 Overview of the Student Precalculus Package - Maple Help

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The Student[Precalculus] Package

The Student[Precalculus] package contains routines that can be used to learn and understand precalculus concepts.  This worksheet demonstrates how you can launch the Precalculus tutors. Getting Started

While any command in the package can be referred to using the long form, for example, Student[Precalculus][LineTutor], it is often easier to load the package and then use the short form command names.

 > $\mathrm{restart}$
 > $\mathrm{with}\left(\mathrm{Student}\left[\mathrm{Precalculus}\right]\right):$ The Student[Precalculus] Tutors

The following sections explain the functionality of each of the tutor routines and demonstrate how to launch the interactive tutors. CompositionTutor

The CompositionTutor is an interface that accepts at most two single-variable functions, $f$ and $g$, to compose.

If functions are not specified, defaults are used.
If only one function is specified, a default value of 1 is assigned to the second function.

The tutor computes the result of composing $f$ with $g$, or $g$ with $f$.

Note: The specified functions must be in only one variable.

To launch the tutor routine using the default function values, use:

 > $\mathrm{CompositionTutor}\left(\right)$ To compose a function, for example, $\mathrm{sin}\left(x\right)$, with the constant function 1, use:

 > $\mathrm{CompositionTutor}\left(\mathrm{sin}\left(x\right)\right)$ To compose two functions, for example, $f\left(x\right)=\frac{1}{x}$ and $g\left(x\right)=\mathrm{sin}\left(x\right)$, use:

 > $\mathrm{CompositionTutor}\left(\frac{1}{x},\mathrm{sin}\left(x\right)\right)$ For help using the CompositionTutor, launch the tutor and select Help, then Using this Tutor. FunctionSlopeTutor

The FunctionSlopeTutor is an interface that demonstrates that secant lines close to a point on a function approach the tangent line at that point.

If a function is not specified, a default function and point are used.

If a function is specified but a point is not, a default point is used.

The tutor graphs the specified function, as well as the secant and tangent lines at the specified point.

Note: The specified function must be in only one variable. The point must be specified as a constant or an expression of the form name=constant, where name is the name of the indeterminate that is used in the specified function.

To launch the tutor routine using the default function and point values, use:

 > $\mathrm{FunctionSlopeTutor}\left(\right)$ To examine a specific function, for example, $\mathrm{sin}\left(x\right)$, at the default point, use:

 > $\mathrm{FunctionSlopeTutor}\left(\mathrm{sin}\left(x\right)\right)$ To examine a specific function, for example, $\mathrm{sin}\left(x\right)$, at a specific point, $x=1$, use:

 > $\mathrm{FunctionSlopeTutor}\left(\mathrm{sin}\left(x\right),x=1\right)$ or

 > $\mathrm{FunctionSlopeTutor}\left(\mathrm{sin}\left(x\right),1\right)$ For help using the FunctionSlopeTutor, launch the tutor and select Help, then Using this Tutor. LimitTutor

The LimitTutor is an interface that accepts a single-variable function and a point at which to examine the function value.

If a function and point are not specified, a default function and point are used.
If only a function is specified, the function is examined at a default point.

The tutor computes the limiting value of the specified function, at the specified point.

Note: The specified function must be in only one variable. The point must be specified as a constant or an expression of the form name=constant, where name is the name of the indeterminate that was used in the specified function.

To launch the tutor routine using the default function and point values, use:

 > $\mathrm{LimitTutor}\left(\right)$ To compute the limiting value of a specific function, for example, $\mathrm{sin}\left(x\right)$, at a default point, use:

 > $\mathrm{LimitTutor}\left(\mathrm{sin}\left(x\right)\right)$ To compute the limiting value of a specific function, for example, $\mathrm{sin}\left(x\right)$, at a specific point, $x=1$, use:

 > $\mathrm{LimitTutor}\left(\mathrm{sin}\left(x\right),x=1\right)$ or

 > $\mathrm{LimitTutor}\left(\mathrm{sin}\left(x\right),1\right)$ For help using the LimitTutor, launch the tutor and select Help, then Using this Tutor. LineTutor

The LineTutor is an interface that accepts an equation of a line, plots the line, and provides the various forms of the equation of the line.

