Chapter 1.2, Problem 4E

(a)

To determine

To match: The equation $y=3x$ with its graphs without using a computer or graphing calculator.

Answer to Problem 4E

The equation $y=3x$ matches with the graph G.

Explanation of Solution

The equation $y=3x$ is in the form of $y=mx$ that represents the equation of straight line.

Here, the slope $\left(m\right)$ of the straight line is 3 and the y-intercept is 0.

Thus, the graph with slope $m=3$ and y-intercept is 0 is shown in Figure 1.

From Figure 1, it can be concluded that the graph of the equation $y=3x$ matches with the graph G.

(b)

To determine

To match: The equation $y=3^x$ with its graphs without using a computer or graphing calculator.

Answer to Problem 4E

The equation $y=3^x$ matches with the graph f.

Explanation of Solution

The equation $y=3^x$ represents an exponential function passing through the point $\left(0,1\right)$.

Even for the null value of $x$, the value of y remains 1, so the graph of the equation $y=3^x$ will be on the positive half of y-axis.

Thus, the graph of the equation $y=3^x$ is shown in Figure 2.

From Figure 2, it can be concluded that the graph of the equation $y=3^x$ matches with the graph f.

(c)

To determine

To match: The equation $y=x^3$ with its graphs without using a computer or graphing calculator.

Answer to Problem 4E

The equation $y=x^3$ matches with the graph F.

Explanation of Solution

The equation $y=x^3$ represents a polynomial function that is cubic in nature.

For the null value of $x$, the value of $y$ is zero, so the graph of the equation passes through the origin $\left(0,0\right)$.

Thus, the graph of a polynomial function with three roots is shown in Figure 3.

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

(d)

To determine

To match: The equation $y=\sqrt[3]{x}$ with its graphs without using a computer or graphing calculator.

Answer to Problem 4E

The equation $y=\sqrt[3]{x}$ matches with the graph g.

Explanation of Solution

The equation $y=\sqrt[3]{x}$ represents a polynomial function with power value of $\frac{1}{3}$.

The graph of a polynomial equation with power $\left(\frac{1}{3}\right)$ is shown in Figure 4.

From Figure 4, it can be concluded that the graph of the equation $y=\sqrt[3]{x}$ matches with the graph g.