1129
Identify points for quadratic and linear function.
Construct the product.
The result looks consistent with a degree-3 polynomial.
(m x + k) ( a x^2 + b x + c) is degree 3.
Degree 3 factors into (x - x1) * ( irreducible quadratic) or
into (x - z1) ( x - z3) ( x - z3).
The former is the case here.
We could get the equations of the linear and quadratic if we
knew the x scale. We can impose any x scale.
Exponential * linear ...
Dividing by small numbers: stacks of thin f(x) blocks.
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)?