Download MA134 College Algebra

MA134 College Algebra
Study Guide for Test over 3.3-3.5, 4.1-4.5
x1  x2 y1  y2 
,

2 
 2
Formulas to be supplied: M = 
d = ( x2  x1 ) 2  ( y2  y1 ) 2
x
3.3

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3.4
3.5
b  b2  4ac
2a
y  mx  b
m
y2  y1
x2  x1
y  y1  m( x  x1 )
( x  h)2  ( y  k )2  r 2
f ( x )  a ( x  h) 2  k
(b / 2a, f ( b / 2a ))
Use transformations to graph a new function from a basic function. The basic function can be a given graph or
one of the 9 common functions in 3.2. Be able to graph the parent function, state the transformations and graph
the final function tracking 3 key points (page 266-273 Ex. 1, 2, 3, 4, 6, 8).
Be able to write the equation of a function from a given parent function and a list of transformations (page 275
#17, 21, 24)
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Be able to add, subtract, multiply and divide functions and find the resulting domain (page 280 Ex. 1, 2)
Be able to perform composition of functions and find the resulting domain (page 282-283 Ex. 3, 4, 6).
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Determine whether a function is one-to-one from a mapping, a list of ordered pairs or a graph (page 290 #1, 2,
also notes from class).
Be able to verify whether two functions are inverse functions using the definition (page 293, definition and Ex. 4,
5, also notes from class).
Given the graph of a function, be able to graph its inverse (page 295 Ex. 6).
Find the equation of the inverse of a function and its domain and range (page 297 Ex. 7, 8, 9).
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4.1
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4.2
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Be able to use the formula
to find the vertex of a parabola (page 333 Ex. 5).
Be able to find the equation of a parabola given the vertex and another point (page 334 Ex. 6).
Be able to do word problems with maximum and minimum values (page 335-336 Ex. 7, 8, 9).
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Be able to identify a polynomial and state its degree (page 343 Ex. 1)
Be able to graph the function,
, and functions derived from it using transformations (page 346 Ex. 2).
Understand the relationship between real zeros of polynomial functions (see box on page 347).
Be able to find the zeros and corresponding multiplicities of a polynomial function (page 348 Ex. 3).
Be able to find the equation of a polynomial function given the zeros and corresponding multiplicities (page 349
Ex. 4, 5).
Be able to graph a polynomial function by determining the end behavior, finding the x-intercepts (zeros) and
sketching the function. Be sure you can sketch the graph without the aid of a graphing calculator (page 353 Ex. 7)
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4.3
Know that a quadratic function is a function of the form
and that the graph of a quadratic
function is a parabola.
From standard form of a quadratic function,
, be able to state which way the parabola opens,
the vertex and the equation of the axis of symmetry. Be able to find the x-and y-intercepts. Use this information
to graph the parabola (page 329 Ex. 1).
Be able to use the method of completing the square to write the equation of a parabola in standard form (page
331-332 Ex. 3, 4).
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Be able to perform synthetic division of polynomials (page Ex. 5)
4.4 and 4.5
 Practice applying the Remainder and Factor Theorems. See page 367, examples 1 and 2.
 Know that a polynomial cannot have more real number zeros than its degree but the number of real and complex
zeros, counting multiplicities, is the same as the degree. See pages 369 and 383.
 Practice applying the Rational Zeros Theorem.
 Know that complex conjugates occur in pairs. See page 383, Complex Zeros Theorem and example 1.
 Practice finding the zeros of a polynomial, using the method outlined in class. See the in-class quiz.
 Given zeros, find the remaining zeros and write the polynomial as a product of linear factors.
4.6
 Given an equation, practice sketching the equation’s graph by determining the domain, locating the vertical or
horizontal asymptotes, plotting the x- and y-intercepts, and locating any holes. Sketch the graph by locating a few
points “between and beyond” the vertical asymptotes. Remember these graphs can never cross a vertical
asymptote but can cross a horizontal asymptote. Check if a graph crosses the horizontal asymptote by
determining if there are solutions to the equation Rational Function = HA value.
 Recall that you shouldn’t have to rely on your calculator to graph a function, one of many reasons why you were
given the gift of a brain. As suggested, always graph by hand, and then check on your calculator.
 See examples 1, 2, 3, 4, 5a and 5b, 7, 9, 11
 Be able to do word problems.
Problems to do when reviewing. If you need more practice, do some odd exercises from the individual section:
Page 317
49, 51, 53 (On # 49, 51, 53 graph and state the parent function, state the transformations, graph the final function
tracking 3 key points),
55 – 63 odd, 67 – 111 odd
Page 414
1 – 4, #5, 7 (On #5, 7 state which way the parabola opens, the vertex, the equation of the axis of symmetry and find the
x-and y-intercepts, then graph.),
9, 11, 15 (On #9, 11, 15 rewrite the quadratic function in standard form by completing the square, then state the
vertex. You may also want to graph for extra practice),
# 17, 19 (On #17, 19, find the vertex using the formula and state which way the parabola opens.)
21, 25, 29, 37, 39, 41, 43, 48, 48, 49 (There is no need to expand #49 with multiplication.),
54 (On #54 determine the end behavior, state the x-intercepts and sketch the graph.),
55, 65, 71 – 81 odd, 87 – 93 odd, 97bdeg, 99 bdge, 101 – 115 odd, 117 – 127 odd