Use the results of Exercise 48 To guess the
shapes of the graphs of the functions ƒ, g, and h. Then use a
graphing utility to graph each function and compare the result
with your guess.

(a) ƒ(x) = x²(x - 6)²

(b) g(x) = x³(x − 6)²

(c) h(x) = x³(x - 6)³

Data from in Exercise 48

Use a graphing utility to graph the functions ƒ, g, and h in the same viewing window. Write a description of any similarities and differences you observe among the graphs.

Use the result in part (a) to make a conjecture about the graphs of the functions y = x⁷ and y = x⁸. Use a graphing utility to verify your conjecture.

Transcribed Image Text:

Odd powers: f(x) = x, g(x) = x³, h(x) = x² Even powers: f(x) = x², g(x) = x4, h(x) = x6