To answer question 3, let's work step-by-step. Here's the question from the uploaded image:

3. 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?

Let's analyze the graph and address each part:

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

From the graph, find the $y$-coordinate of the point where $x = -1$. Based on the graph,
$f(-1) = 2.$

(b) Estimate the value of $f(1)$.

At $x = 1$, locate the corresponding $y$-value. From the graph,
$f(1) \approx 0.$

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

To find where $f(x) = 1$, locate the $x$-values where the graph crosses $y = 1$. From the graph:
$f(x) = 1 \text{ at } x = -2 \text{ and } x = 2.$

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

To find where $f(x) = 0$, locate the $x$-values where the graph crosses the $x$-axis. From the graph:
$f(x) = 0 \text{ at } x \approx 1.5 \text{ and } x \approx -0.5.$

(e) State the domain and range of $f$.

Domain:

The domain includes all possible $x$-values covered by the graph. From the graph,
$\text{Domain: } [-3, 3].$

Range:

The range includes all possible $y$-values the graph takes. From the graph,
$\text{Range: } [-1, 2].$

(f) On what interval is $f$ increasing?

To determine where $f$ is increasing, find the intervals of $x$ where the graph slopes upwards. From the graph:
$f(x) \text{ is increasing on } [-2, 0].$

Final Answer:

(a) $f(-1) = 2$
(b) $f(1) \approx 0$
(c) $f(x) = 1$ at $x = -2$ and $x = 2$
(d) $f(x) = 0$ at $x \approx 1.5$ and $x \approx -0.5$
(e) Domain: $[-3, 3]$, Range: $[-1, 2]$
(f) $f$ is increasing on $[-2, 0]$.

Would you like a detailed explanation of any step? Let me know!

Here are 5 related questions you might find useful:

1. How do we determine the domain of a function from its graph?
2. What is the difference between an increasing and decreasing interval?
3. How do we find the range of a function graphically?
4. What are other ways to solve $f(x) = 0$ besides graphing?
5. How can we estimate values from a graph more accurately?

Tip: When estimating graph values, always consider the scale of the axes to avoid mistakes.