To give: An example of linear function.

Single Variable Calculus: Concepts...

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

Single Variable Calculus: Concepts...

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

Solutions

Chapter 1, Problem 6RCC

(a)

To determine

To give: An example of linear function.

Expert Solution

Solution:

The function y=x is a linear function.

Explanation of Solution

Reason:

A linear function is of the form f(x)=mx+c,a0, where m is the slop and c is the y-intercept. Thus, the function y=x is said to be linear. The degree of the linear function is always 1.

(b)

To determine

To give: An example of power function.

Expert Solution

Solution:

The function y=x6 is a power function.

Explanation of Solution

Reason:

The power function is of the form f(x)=xn, where n is a positive integer,  the variable x is called as base. Thus, the function y=x6 is said to be a power function.

(c)

To determine

To give: An example of exponential function.

Expert Solution

Solution:

The function y=2x is an exponential function.

Explanation of Solution

Reason:

An exponential function is of the form f(x)=bx, where b is a positive constant and x is an exponent. Here, b=2. Thus, the function y=2x is said to be an exponential function.

(d)

To determine

To give: An example of quadratic function.

Expert Solution

Solution:

The function y=x2(23x) is a quadratic function.

Explanation of Solution

Reason:

Rewrite the given function as y=2x23x.

A quadratic function is of the form f(x)=ax2+bx+c,a0. Thus, the function y=x2(23x) is a quadratic function. A function of degree 2 is a quadratic function.

(e)

To determine

To give: An example of polynomial of degree 5.

Expert Solution

Solution:

The function v(t)=9+2.54t23t3+12t5 is a polynomial function of degree 5.

Explanation of Solution

Reason:

Rewrite the given function as v(t)=12t53t3+2.54t2+9.

The function is of the form p(x)=anxn+an1xn1+...+a1x+a0, where n is a positive integer and a0,a1,...,an are constants is said to be polynomial function. Thus, the function v(t)=9+2.54t23t3+12t5 is said to be a polynomial function. Observe that the maximum degree of v(t) is 5.

(f)

To determine

To give: An example of rational function.

Expert Solution

Solution:

The function y= x 3+x  is a rational function.

Explanation of Solution

Reason:

A function is of the form f(x)=p(x)q(x), where p(x) and q(x) are the polynomials and q(x)0 is said to be a rational function. Thus, the function y=x3+x is said to be rational function.

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