Who can do this Algebra Assignment

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WA 3, p. 5

For the points P and Q , find (a) the distance d ( P,Q ) and (b) the coordinates of the midpoint of the segment PQ .

P(–4, 3), Q(2, –5)

Determine whether the three points are collinear.

(–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.*

4

yx

=-+

(a) Find the center-radius form of the equation of the circle, and (b) graph it.*

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.

22

121025

xyxy

+-+=-

Decide whether the relation defines a function, and give the domain and range.

Let

()34

fxx

=-+

 and

2

()41

gxxx

=-++

 . Find and simplify each of the following.

(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

Determine the intervals of the domain for which the function is (a) increasing, (b) decreasing, and (c) constant.

Graph the linear function.* Identify any constant functions. Give the domain and range.

()3

fx

=

Find the slope of the line satisfying the given conditions.

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.

  • 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.

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.

2316

xy

+=

Write an equation (a) in standard form and (b) in slope-intercept form for the line described.

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.

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

---

Refer to graphs A–I to answer the following questions.

  • Which one is the graph of

    yx

    =

    ? On what interval is it increasing?

    • Which one is the graph of

      §

      ¨

      yx

      =

      ? What is the value of y when x = 1.5?

    • Which graphs of functions decrease over part of the domain and increase over the rest of the domain? On what intervals do they increase? decrease?

    For the following piecewise-defined function, find (a)

    (5)

    f

    -

    , (b)

    (1)

    f

    -

    , (c)

    (0)

    f

    , and (d)

    (3)

    f

    .

    2 if 3

    ()

    5 if 3

    xx

    fx

    xx

    -<

    ì

    =

    í

    -³

    î

    Without graphing, determine whether each equation has a graph that is symmetric with respect to the x -axis, the y -axis, the origin, or none of these.

    4

    23

    yx

    =-

    15

    yx

    =+

    Graph the function.*

    32

    yx

    =++

    Let

    2

    ()3

    fxx

    =+

     and

    ()26

    gxx

    =-+

     . Find each of the following.

    ()(5)

    fg

    +-

    ()(3)

    fg

    -

    (5)

    f

    g

    æö

    ç÷

    èø

    For the following function, find (a)

    ()

    fxh

    +

     (b)

    ()()

    fxhfx

    +-

    , and (c)

    ()()

    fxhfx

    h

    +-

     .

    ()411

    fxx

    =+

    Given functions f and g , find (a)

    ()()

    fgx

    o

     and its domain, and (b)

    ()()

    gfx

    o

     , and its domain .

    ()2

    fxx

    =+

     ,

    42

    ()4

    gxxx

    =+-