Calculus, 8th Edition,stewart; page 33 problem 3

Question

Match each equation with its graph. Explain your choices. (Dont use a computer or graphing calculator.)

(a) y = x^2     (b) y = x^5       (c)  y = x^8

Answer 1

Step:1

(a)

The function is .

The function resembles power function , where  is a positive integer.

Compare the function with power function.

Here , then the function  is a even power function.

It is also a polynomial function of degree .

Graph  resembles the function .

Step:2

(b)

The function is .

Compare the equation with  is a power function.

Where  is a positive integer.

Here  so the function  is an odd power function.

It is also a polynomial function of degree .

Graph  resembles the function .

Step:3

(c)

The function is .

Compare the equation with  is a power function.

Where  is a positive integer.

Here  so the function  is a even power function.

It is also a polynomial function of degree .

Graph  resembles the function .

Solution:

(a) .

(b) .

(c) .