Chapter 1.2, Problem 3E

(a)

To determine

To match: The equation $y=x^2$ with its graph without using a computer or graphing calculator.

Answer to Problem 3E

The equation $y=x^2$ is match with the graph h.

Explanation of Solution

The equation $y=x^2$ represents a polynomial function that is quadratic in nature. For the null value of $x$, the value of $y$ is zero, so the graph of the equation passes through the origin $\left(0,0\right)$ and symmetric about y-axis. Thus, the graph of $y=x^2$ is shown below in Figure 1.

From Figure 1, it can be concluded that the equation $y=x^2$ matches with the graph h.

(b)

To determine

To match: The equation $y=x^5$ with its graph without using a computer or graphing calculator.

Answer to Problem 3E

The equation $y=x^5$ is match with the graph f.

Explanation of Solution

The equation $y=x^5$ represents an odd polynomial function of degree 5. For the null value of $x$, the value of $y$ is zero, so the graph of the equation passes through the origin $\left(0,0\right)$. Since the function is odd, it is symmetric about the origin. Thus, the graph of an odd polynomial function of degree 5 is shown below in Figure 2.

From Figure 2, it can be concluded that the equation $y=x^5$ matches with the graph f.

(c)

To determine

To match: The equation $y=x^8$ with its graph without using a computer or graphing calculator.

Answer to Problem 3E

Solution:

The equation $y=x^8$ is match with the graph g.

Explanation of Solution

The equation $y=x^8$ represents an even polynomial function. For the null value of $x$, the value of $y$ is zero, so the graph of the equation passes through the origin $\left(0,0\right)$. Since the function is even, it is symmetric about y-axis. Thus, the graph of an even polynomial function of degree 8 is shown below in Figure 3.

From Figure 3, it can be concluded that the equation $y=x^8$ matches with the graph g.