Prof. G. Battaly, Westchester Community College, NY
Step by Step Instructions
|Evaluate Functions||1. Replace the independent variable, x, with place holders.
2. Insert value or variable or function in the placeholder.
3. Complete the algebraic evaluation.
eg: G: f(x) = 3x - 1 F: f(2), f(a+1)
f( ) = 3 ( ) -1
f(2) = 3(2) - 1 = 5
f(a+1) = 3(a+1) - 1 = 3a + 3 - 1 = 3a +2
|Solving Rational Eq.||1. Find LCD (factor if necessary)
2. Is check required? MUST check if LCD contains a variable.
3. Use Multiplication Property of Equality to multiply all terms by the LCD.
4. Simplify using distributive property or combining like terms, etc.
5. Solve the equation.
6. Check if MUST. If checks correctly, then step 5 solution is the answer.
If does not check correctly, then there is no solution.
||1. Determine degree n, and leading cooeficient, an of
2. Overview sketch: a) end behavior, b) max # zeros, c) max # extrema
3. Find zeros.
4. Set up table of intervals using the zeros as endpoints and selecting
convenient values of x within the intervals.
5. Find the corresponding y values or each x selected above,
and enter the y value and the ordered pair (x,y) into the table.
6. Plot the known points, including the zeros.
7. Use your overview, together with the plotted points to complete an
estimated sketch. Note that we do not know the exact locations of
extrema, only approximations.
1. Determine c.
Exact Values of Trig Functions
of Special Angles
1. Sketch the x-y coordinate system.
2. Draw the given angle.
a) Use the quadrantal angles as reference:
π / 2 = 90° π = 180° 3π / 2 = 270° 2π = 360°
b) Determine the location of the terminal ray.
3. Drop a perpendicular to form the right triange.
4. Label the sides and hypotenuse.
a) For the magnitude, use measures associated with the special triangle.
in degrees: sin 30° = 1/2 tan 45° = 1
in radians: sin π/6 = 1/2 tan π/4 = 1
b) For each side use the sign appropriate for the quadrant.
The radius is always positive.
5. Determine the trig function, using the appropriate ratio of definition.
Symmetry Axis Point Graph
|On-Line Math||Symmetry Transformations|
|Analyze Math||Unit Circle Special Angles|
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By Prof. Battaly