Mat 117 Fall 2011 Instructor: Dr. Firoz September 28, 2011

MAT 117

  1. Factor the following:

a)Answer:

b)Answer:

c)Answer:

d)Answer:

e)Answer:

f)Answer:

g)Answer:

h)Answer:

i)Answer:

j)Answer:

  1. Use synthetic division to find remainder and quotient, also decide if you have found factor:

a)Divide by

b)Divide by

c)Divide by

d)Divide by

Answers: R: Remainder, and Q: Quotient

a), , is NOT a factor

b), , is NOT a factor

c), , is a factor

d), , is NOT a factor

  1. Consider the quadratic equation , having vertex at and . The zeros are found at . The line of symmetry is at , the y intercept is at . If the graph opens upward showing vertex a minimum and if the graph opens downward showing vertex a maximum

Find vertex, intercepts, axis of symmetry and all zeros, determine if vertex is max or min:

a)Answer:

b)Answer:

c)

Answer:

d)

e)

f)

g)

h)

i)

  1. Transformation:
  • The function has k > 0 units upward shift when and k > 0 units downward when .
  • The function has h > 0 units shift to the right when and h > 0 units shift to the left when .
  • The function has reflection along x axis when
  • The function has reflection along y axis when

Stretch (Elongate or expand) and Shrink (Compress or contract)

The following diagram is useful to remember the stretch and shrink of a graph by a known factor c, with the following values. We consider the cases for horizontal stretch () or horizontal shrink () and for vertical stretch () or vertical shrink ().

. /
/ 1 /

Rule on vertical stretch and shrink: The graph of is found by

  • Shrinking vertically the graph of by a factor of when
  • Stretching vertically the graph of by a factor of when

Note: Remember that for , when c is negative we have horizontal reflection or reflection along x-axis.

Rule on horizontal stretch and shrink: The graph of is found by

  • Stretching horizontally the graph of by a factor of 1/ when
  • Shrinking horizontally the graph of by a factor of 1/ when

Note: Remember that for some cases of , when c is negative we have vertical reflection or reflection along y-axis.

Discuss the transformation:

a) compared to

b) compared to

c) compared to

d) compared to , and compare with c)

e) compared to

f) compared to

  1. Determine the quadratic function looking at the graph:

  1. The graph of has vertex at (0, 5) and passes through the point (1, 8). Determine the function.
  1. Identifying polynomial:

a) is a polynomial of degree 2

b) is a polynomial of degree 5

c) is a not polynomial because of negative exponent.

d) is a polynomial of degree 5

e) is a not polynomial because of decimal exponent

  1. How to find a polynomial if zeros are known:

a)A polynomial with zeros 1, -2, and 3 is with leading coefficient 1.

b)A polynomial with zeros 1 of multiplicity 2, -2, and 3 is with leading coefficient -3

c)A polynomial with zeros 1 of multiplicity 2, -2, and 3 is with leading coefficient -3

d)Find a polynomial with a zero 1 of multiplicity 2, a zero of multiplicity 1 and a zero -3 of multiplicity 2, and leading coefficient -2.

  1. End behavior of a polynomial:

a)Discuss the degree and end of

b)Discuss the degree and end of

c)Discuss the degree and end of

d)Discuss the degree and end of

  1. Domain and asymptotes of rational functions:

a)

b)

c)

d)

Class activity: 10/04/2011

  1. Factor completely:
  2. Is a factor of ?
  3. Discuss the domain and end behavior of

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