Questions tagged [functions]
For questions about the teaching of the function concept, function properties, and various types of functions.
71 questions
15 votes
8 answers
1k views
How could a student find where this exponential function 'catches up with' the power function?
Consider the two functions $f(x) = 1000x^{100}$ and $g(x)= 0.0001e^{0.001x}$. Students in my Calculus class "know" (by which I mean: they are supposed to know) that $f(x)$ is a power ...
- 17.8k
2 votes
1 answer
220 views
Is "well-supported" a synonym for "total relation"? "Well-defined" for "single-valued"?
I was reading this answer to a question about injective functions and was caught off guard by the terms "total" and "single valued" describing properties a relation might have. ...
- 8,434
3 votes
1 answer
206 views
Iconic and symbolic representations
My students (grade 7, age 12/13) have learned how to solve equations, I introduced them to the scale model and the learned equivalent transformations in order to solve equations of the type $$ ax+b=cx+...
3 votes
2 answers
563 views
Order of function transformations
Here is a question that arose during class today (taken from: https://madasmaths.com/archive/maths_booklets/standard_topics/various/transformations_of_graphs_exam_questions.pdf) Three geometric ...
- 33
5 votes
3 answers
260 views
Sources of sample data for regressions
I'm looking for sample data to give algebra 2 students to teach about using Desmos to do regressions. Some example data sets folks at my school already have compiled are: Number of Lego pieces vs ...
- 151
2 votes
1 answer
218 views
Define logarithmic function by functional relation [closed]
My son was working the other day with exercises such as: Find all the mappings $f:\mathbb{N}\rightarrow\mathbb{Z}$ verifying $$\forall m,n \in \mathbb{N}, f(m+n)=f(n)+f(m).$$ As another example: Find ...
- 165
5 votes
4 answers
530 views
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.&...
- 13.1k
6 votes
3 answers
1k views
Composite functions
How would you describe the existence of a composite function $f(g(x))$in terms of range of $g$ and domain of $f$ . Does range of $g$ need to be subset of domain of $f$ or is it sufficient if the two ...
- 1,242
4 votes
1 answer
272 views
Why is there variation in the meaning of "Standard form" for a quadratic?
I'm teaching this year out of "Precalculus with limits" by Ron Larson [7th ed], and the following expression appears in the unit introducing polynomial functions: $f(x)=a{(x-h)}^2+k$ He ...
- 539
7 votes
7 answers
2k views
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 ...
- 4,319
1 vote
0 answers
214 views
Manipulative materials to teach functions
I am looking for manipulative materials to teach functions (the concepts including domain, image, etc.) and kind of function (affine, quadratic, exponential logarithmic, polynomial, trigonometric) ...
- 2,652
0 votes
3 answers
215 views
The two paradigms of seeing a functions
When we are first taught functions , we are typically taught of them as maps between real numbers and we taught to think of them mainly as a mapping between elements. It seems intuitive to take this ...
12 votes
14 answers
8k views
Examples of relations that are not functions
When teaching functions, one key aspect of the definition of a function is the fact that each input is assigned exactly one output. I always felt that the "exactly one" part is confusing to ...
- 2,799
5 votes
3 answers
3k views
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, ...
- 805
6 votes
3 answers
514 views
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 ...
- 4,881