Maths Help Urgent Please
jhayes
new_hw.docx Sketch by hand the graph of a function that satisfies: (a)
and (b)
. Is the function
continuous at
? Explain.
Sketch by hand the graph of a function that satisfies: (a)
and (b)
and(c)
. Is the function
continuous from the left at
? Is the function
continuous at
from the right? Is the function
continuous at
? Explain.
Sketch by hand the graph of a function that satisfies: (a)
is not defined, (b)
does not exist and (c)
. Is the function
continuous from the left at
? Is the function
continuous at
from the right? Is the function
continuous at
? Explain.
4 (a) Use the Intermediate Value Theorem to show that if part of the graph of a polynomial function is located below the
-axis and above the
-axis, then it must intersect the
-axis at some number
. (This number
such that
is called a
zero
of
). In algebraic terms: if for some numbers
,
,
but
, then for some
in the interval
,
. (b) Then give an example of a polynomial
without a zero (a zero is a number
such that
).
(c) Give an example of a function whose graph is above the
-axis and below the
-axis, yet
does not intersect the
-axis.
