Function¶

Answer type: numfunc

The student types a function expression. It is graded by evaluating both their answer and the correct one at sample points across a domain, so any equivalent form passes.

This is a typed answer, not a graphing input

Earlier versions of this page described the Function type as "graph drawing". It is not — the student types a formula. For a student-drawn graph, see Drawing.

The minimum¶

Common Control:

$answer = "x^2 - 4"
$variables = "x"

Options¶

Variable	Effect
`$answer`	the correct function — required
`$variables`	the variable names the expression may use
`$domain`	the interval sampled during comparison
`$abstolerance` / `$reltolerance`	tolerance at each sample point
`$requiretimes`	format restriction: comma-separated pairs of a symbol and a count rule, e.g. `"(,=0"` (no parentheses) or `"*,>=1"`; a correct function that breaks the rule scores 0
`$partialcredit`	alternative answers worth partial credit, as answer/credit pairs: `array("3x-6", .5)` or `"3x-6,.5"` (ignored for `list` answers)
`$answerformat`	accepted-format flags
`$formatfeedbackon`	when set, a correct function rejected only by `$requiretimes` or the `sameform` format is flagged as "right answer, wrong format" (it still scores 0)
`$ansprompt`, `$answerboxsize`, `$hidepreview`	input box

`$variables`¶

Declare every variable the answer may contain. A multivariable answer lists them all:

$variables = "x,y"

`$domain`¶

The interval over which the two functions are compared; the default is -10,10. Test points where your $answer is undefined are skipped, so sqrt(x) or ln(x) on the default window does not by itself mark a correct answer wrong. The risk runs the other way: when your $answer is defined where a student's equivalent form is not, those points count against the student — on the default window $answer = "ln(x^2)" marks 2ln(x) wrong, and $answer = "x" marks sqrt(x)^2 wrong. Set $domain to the interval the question is about whenever an equivalent form could be undefined somewhere in the default window.

$answer = "ln(x)"
$variables = "x"
$domain = "0.1,10"

Example¶

Common Control — setup:

$a = nonzerorand(-5, 5)
$h = nonzerorand(-4, 4)
$fn = "$a*(x - $h)^2"

Question Text:

<p>Write the parabola with vertex `($h, 0)` and leading coefficient `$a`.</p>

Common Control, continued — answer and options:

$answer = $fn
$variables = "x"
$domain = "-10,10"
$ansprompt = "f(x) = "