# Domain and Range Overview

I observed that for the past few years the questions about range and domains from grade 7 to 10 for Metrobank –MTAP –Dep –Ed Math Challenge has been a challenge for almost everyone. In this topic I will illustrate what are these in a way that even not a math person could understand. Getting the solution for each type of equation will be a different discussion. I personally advised to check this topic for future references.

Definition: (Author’s definition)

*Range* – these are the points or point on ordinate in which the graph of an equation passed through.

e.g.: (2,3) the range is 3.

*Domain* – This is the counterpart of range. This speaks about the abscissa of a point or points.

e.g.: (2,3) the domain is 2.

Usually we do not deal with just points. We deal with equations. To better understand the topic. Check the diagram below.

Consider a straight line ( linear equation) but this time, I cut it so it didn’t extend. The range of this line are the points passed by the blue line. The domain are the points where the red line passed through.

Range : Between -3 and 3 inclusive in symbols, [-3,3]

Domain: Between -3 and 3 inclusive in symbols [-2,4]

Worked Problem 1:

Find the range and domain of the graph. The graph extends itself to the right and upward.

Range: From 0 to positive all positive y or [0,+∞)

Domain : From 1 to all positive x or [0,+∞)

Worked Problem 2:

Find the range and domain of the parabolic curve. The curve extends itself.

Range: From -4 and the points on ordinate and upward or [-4,+∞)

Domain: The graph extends itself through all points(all real numbers) on abscissa or (-∞,+∞)

The range and domain discussion for each type of equation from linear function to trigonometric function will be available very soon.

### Dan

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