1119
- Run Multiple Choice Generator at
h:\shares\physics
- Run Core Problems by giving the program 174 as your
'course'--enter this when asked for your 3-digit course number.
- Do the 'quizzes' on Exponential Functions: Numbers and
Exponential Functions: Graphs.
- If you miss a problem be sure to click on Comment and
explain what you do and do not understand about the question and the given
solution
http://www.vhcc.edu/dsmith/images/graph_series_1.htm
Give the formula for a polynomial function which passes
through the points (-3, 0), (2, 0) and (5, 0), having a y-intercept of 4.
We can get the points on the x axis from (x+3)(x-2)(x-5).
The y-intercept of (x+3)(x-2)(x-5) is 30 and we want a
y-intercept of 4. So we vertically stretch by factor 4/30 to get
- y = 4/30 (x+3)(x-2)(x-5) = 2/15 (x+3)(x-2)(x-50.
What are the possible shapes of the graph of a degree-4
polynomial?
(x-2)(x-1)(x+1)(x+3)

(x-2)^2(x-1)(x+3)

(x-1)^3(x+3)

(x-1)^4

(x-1)^2(x+3)^2

(x-2)(x+3)(x^2+x+2)

(x-1)^2(x^2+x+2)

Sketch graphs of f(x) = (x - 3) and g(x) = (x+ 2).
- Identify the points on the x axis at which either f(x)
= 0 or g(x) = 0.
- Identify the points on the x axis at which either |
f(x) | = 1 or | g(x) | = 1.
- Identify the interval(s) of the x axis over which |
f(x) | < 0.
- Identify the interval(s) of the x axis over which |
g(x) | < 0.
- Identify the interval(s) of the x axis over which |
f(x) | < 1.
- Identify the interval(s) of the x axis over which |
g(x) | < 1.
- Identify the point(s) of the x axis for which f(x) = -
g(x).
For the functions f(x) and g(x) of the preceding problem
- If f(x) = 0 then what is the value of the function
f(x) + g(x)?
- If g(x) = 0 then what is the value of the function
f(x) + g(x)?
- If f(x) = - g(x) then what is the value of the
function f(x) + g(x)?
- If f(x) < 0 then what is the value of the function
f(x) + g(x)?
- If f(x) > 0 then what is the value of the function
f(x) + g(x)?
- Can you use this information to construct a graph of
f(x) + g(x)?
For the functions f(x) and g(x) of the preceding problem
- If f(x) = 0 then what is the value of the function
f(x) * g(x)?
- If g(x) = 0 then what is the value of the function
f(x) * g(x)?
- If f(x) = 1 then what is the value of the function
f(x) * g(x)?
- If g(x) = 1 then what is the value of the function
f(x) * g(x)?
- If f(x) < 0 then what can we say about the value of
the function f(x) * g(x)?
- If g(x) < 0 then what is the value of the function
f(x) * g(x)?
- If f(x) < 0 and g(x) < 0 then what can we say about
the value of g(x)?
- If f(x) < 0 and g(x) > 0 then what can we say about
the value of g(x)?
- If f(x) > 0 and g(x) < 0 then what can we say about
the value of g(x)?
- If f(x) > 0 and g(x) > 0 then what can we say about
the value of g(x)?
- If | f(x)| = 1 then what is the value of the function
f(x) * g(x)?
- If | g(x)| = 1 then what is the value of the function
f(x) * g(x)?