7) x + 3 = (x – 5)2 8) x4 = x – 10 9) x3 = 5 – x

Question

Find the number of real solutions to the functions below by graphing.

You may use a graphing calculator and then sketch a graph similar to what the calculator gives you, or you may use an online graphing utility such as www.gcalc.net. (Once you go to the website, be sure to use “GCalc 2 applet” on the right of the page

Answer 1

The independant variable is IMPLIED/UNDERSTOOD to be y = f(x)

y as a function of x. You can then solve it by setting it the equation equal

to zero, that is, the SOLUTIONS, are where the graph of the function

crosses the x-axis

7) x+3 = (x-5)^2

x+3 = x^2 - 10x + 25

0 = x^2 - 11x - 22 = f(x)

x = 12.728, x=-1.728

8) x^4 - x + 10 = 0 has no real solutions; so all four solutions are imaginary/comples

9) x^3 + x - 5 = 0

x = 1.516

so two of the solutions are imaginary/complex