Chapter T, Problem 1CDT

FIGURE FOR PROBLEM 1

1. The graph of a function f is given at the left

1. (a) State the value of f(−1)
2. (b) Estimate the value of f(2)
3. (c) For what values of x is f(x) = 2?
4. (d) Estimate the values of x such that f(x) = 0.
5. (e) State the domain and range of f.

To determine

To state: The value of $f\left(-1\right)$.

Answer to Problem 1CDT

The value of $f\left(-1\right)$ is $-2$.

Explanation of Solution

Spot the point $\left(-1,0\right)$ in the negative x-axis in the figure.

To find the value of $f\left(-1\right)$, 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 $f\left(-1\right)$.

From the figure, it is clear that the value of $f\left(-1\right)$ is $-2$.

Thus, the value of $f\left(-1\right)$ is $-2$.

To determine

To estimate: The value of $f\left(2\right)$.

Answer to Problem 1CDT

The value of $f\left(2\right)$ is $2.8$.

Explanation of Solution

Spot the point $\left(2,0\right)$ in the positive x-axis in the figure.

To find the value of $f\left(2\right)$, 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 $f\left(2\right)$.

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

Thus, the value of $f\left(2\right)$ is $2.8$.

To determine

To find: The value of x such that $f\left(x\right)=2$.

Answer to Problem 1CDT

The value of $x$ is $-3$ and $1$ such that $f\left(x\right)=2$.

Explanation of Solution

Spot the point $\left(0,2\right)$ 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 $f\left(x\right)=2$ is for $x=-3$ and $x=1$.

Thus, the value of $x$ is $-3$ and $1$ such that $f\left(x\right)=2$.

To determine

To estimate: The value of x such that $f\left(x\right)=0$.

Answer to Problem 1CDT

The value of $x$ is $-2.5$ and $0.3$ such that $f\left(x\right)=0$.

Explanation of Solution

Spot the point $\left(0,0\right)$ 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 $f\left(x\right)=0$ is for $x=-2.5$ and $x=0.3$.

Thus, the value of $x$ is $-2.5$ and $0.3$ such that $f\left(x\right)=0$.

To determine

To state: The domain and range of the function $f\left(x\right)$.

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 $f\left(x\right)$ is defined on the interval $\left[-3,3\right]$.

Thus, the domain of the function $f\left(x\right)$ is $\left[-3,3\right]$.

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

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

Thus, the range of the function $f\left(x\right)$ is $\left[-2,3\right]$.