BuyFind

Single Variable Calculus: Concepts...

4th Edition
James Stewart
Publisher: Cengage Learning
ISBN: 9781337687805
BuyFind

Single Variable Calculus: Concepts...

4th Edition
James Stewart
Publisher: Cengage Learning
ISBN: 9781337687805

Solutions

Chapter 1.2, Problem 4E

(a)

To determine

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

Expert Solution

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 (m) 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.

Single Variable Calculus: Concepts and Contexts, Enhanced Edition, Chapter 1.2, Problem 4E , additional homework tip  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=3x with its graphs without using a computer or graphing calculator.

Expert Solution

Answer to Problem 4E

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

Explanation of Solution

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

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

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

Single Variable Calculus: Concepts and Contexts, Enhanced Edition, Chapter 1.2, Problem 4E , additional homework tip  2

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

(c)

To determine

To match: The equation y=x3 with its graphs without using a computer or graphing calculator.

Expert Solution

Answer to Problem 4E

The equation y=x3 matches with the graph F.

Explanation of Solution

The equation y=x3 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 (0,0).

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

Single Variable Calculus: Concepts and Contexts, Enhanced Edition, Chapter 1.2, Problem 4E , additional homework tip  3

From Figure 3, it can be concluded that the graph of the equation y=x3 matches with the graph F.

(d)

To determine

To match: The equation y=x3 with its graphs without using a computer or graphing calculator.

Expert Solution

Answer to Problem 4E

The equation y=x3 matches with the graph g.

Explanation of Solution

The equation y=x3 represents a polynomial function with power value of 13.

The graph of a polynomial equation with power (13) is shown in Figure 4.

Single Variable Calculus: Concepts and Contexts, Enhanced Edition, Chapter 1.2, Problem 4E , additional homework tip  4

From Figure 4, it can be concluded that the graph of the equation y=x3 matches with the graph g.

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