find the fixed point of the rule y=.75x-10. explain what the orbits generated by this rule would look like

Question

thanks so much! please show work. also i dont know what a fixed point is

Answer 1

A fixed point of y=f(x) is a point c such that y = f(c) = c (that is you pick a value of x, say x=c, plug in c, and the function produces c as output).

y = 0.75x - 10 --> at the fixed point c: c = 0.75c - 10 ---> 0.25c = -10 ---> c = -40

Check: y = 0.75(-40) - 10 = -30 - 10 = -40 (ok, plugging in x = -40 generates y = -40 out)