Based on graph, the range of the function \( f(x)=\frac{5 x^{2}+1}{2 x^{2}} \) is \( \left\{y \in \mathbb{R} \left\lvert\, y \neq \frac{5}{2}\right.\right\} \). ACTIVITIES Activity 1. Find the domain and range of the following rational functions. 1. \( f(x)=\frac{6}{x-5} \) 2. \( f(x)=\frac{x}{x^{2}-5 x+6} \) 3. \( f(x)=\frac{x^{3}-1}{x^{2}} \) 4. \( f(x)=\frac{5 x-2}{x} \) 5. \( f(x)=\frac{3 x}{5 x-1} \) Aotivity 2. Find the domain and range of the given graph. 1. 2.
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1. \( f(x) = \frac{6}{x-5} \) - Denominator: \( x-5 = 0 \) implies \( x = 5 \). - Domain: \( x \in \mathbb{R}, x \neq 5 \). 2. \( f(x) = \frac{x}{x^2 - 5x + 6} \) - Denominator: \( x^2 - 5x + 6 = 0 \) factors to \( (x-2)(x-3) = 0 \). - Solutions: \( Show more…
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