All Questions
Tagged with precalculus functions
13 questions
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Educational resources commonly address slant asymptotes. Why not general polynomial asymptotes?
Back in 2018, I wrote a post about asymptotes of rational functions in which I addressed not only horizontal and slant/oblique asymptotes, but also the general case of "polynomial asymptotes.&...
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Write $y=\sqrt{3+x}$ as the composite of two functions
For the question "Write $y=\sqrt{3+x}$ as the composite of two functions", what if a student gives the answer $f(x)=\sqrt{3+x}$ and $g(x)=x$? This answer would be technically correct but it ...
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What are some examples of great functions that are not too elementary (easy)?
I am teaching precalculus/basic calculus to my class (high schoolers of around 18 years of age), and I'm always searching for nice functions to plot and study (finding the domain, the function's sign, ...
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How can you elicit the $\log x = {\log} \cdot x$ error?
You know the error, when you're watching a student work through an algebraic calculation to solve for a variable trapped in the argument of a function, usually $\log$ or a trig function, and you watch ...
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How to help new students accept function notation
I am struggling to help some of my new precalculus students accept function notation -- something new to them this term. I am looking for strategies to help them adopt this new notation.
Their main ...
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Examples (for beginners) of real functions which are not given by elementary formulae
Question: What are good examples of functions $f: \Bbb R \rightarrow \Bbb R$ (or $f: D \rightarrow \Bbb R$ with $D \subseteq \Bbb R$) which are not just given by "a formula" (or finitely many formulae ...
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How can I make "complex" graphs that combine multiple functions with a software?
Til today I've been using geogebra to sketch functions for my students quizzes or homework. Sometimes I use the ones that I found searching in google, but this takes a lot of time specially because I ...
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Why do we teach even and odd functions?
I've been either a student or an instructor in Precalculus or Calculus 1 at about 6 institutions now, and teaching the definition of even functions (where $f(-x) = f(x)$) and odd functions (where $f(-...
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Functions, Domains, and Ranges in Precalculus
Possibly related, though of a different flavour.
Background
In most of the precalculus texts with which I am familiar, readers/students are given a crash course in set theory, handed the definition ...
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How should I introduce the concept of a function to a precalculus student?
My brother has not taken a math class in $10-15$ years. He is studying for the GRE so I have been teaching him a chapter or two from my precalculus book. So far, he has learned (and excelled at) basic ...
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How to explain the range to students?
I mostly tutor students ranging from beginning algebra to calculus level. I think the explaining the range as "the set of all possible outputs" would not really cut it for someone struggling with math ...
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Explaining the domain of a function to students?
I mostly tutor community college students ranging from beginning algebra to calculus level. There are several ways in which I explain the domain:
"The domain of a function is all the values you can ...
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15
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For purposes of teaching, should constant functions be considered "linear functions"?
I can see arguments both for and against classifying constant functions as linear functions.
Against: "Linear function" means "first-degree polynomial function", and constant functions are not first-...
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