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WA 5, p. 4

Name:

College ID:

Thomas Edison State College

College Algebra (MAT-121-GS)

Section no.:

Semester and year:

Written Assignment 5

Answer all assigned exercises, and show all work. An asterisk indicates an exercise for which a graph pool is provided in the assignment submission link.

For the points P and Q , find (a) the distance d ( P,Q ) and (b) the coordinates of the midpoint of the segment PQ . (See section 2 . 1 , Example s 2 and 5(a) .) [ 8 points]

P(–4, 3), Q(2, –5)

(7,83),(57,3)

PQ

--

    • Determine whether the three points are collinear. (See section 2 .1 , Example 4 .) [ 4 points]

    (–1, 4), (–2, –1), (1, 14)

    For the following equation, (a) give a table with at least three ordered pairs that are solutions, and (b) graph the equation.* ( S ee section 2 .1 , Example s 7 and 8. ) [ 8 points]

    2

    2

    yx

    =+

  • 4

    yx

    =-+

    • (a) Find the center-radius form of the equation of the circle, and (b) graph it.* (S ee section 2.2 , Example s 1 and 2. ) [ 8 points]

    • center (0, 0), radius 9

    • center (–3, –2), radius 6

    Decide whether or not the equation has a circle as its graph. If it does, give the center and the radius. If it does not, describe the graph. (S ee section 2.2 , Example s 3–5. ) [ 8 points]

    22

    121025

    xyxy

    +-+=-

    22

    4480

    xyxy

    ++++=

    Decide whether the relation defines a function, and give the domain and range. (S ee section 2.3 , Example s 1–4. ) [ 4 points]

    Let

    ()34

    fxx

    =-+

     and

    2

    ()41

    gxxx

    =-++

     . Find and simplify each of the following. (S ee section 2.3 , Example 6. ) [ 8 points]

  • (3)

    f

    -

    • (32)

    ft

    -

    Use the graph of

    ()

    yfx

    =

     to find each function value: (a)

    (2)

    f

    -

     , (b)

    (0)

    f

     , (c)

    (1)

    f

     , and (d)

    (4).

    f

     (S ee section 2.3 , Example 7(d). ) [ 4 points]

    Determine the intervals of the domain for which the function is (a) increasing, (b) decreasing, and (c) constant. (S ee section 2.3 , Example 9. ) [ 4 points]

    Graph the linear function.* Identify any constant functions. Give the domain and range. ( S ee section 2 . 4 , Example s 1 and 2. ) [ 4 points]

    ()3

    fx

    =

    Find the slope of the line satisfying the given conditions. ( S ee section 2 . 4 , Example 5. ) [ 4 points]

    through

    (5,3)

    -

     and

    (1,7)

    -

    Graph the line passing through the given point and having the indicated slope.* Plot two points on the line. ( S ee section 2 . 4 , Example 7. ) [ 8 points]

    • through

      3

      (2,3),

      4

      m

      --=-

    • through

      9

      ,2

      4

      æö

      ç÷

      èø

      , undefined slope

    Write an equation for the line described. Give answers in standard form. ( S ee section 2 . 5 , Example s 1 and 2. ) [ 12 points]

    through (2, 4),

    1

    m

    =-

    • through

      3

      (4,3),

      4

      m

      -=

    • through

      (5,1),

       undefined slope

    Give the slope and the y -intercept of the line. (See section 2 . 5 , Example 3 .) [ 4 points]

    2316

    xy

    +=

    Write an equation (a) in standard form and (b) in slope-intercept form for the line described. (See section 2 . 5 , Example 6 .) [ 8 points]

    a. through

    (3,2),

    -

    parallel to

    25

    xy

    -=

    b. through

    (4,4),

    -

    perpendicular to

    4

    x

    =

    Determine whether the three points are collinear by using slopes. [ 4 points]

    (0,7), (3,5), (2,15)

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