(a) Find a linear function that contains the points ( − 2 , 3 ) and ( 1 , − 6 ) . What is the slope? What are the intercepts of the function? Graph the function. Be sure to label the intercepts. (b) Find a quadratic function with the vertex ( 1 , − 6 ) that contains the point ( − 2 , 3 ) . What are the intercepts of the function? Graph the function. (c) Show that there is no exponential function of the form f ( x ) = a e x that contains the points ( − 2 , 3 ) and ( 1 , − 6 ) .
(a) Find a linear function that contains the points ( − 2 , 3 ) and ( 1 , − 6 ) . What is the slope? What are the intercepts of the function? Graph the function. Be sure to label the intercepts. (b) Find a quadratic function with the vertex ( 1 , − 6 ) that contains the point ( − 2 , 3 ) . What are the intercepts of the function? Graph the function. (c) Show that there is no exponential function of the form f ( x ) = a e x that contains the points ( − 2 , 3 ) and ( 1 , − 6 ) .
Solution Summary: The author calculates the equation, slope, and intercepts of the line containing the points (-2,3) and
(a) Find a linear function that contains the points
(
−
2
,
3
)
and
(
1
,
−
6
)
. What is the slope? What are the intercepts of the function? Graph the function. Be sure to label the intercepts.
(b) Find a quadratic function with the vertex
(
1
,
−
6
)
that contains the point
(
−
2
,
3
)
. What are the intercepts of the function? Graph the function.
(c) Show that there is no exponential function of the form
f
(
x
)
=
a
e
x
that contains the points
(
−
2
,
3
)
and
(
1
,
−
6
)
.
4. Use method of separation of variable to solve the following wave equation
მłu
J²u
subject to
u(0,t) =0, for t> 0,
u(л,t) = 0, for t> 0,
=
t> 0,
at²
ax²'
u(x, 0) = 0,
0.01 x,
ut(x, 0) =
Π
0.01 (π-x),
0
Solve the following heat equation by method of separation variables:
ди
=
at
subject to
u(0,t) =0, for
-16024
ძx2 •
t>0, 0 0,
ux (4,t) = 0, for
t> 0,
u(x, 0) =
(x-3,
\-1,
0 < x ≤2
2≤ x ≤ 4.
ex
5.
important aspects.
Graph f(x)=lnx. Be sure to make your graph big enough to easily read (use the space given.) Label all
6
33
Chapter 5 Solutions
Pearson eText for Precalculus: Concepts Through Functions, A Unit Circle Approach to Trigonometry -- Instant Access (Pearson+)
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