\check

Description

Declares a criterion that a student's response must satisfy in a Sketch question.

This macro must appear within a sketch environment.

Syntax

\check[a,b]{criterion}
a,b option
Endpoints of the interval on which this criterion is to be met.
criterion
A criterion for the student's response.

Available criteria

goes_through(xcoord, ycoord)
The curve must pass through the point (xcoord, ycoord).
increasing
The sketched function must be increasing.
decreasing
The sketched function must be decreasing.
concave_up
The sketched function must be concave up.
concave_down
The sketched function must be concave down.
linear
The sketched function must be linear.

To restrict one of these criteria to an interval [a,b], use \check[a,b]{criterion} (this has no effect for goes_through).

The criterion may also be a boolean expression; useful statements in this case are

slope_at(xval)
Return the slope of the curve at the given x-value.
value(xval)
Return the y-value for the given x-value.
expr1 == expr2
Return true if expr1 is equal to expr2 , false otherwise.
expr1 < expr2
Return true if expr1 is less than expr2 , false otherwise.
expr1 > expr2
Return true if expr1 is greater than expr2 , false otherwise.
true
Boolean constant.
false
Boolean constant.
bool1 && bool2
Return true if bool1 and bool2 both evaluate to true, false otherwise.
bool1 || bool2
Return true if either bool1 or bool2 (or both) evaluates to true, false otherwise.

For instance, value(xcoord) == ycoord is equivalent to goes_through(xcoord, ycoord).

More than one \check statement may appear, in which case every criterion must be satisfied. That is,

\check{criterion1}
\check{criterion2}
\check{criterion3}

is equivalent to

\check{criterion1 && criterion2 && criterion3}