Inequality regions

In a nutshell

Shading graphs can help to identify regions on a curve or curves which satisfy given inequalities. 

Shading regions

Shaded regions on a graph can be used to identify values which satisfy an inequality. Moreover, the curve being a solid or dotted line can be used to identify whether or not the curve of the function is included in the shaded region.

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Example 1

A function is given by $$f(x)=0.5x^2$$. Sketch the function and shade in the area which satisfies the inequality $$y \gt f(x)$$.

Sketch the function. 

Note: As the curve is not included in the inequality, the curve is sketched with a dotted line.

Example 2

Sketch and shade the region which satisfies the inequalities $$y \le 2x$$ and $$y \gt x^2-9x+18$$. 

For the quadratic, the $$\gt$$​ symbol means that the curve isn't included in the shaded region, so sketch it with a dotted line.

For $$y\leq 2x$$​, the $$\leq$$​ symbol means that the line is included in the shaded region, so sketch it with a solid line.

Shade the area above the quadratic and below the linear curve:

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