Grade 9 Math | Domain and Range of Function First Term (Term 1) Week 3 Revised K to 10 Curriculum

The video begins by defining the domain as the set of all input values or x-values for which a function is defined, and the range as the set of all output values or y-values that the function can produce. It clarifies that domain corresponds to x and range to y, establishing this fundamental concept for understanding functions.

Domain and range can be determined from different representations: ordered pairs, equations, graphs, and table of values. The video emphasizes the use of set builder notation for writing the domain and range of a function, explaining how to read and interpret this notation.

This section demonstrates how to find the domain and range when a function is given as a set of ordered pairs. It explains how to list x-values for the domain and y-values for the range, and then convert these lists into set-builder notation, arranging values in increasing order. The discussion highlights that for ordered pairs, the domain and range are finite and measurable.

The video delves into determining domain and range from equations, starting with simple linear equations like y = x + 5 where both the domain and range are all real numbers. It then progresses to equations involving x² + y - 6 = 0, explaining how to rewrite the equation in terms of y to find the domain and in terms of x to find the range. Restrictions due to square roots (negative radicants are not allowed) are introduced, illustrating how they impact the range.

This part continues with more complex equations. For y = √x + 2, the domain is restricted by the non-negative nature of the radicand, leading to x ≥ -2, and the range is y ≥ 0. For y = |x|, the domain covers all real numbers, but the range is restricted to y ≥ 0 due to the absolute value always yielding a positive result.

The tutorial addresses fractional equations, such as y = 2 / (x - 5). It emphasizes that the denominator cannot be zero, setting a restriction for the domain (x ≠ 5). To find the range, the equation is rewritten in terms of x, leading to a similar restriction for y (y ≠ 0).

For y = (3x + 1) / (x - 2), the domain is all real numbers except x = 2. The process to determine the range involves cross-multiplication, rearranging the equation to solve for x, and identifying the restriction that y cannot be equal to 3.

This section explains how to determine domain and range from various graphs, including lines and parabolas. It teaches viewers to examine the x-axis for domain and the y-axis for range, paying close attention to endpoints (shaded vs. open circles) to correctly apply 'less than or equal to' or 'less than' in set-builder notation. Multiple examples with different graph types are provided.

The video simplifies finding domain and range from a table of values. It explains that for a table, the domain and range are finite and can be directly read from the x-values and y-values, respectively. The smallest and largest values are then used to construct the set-builder notation.

The lesson concludes with activities to test understanding, covering ordered pairs, equations, graphs, and tables. Viewers are encouraged to pause the video and answer, with solutions provided afterwards. A 'Math Sign Language' self-assessment scale is introduced (Mastered, Almost There, Trying Hard, Haven't Got It) to help students gauge their comprehension. Final formative assessment questions are given for viewers to answer in the comments.