Chapter 1.1, Problem 1E

The graph of a function f is given.

(a) State the value of f(1).

(b) Estimate the value of f(‒1).

(c) For what values of x is f(x) = 1?

(d) Estimate the value of x such that f(x) = 0.

(e) State the domain and range of f.

(f) On what interval is f increasing?

To determine

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

Answer to Problem 1E

The value of $f\left(1\right)$ is 3.

Explanation of Solution

Given:

Plot the points in the given graph as shown below in Figure 1.

Calculation:

In Figure.1, x-axis represents the values of x, and y-axis represents the values of $f\left(x\right)$.

From Figure 1, it is noticeable that the point (1, 3) is plotted.

Therefore, the value of $f\left(1\right)=3$.

To determine

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

Answer to Problem 1E

The value of $f\left(-1\right)$ is approximately −0.2.

Explanation of Solution

From Figure 1, it is seen that when x = −1 the f(x) is approximately equal to −0.2.

Therefore, the value of $f\left(-1\right)\approx -0.2$.

To determine

The value of x if $f\left(x\right)=1$.

Answer to Problem 1E

If $f\left(x\right)=1$, then the values of x are 0 and 3.

Explanation of Solution

From Figure 1, it is it is noticeable that the points (0, 1) and (3, 1) are plotted.

Therefore, when $f\left(x\right)=1$ the values of $x=0,3$.

To determine

The value of x if $f\left(x\right)=1$.

Answer to Problem 1E

If $f\left(x\right)=1$, then the values of x is approximately −0.8.

Explanation of Solution

It is seen from the Figure 1 that when f(x) = 0, the value of x is approximately −0.8.

Therefore, when $f\left(x\right)=1$ the value of $x\approx -0.8$.

To determine

The domain and range of f.

Answer to Problem 1E

The domain of f is $\left[-2,4\right]$ and range of f is $\left[-1,3\right]$.

Explanation of Solution

Since, the domain of a function is the set of all x values of the graph, the domain is $\left[-2,4\right]$. In the interval notation, it can be written as $-2\le x\le 4$.

Since, the range of a function is the set of all y values of the graph, the range of the function is $\left[-1,3\right]$. In the interval notation, it can be written as −1 ≤ y ≤ 3.

To determine

The increasing interval of f.

Answer to Problem 1E

The increasing interval of f is $\left[-2,1\right]$.

Explanation of Solution

From Figure 1, it is noticeable that the curve is increasing between $x=-2$ and $x=1$.

Therefore, the increasing interval of f is $\left[-2,1\right]$.