x-intercepts of each function in part aw. round your answer to 1 decimal place
c)give the approximate domain and range of each functin in part a. round your answer to one decimal place

Answer 1

if we rename the two functions f and g, then g(x) = f(x+3) - 1

So, the graphs are identical in shape, but g is shifted two units to the left, and up 1.

So, since f(x) = x^3 (x+1) the zeroes are at 0,-1

Now, if we draw two new axes, and call them v and v, then the zeroes of g are the solutions to u^4 + u^3 - 1. That's a little tougher to solve.

A graphing tool will show the approximate ranges. Domain is, of course, all real numbers.