Uploads: You must upload your work in the last question on the assessment. Your score is not valid unless all work is uploaded on that question and can be viewed and read by your instructor. Work: Unless a problem says otherwise, you may only use graphing calculators (ie Desmos) to check your answers. All algebraic work and steps must be shown and be consistent with the appropriate readings. Resources: These are the ONLY authorized resources you may use on this assessment: For each equation below, determine if the function is Odd, Even, or Neither. If this is a quiz or exam question, all steps and logic must be shown for full credit. \( f(x)=x^{2}+4 \) Select an answer \( v \) \( g(x)=(x-4)^{2} \) Select an answer \( v \) \( h(x)=\frac{4}{x} \) Select an answer \( v \)
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When determining if functions are odd, even, or neither, a helpful trick is to analyze the behavior of the function when you substitute \(-x\) for \(x\). For a function to be even, \(f(-x) = f(x)\) must hold true. For a function to be odd, \(f(-x) = -f(x)\) should be satisfied. For example, with \(f(x) = x^2 + 4\): \(f(-x) = (-x)^2 + 4 = x^2 + 4\), which equals \(f(x)\) - so it's even! Similarly, for \(g(x) = (x - 4)^2\), you'll find it’s even too. But for \(h(x) = \frac{4}{x}\), \(h(-x) = \frac{4}{-x} = -\frac{4}{x}\), indicating it's odd. Now, isn't that fascinating? If you want to dive deeper into understanding these properties, consider practicing with various functions and their characteristics. Like, what about \(k(x) = x^3 - 2x\)? Find out whether it's odd, even, or neither by applying the substitution method! You'll uncover a treasure trove of mathematical insights just waiting for you!
