Q7. For the following graph of f(x), find:

• (a) Domain

• (b) Range

• (c) Interval(s) where increasing

• (d) f(0)

• (e) The value(s) of x for which f(x) = -1

Background

Topic: Function Analysis and Graph Interpretation

This question tests your ability to interpret a graph of a function and extract important information such as domain, range, intervals of increase/decrease, and specific function values.

Key Terms:

• Domain: The set of all possible input values (x-values) for which the function is defined.

• Range: The set of all possible output values (y-values) the function can take.

• Increasing Interval: Where the function's output increases as x increases.

• f(0): The value of the function when x = 0.

• f(x) = -1: The x-value(s) where the function's output is -1.

Step-by-Step Guidance

1. Examine the graph to determine the domain. Look for the leftmost and rightmost x-values where the function exists. Pay attention to any endpoints or open circles.

2. Identify the range by observing the lowest and highest y-values the function attains. Check for any gaps or endpoints.

3. Find the interval(s) where the function is increasing. Trace the graph from left to right and note where the y-values are rising as x increases.

4. To find f(0), locate x = 0 on the graph and read the corresponding y-value.

5. For f(x) = -1, look for the point(s) on the graph where the y-value is -1 and record the corresponding x-value(s).

Try solving on your own before revealing the answer!