# Questions tagged [functions]

For questions about the teaching of the function concept, function properties, and various types of functions.

67 questions
Filter by
Sorted by
Tagged with
186 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
191 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
364 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.&...
• 11.2k
863 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 ...
• 1,153
208 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 ...
• 409
1k 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 ...
• 4,275
190 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) ...
193 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 ...
• 595
6k 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 ...
• 2,699
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
472 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 ...
• 4,845
2k views

### Why do we use functional composition in the order we do?

Function composition means, roughly, taking the output of a function and applying it to the input of another function. If we define an object C to represent this operation, we could say $C(f,g) = f∘g$ ...
• 383
4k views

### Why is there a disconnect in the usage of "domain" between high school and higher mathematics, and where does it come from?

In high school (in the US, at least), it is common to define the domain of a function as the set of real numbers for which the function is well-defined and returns a real result. Then students are ...
• 412
192 views

### What is the most fundamental continuous function in calculus after a constant (totally straight) line?

What would be to teach in most countries and education systems? (Taught before "high education frames", i.e. before doing bachelor of arts in mathematics).
1k views

### Does the way we often introduce the concept of a function make sense?

Here are some ideas and a few questions I've been pondering lately related to the teaching of functions in college algebra and precalculus: Based on my experience, the teaching of functions usually ...
• 561
607 views

### Proportional density function question

Here is a question I gave on an exam last year. Please let me know what you think of the question (eg: if it is a fair question, easy, difficult, etc). A lot of students were upset for questions like ...
• 187
489 views

• 147
815 views

### Why is a translated exponential function considered an exponential function?

I am tutoring a student preparing to take Calculus 1 at a university. This student hasn't taken precalculus for a year, so I have been drilling him on definitions, rules, and theorems from a college ...
440 views

### Students writing $f(x^2+1)$ when they probably mean $f(x)=x^2+1$

Over the past years teaching freshmen calculus I've repeatedly seen students make the following type of error: Suppose they have to express some quantity $y$ as function of $x$, when the relation ...
• 2,039
326 views

• 21.7k