If an equation is not specified, a default is used.

The tutor plots the specified line and provides the various forms of its equation.

Note: The equation of a line must be of degree 1.  The specified equation must use the variable names $x$ and $y$.

To launch the tutor routine using a default equation of a line, use:

 > $\mathrm{LineTutor}\left(\right)$ To plot a specific line, for example, $y=x+1$, use:

 > $\mathrm{LineTutor}\left(y=x+1\right)$ For help using the LineTutor, launch the tutor and select Help, then Using this Tutor. LinearInequalitiesTutor

The LinearInequalitiesTutor is an interface that accepts at most six linear inequalities and determines the resulting region.

If inequalities are not specified, defaults are used.

The tutor plots the region corresponding to the constraints defined by the specified linear inequalities.

Note: The inequalities must be of degree 1. The specified inequalities must use the variable names $x$ and $y$.

To launch the tutor routine using default inequalities, use:

 > $\mathrm{LinearInequalitiesTutor}\left(\right)$ To plot the region defined by a single linear inequality, for example, $x, use:

 > $\mathrm{LinearInequalitiesTutor}\left(x To plot the region defined by a set of linear inequalities, for example, $\left\{x, use:

 > $\mathrm{LinearInequalitiesTutor}\left(\left\{x For help using the LinearInequalitiesTutor, launch the tutor and select Help, then Using this Tutor. PolynomialTutor

The PolynomialTutor is an interface that graphs a polynomial.

If a polynomial is not specified, a default is used.

The tutor graphs the specified polynomial.

Note: The specified polynomial must be in only one variable.

To launch the tutor routine using the default polynomial, use:

 > $\mathrm{PolynomialTutor}\left(\right)$ To graph a specific polynomial, for example, $1+{x}^{2}+{x}^{3}$, use:

 > $\mathrm{PolynomialTutor}\left(1+{x}^{2}+{x}^{3}\right)$ For help using the PolynomialTutor, launch the tutor and select Help, then Using this Tutor. RationalFunctionTutor

The RationalFunctionTutor is an interface that graphs a rational polynomial in one variable including any asymptotes.

If a rational polynomial is not specified, a default is used.

The tutor graphs the specified rational polynomial including any asymptotes.

Note: The specified rational polynomial must be in only one variable.

To launch the tutor routine using the default rational function, use:

 > $\mathrm{RationalFunctionTutor}\left(\right)$ To graph a specific rational function, for example, $\frac{1}{x-1}$, use:

 > $\mathrm{RationalFunctionTutor}\left(\frac{1}{x-1}\right)$ For help using the RationalFunctionTutor, launch the tutor and select Help, then Using this Tutor. StandardFunctionsTutor

The StandardFunctionsTutor is an interface that graphs various standard functions.

If you do not specify a function, a default function is used.

The tutor plots the specified function.

To launch the tutor routine using the default function, use:

 > $\mathrm{StandardFunctionsTutor}\left(\right)$ To graph a specific function, for example, $\mathrm{cos}\left(x\right)$, use:

 > $\mathrm{StandardFunctionsTutor}\left(\mathrm{cos}\left(x\right)\right)$ You can also graph transformations of a standard function.  When the tutor is open, enter values for a, b, h and k to view the graphs of $f\left(x\right)$ and .  For example, to see  the graph of  $y=-\mathrm{ln}\left(x\right)+2$, launch the tutor for $\mathrm{ln}\left(x\right)$ and then enter values .

 ${\mathrm{ln}}{}\left({x}\right)$ (2.8.1)

Alternatively, you can launch the tutor directly with the function $-\mathrm{ln}\left(x\right)+2$.

 > $\mathrm{StandardFunctionsTutor}\left(-\mathrm{ln}\left(x\right)+2\right)$
 ${-}{\mathrm{ln}}{}\left({x}\right){+}{2}$ For help using the StandardFunctionsTutor, launch the tutor and select Help, then Using this Tutor.