# To classify: The function f ( x ) = log 2 x as one of the type of functions.

### 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 1.2, Problem 1E

(a)

To determine

## To classify: The function f(x)=log2x as one of the type of functions.

Expert Solution

The function f(x)=log2x is a logarithmic function.

### Explanation of Solution

Reason:

The function is of the form f(x)=logbx , where b is a positive constant is said to be a logarithmic function. It is a reciprocal of an exponential function.

(b)

To determine

### To classify: The function g(x)=x4 as one of the type of functions.

Expert Solution

The function g(x)=x4 is a root function.

### Explanation of Solution

Reason:

The function is of the form f(x)=xn , is said to be a root function. Note that the expression inside the root is always positive.

(c)

To determine

### To classify: The function h(x)=2x31−x2 as one of the type of functions.

Expert Solution

The function h(x)=2x31x2 is a rational function.

### Explanation of Solution

Reason:

The 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. Here, p(x)=2x3 and q(x)=1x2 . Thus, the function h(x) is a rational function.

(d)

To determine

### To classify: The function u(t)=1−1.1t+2.54t2 as one of the type of functions.

Expert Solution

The function u(t)=11.1t+2.54t2 is a polynomial function with degree 2.

### Explanation of Solution

Reason:

Rewrite the given function as u(t)=2.54t21.1t+1 .

The polynomial function is of the form p(x)=anxn+an1xn1+...+a1x+a0 , where n is a positive integer and a0,a1,...,an are constants. Thus, the given function is a polynomial function with degree 2. Therefore, the function is a quadratic function.

(e)

To determine

### To classify: The function v(t)=5t as one of the type of functions.

Expert Solution

The function v(t)=5t 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=5 and x=t . Thus, the given function is said to be an exponential function.

(f)

To determine

Expert Solution