Exam (elaborations)
MATH 136 Test 3 Topics
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- MATH 2024\\2025
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- MATH 2024\\2025
MATH 136 Test 3 Topics
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MATH 136 Test 3 Topics(3.6) 2 Methods:
Complete the square (be careful if x-squared term doesn't have a 1 coefficient), or
Use vertex formula to find h and k and fill in the blanks. h=-b/2a, k=f(-b/2a) - ANS-Quadratic
Functions to Vertex Form
(3.6) positive a, opens up. Negative a, opens down. Vertex, h=--b/2a. k= f(-b/2a). Axis of
symmetry, x=-b/2a. - ANS-Graphing Quadratic Functions
(3.7) Domain is the intersection of the domains of the 2 original functions. That is, find the
domain of f. Then find the domain of g. Then put them together. - ANS-Domain of sum,
difference, or product of 2 functions
(3.7) Domain is the intersection of the domains of the 2 original functions. Also exclude any
value that makes the denominator function=0.
For f/g: Find the domain of f. Find the domain of g. Find any values that make g=0. Put them all
together. - ANS-Domain of quotient of 2 functions
(3.7) Use one function as the input to the other function. Pay careful attention to which function
comes first and which comes second. The second is the input. - ANS-Composite functions
(3.7) Domain is the intersection of the domain of the inside function and the domain of the
composite.
For f(g(x)): Find the domain of g. Find the domain of the combination, f(g(x)). Put the two
together. - ANS-Domain of Composite Functions
(4.1) Find the zeros (x-intercepts) by setting equation equal to zero and solve. Consider
multiplicity and end behavior or test points to draw graph. - ANS-Graphing polynomials
(4.2) Include every power of x in the dividend. Line up like terms after multiplication step. -
ANS-Long division
(4.2) Include every power of x when writing out coefficients. Number in the box is the opposite
sign as the resulting factor. - ANS-Synthetic division
(4.4) List c=factors of constant. d=factors of highest order coefficient. Find ratio c/d. Test values
with synthetic division. - ANS-Find the zeros of a polynomial
(4.5) Holes exist where the same factor appears in the numerator and denominator. -
ANS-Rational functions - Finding holes
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