Your Algebra Homework Can Now Be Easier Than Ever!

OBJECTIVES FOR THE MMPT

G. Functions

Be able to;

• tell whether a given relation is also a function

Ex. Is the relation { (x,y) | x2 + y2 = 4 } a function?

• given a function f(x), evaluate f(a) for some given value ‘a’
Ex.. Evaluate f(-2).
• given a function f(x), simplify the expression :
Ex. Given f (x) = x2 + 2x − 3 , simplify the expression:

• find the domain and the range of a given relation or function

Ex. Determine the domain and the range of { (x,y) | y = x2 − 4 };

• tell whether a function is even, odd or neither;

Ex. Is f(x) = x|x| an even, odd or neither function?

• perform operations with functions ( addition , subtraction, multiplication, division &
composition of functions) stating the domain of definition of the resulting function

Ex. Given and g(x) = x2 + 5, evaluate (f o g)(3) ; Next, determine
(f o g)(x) and its domain;

• find the inverse of a given function

Ex. Find f -1(x) if ;

• Apply rigid &/or non-rigid transformations on the basic functions

to graph related functions,

or given the graph of functions obtained by applying rigid or non-rigid transformations,
determine their equation.

Ex. The graph of f(x) is the same as y = x2 stretched vertically by a scaling
factor of 2, then shifted to the right 3 units and up 2 units. What is the
equation of f (x)?

H. Midpoint, Distance & Equations of Circles

Given the coordinates of two points A & B, be able to:

• determine the coordinates of the midpoint M of the segment

Ex. Given: A(-2,3), B(-6, 9). Determine the coordinates of the midpoint of ;

• determine the distance from A to B

Ex. Given: A(-2,3), B(-6, 9). Determine the distance from A to B;

Be able to:

• find an equation of the circle given its center and radius

Ex. The center of a circle is at C(2,-5) and its radius 6. Find the equation of the
circle.

• given the equation of a circle determine its center and radius

Ex. A circle has for equation: x2 + y2 − 6x + 8y − 75 = 0 . Determine its center
and radius.

solve problems related to midpoint, distance and equations of circles.

I. Linear Functions

Be able to:
• find the slope of the line through two given points
Find the slope of the line through A(2,6) & B(-4,5);

• find the equation of a line given some of its properties or characteristics
Ex. Find an equation of the line with slope 4 and which passes through (2,7);

• determine whether two lines are parallel, perpendicular, or neither
Ex. Are the to lines 3x – 2y = 7 and 2x + 3y = 10 parallel? perpendicular?

• find the equation of a line parallel or perpendicular to a given line
Ex. Find the equation of the line that passes through (0,7) and is perpendicular
to the line whose equation is y = 4x – 5;

• find the coordinates of the point of intersection of two given lines
Ex. y = 2x + 3 and 5y – 2x = 4;

• find the equation and the slope (if any) of vertical or horizontal lines
Ex. Find the equation of the vertical line through (2,6). What is its slope?

• determine the x- & y- intercepts of a line , given it equation.
Ex. Find the x- & y- intercepts of the line 2x – 3y = 12.

J. Quadratic Functions

Be able to:
• determine the coordinates of the x- & y- intercepts of a quadratic function.
Ex. Determine the x- & y- intercepts of the function f (x) = 2x2 − 3x − 5 ;

• express a quadratic function f (x) = ax2 + bx + c in the form: f (x) = a (x − h)2 + k

Ex. Express the function f (x) = 2x2 − 8x + 3 in the form: f (x) = a (x − h)2 + k ;

• determine the concavity of a quadratic function
Ex. Is the graph of the function f (x) = 2x2 − 8x + 3 concave up or down?

• determine the coordinates of the vertex (the max or min) of a quadratic function
Ex. What are the coordinates of the vertex of f (x) = 2x2 − 8x + 3 ?

• determine the maximum or minimum value of a quadratic function
Ex. What is the minimum value of the function f (x) = 2x2 − 8x + 3 ?

• determine the domain and the range of a quadratic function
Ex. Determine the domain and range of the function f (x) = 2x2 − 8x + 3 ;

• apply ones knowledge of the role that the sign of ‘a’, ‘ b2 − 4ac ’, and ‘c’ play in the graph
of the parabola y = ax2 + bx + c , to match the graph of parabolas with such
characteristics.

Ex. Which of the following parabolas has the following characteristics?

a>0, & b2 − 4ac <0?

• match the graph of quadratic functions with their equation.
Ex. Refer to the 4 parabolas drawn above . Which of them could be the graph of
f(x) = −2x2 + 4x − 4 ?
 

Prev Next

Start solving your Algebra Problems in next 5 minutes!

Algebra Helper
Download (and optional CD)

Only $39.99

Click to Buy Now:


OR

2Checkout.com is an authorized reseller
of goods provided by Sofmath

Attention: We are currently running a special promotional offer for Algebra-Answer.com visitors -- if you order Algebra Helper by midnight of July 28th you will pay only $39.99 instead of our regular price of $74.99 -- this is $35 in savings ! In order to take advantage of this offer, you need to order by clicking on one of the buttons on the left, not through our regular order page.

If you order now you will also receive 30 minute live session from tutor.com for a 1$!

You Will Learn Algebra Better - Guaranteed!

Just take a look how incredibly simple Algebra Helper is:

Step 1 : Enter your homework problem in an easy WYSIWYG (What you see is what you get) algebra editor:

Step 2 : Let Algebra Helper solve it:

Step 3 : Ask for an explanation for the steps you don't understand:



Algebra Helper can solve problems in all the following areas:

  • simplification of algebraic expressions (operations with polynomials (simplifying, degree, synthetic division...), exponential expressions, fractions and roots (radicals), absolute values)
  • factoring and expanding expressions
  • finding LCM and GCF
  • (simplifying, rationalizing complex denominators...)
  • solving linear, quadratic and many other equations and inequalities (including basic logarithmic and exponential equations)
  • solving a system of two and three linear equations (including Cramer's rule)
  • graphing curves (lines, parabolas, hyperbolas, circles, ellipses, equation and inequality solutions)
  • graphing general functions
  • operations with functions (composition, inverse, range, domain...)
  • simplifying logarithms
  • basic geometry and trigonometry (similarity, calculating trig functions, right triangle...)
  • arithmetic and other pre-algebra topics (ratios, proportions, measurements...)

ORDER NOW!

Algebra Helper
Download (and optional CD)

Only $39.99

Click to Buy Now:


OR

2Checkout.com is an authorized reseller
of goods provided by Sofmath
Check out our demo!
 
"It really helped me with my homework.  I was stuck on some problems and your software walked me step by step through the process..."
C. Sievert, KY
 
 
Sofmath
19179 Blanco #105-234
San Antonio, TX 78258
Phone: (512) 788-5675
Fax: (512) 519-1805
 

Home   : :   Features   : :   Demo   : :   FAQ   : :   Order

Copyright © 2004-2021, Algebra-Answer.Com.  All rights reserved.