Ma 125-109 Spring 2015 CRN-25213
Intro. Problems Carter
1
Lines
If you have questions on these problems watch one or more of the videos below:
http://youtu.be/hDIUM069wfQ
http://youtu.be/0xUf3S0rcJg
http://youtu.be/0xUf3S0rcJg
http://youtu.be/ZZHClsprFUo
1. Determine the equation of the lines that contain the points indicated and
sketch the graphs.
(a)
P = (−5, 3),
Q = (2, −5).
(b)
P = (3, 5),
Q = (7, 14).
(c)
P = (−1, 0),
Q = (0, 5).
P = (3, 14),
Q = (3, 20).
P = (−2, 6),
Q = (5, 6).
(d)
(e)
2. Determine the x and y intercepts, and sketch the graphs of each of the
lines indicated.
(a)
2x + 3y = 6
(b)
3x − 2y = 6
(c)
−2x + 3y = 6
(d)
3x + 2y = −6
1
2
Parabolas
Use the technique of completing the square to sketch the graph of each of the
parabolas. Your graph should contain the location of the vertex, it should either
hold or spill water, and your should indicate the y-intercept and the x-intercepts
if there are any.
See the following videos if you have questions.
http://youtu.be/_GBtlR4m67g
http://youtu.be/YW1MVXyhJZE
http://youtu.be/ZZHClsprFUo
1.
y = x2 + 2x + 5
2.
y = x2 + 5x − 3
3.
y=
1 2
x + 4x − 7
2
4.
y = −3x2 − 5x + 7
2
3
Linear Fractional Transformations
See the video
http://youtu.be/Kg4mIa8_HMc
Sketch the graph of each of the following linear fractional transformations.
Your graph should indicate the vertical asymptote, the horizontal asymptote,
the x and y intercepts (if these exist), and indicate clearly the quadrants with
respect to the asymptotes that the hyperbolas lie within ([first, third] or [second,fourth]). In order to execute these problems always ask if the x-intercept is
to the left of or to the right of the vertical asymptote.
1.
y=
2.
1
x
y=
x−2
x+3
y=
x+3
x−2
y=
2x − 3
x−5
3.
4.
3