**Category 23 Example 1** - no calculation required

The values can be directly read from the table. The f(x) value for a certain value of x can be read from the corresponding f(x) column. The x value for a certain value of f(x) can be read from the corresponding x column.

**Category 23 Example 2** - no calculation required

It can be observed from the graph that for x = -1, the value of y = 2. Count the number of times the graph intersects the x-axis at y = -2.

**Category 24 Example 2** - no calculation required.

The value of g(4) can be read from the table as -6. The value of f(-6) can be read from the table as 12.

**Category 25 Example 1** - no calculation required

The points where the graph passes through the x-axis or touches the x-axis can be directly read from the graph.

Tip: Passes through = 1 factor. Touches and curves back = 2 identical factors.

**Category 25 Example 2** - no calculation required

Each factor is a distinct zero. Count them.

**Category 25 Example 3** - no calculation required

From the x column read the values where h(x) = 0

Tip: y = 0 at x-intercept.

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