# To state: The value of f ( − 1 ) . ### 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 T, Problem 1CDT

(a)

To determine

## To state: The value of f(−1).

Expert Solution

The value of f(1) is 2.

### Explanation of Solution

Spot the point (1,0) in the negative x-axis in the figure.

To find the value of f(1), go down through the straight line x=1 until the graph of the function is reached.

Now the intersecting point of the graph of the function and the line x=1 is the value of f(1).

From the figure, it is clear that the value of f(1) is 2.

Thus, the value of f(1) is 2.

(b)

To determine

### To estimate: The value of f(2).

Expert Solution

The value of f(2) is 2.8.

### Explanation of Solution

Spot the point (2,0) in the positive x-axis in the figure.

To find the value of f(2), go down through the straight line x=2 until the graph of the function is reached.

Now the intersecting point of the graph of the function and the line x=2 is the value of f(2).

From the figure, it is clear that the value of f(2) is 2.8.

Thus, the value of f(2) is 2.8.

(c)

To determine

### To find: The value of x such that f(x)=2.

Expert Solution

The value of x is 3 and 1 such that f(x)=2.

### Explanation of Solution

Spot the point (0,2) in the positive y-axis in the figure.

To find the value of x, go left and right through the straight line y=2 horizontally until the graph of the function is reached.

Now the x-coordinate of the intersecting point of the graph of the function and the line y=2 is the value of the required x.

From the figure, it is clear that the value of f(x)=2 is for x=3 and x=1.

Thus, the value of x is 3 and 1 such that f(x)=2.

(d)

To determine

### To estimate: The value of x such that f(x)=0.

Expert Solution

The value of x is 2.5 and 0.3 such that f(x)=0.

### Explanation of Solution

Spot the point (0,0) in the positive y-axis in the figure.

To find the value of x, go left and right through the straight line y=0 horizontally until the graph of the function is reached.

Now the x-coordinate of the intersecting point of the graph of the function and the line y=0 is the value of the required x.

From the figure, it is clear that the value of f(x)=0 is for x=2.5 and x=0.3.

Thus, the value of x is 2.5 and 0.3 such that f(x)=0.

(e)

To determine

Expert Solution

### Explanation of Solution

The set of all possible values of the independent variables in a function is called the domain of the function.

From the figure, it is clear that the function f(x) is defined on the interval [3,3].

Thus, the domain of the function f(x) is [3,3].

The resulting set of possible values of the dependent variable is called the range.

From the figure, it is clear that the function f(x) is attains its values in the interval [2,3].

Thus, the range of the function f(x) is [2,3].

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