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: Graphs of Functions

This question tests your ability to interpret a function's graph and determine its domain, range, intervals of increase, and specific function values.

Key Terms:

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

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

• 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 graph exists. Pay attention to any endpoints or open circles.

2. Identify the range by observing the lowest and highest y-values the graph 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 rise as x increases.

4. Locate the point where x = 0 and read the corresponding y-value to find f(0).

Try solving on your own before revealing the answer!