All SAT II Math II Resources
Example Questions
Example Question #2 : Solving Functions
A baseball is thrown straight up with an initial speed of 60 feet per second by a man standing on the roof of a 100-foot high building. The height of the baseball in feet as a function of time in seconds is modeled by the function
To the nearest tenth of a second, how long does it take for the baseball to hit the ground?
When the baseball hits the ground, the height is 0, so we set . and solve for
.
This can be done using the quadratic formula:
Set :
One possible solution:
We throw this out, since time must be positive.
The other:
This solution, we keep. The baseball hits the ground in 5 seconds.
Example Question #1 : Solving Trigonometric Functions
Give the period of the graph of the equation
The correct answer is not among the other choices.
The correct answer is not among the other choices.
The period of the graph of a sine function is
, or
.
Since ,
.
This answer is not among the given choices.
Example Question #1 : Solving Trigonometric Functions
If , what must
be?
Evaluate each trig function at the specified angle.
Replace the terms into the function.
Combine like-terms.
The answer is:
Example Question #1 : Solving Piecewise And Recusive Functions
Define and
as follows:
Evaluate .
by definition.
on the set
, so
.
on the set
, so
.
Example Question #1 : Solving Piecewise And Recusive Functions
Define function as follows:
Give the range of .
The range of a piecewise function is the union of the ranges of the individual pieces, so we examine both of these pieces.
If , then
. To find the range of
on the interval
, we note:
The range of this portion of is
.
If , then
. To find the range of
on the interval
, we note:
The range of this portion of is
The union of these two sets is , so this is the range of
over its entire domain.
Example Question #1 : Solving Piecewise And Recusive Functions
Define function as follows:
Give the range of .
The range of a piecewise function is the union of the ranges of the individual pieces, so we examine both of these pieces.
If , then
.
To find the range of on the interval
, we note:
The range of on
is
.
If , then
.
To find the range of on the interval
, we note:
The range of on
is
.
The range of on its entire domain is the union of these sets, or
.
Example Question #2 : Solving Piecewise And Recusive Functions
Define functions and
as follows:
Evaluate .
Undefined
First, we evaluate . Since
, the definition of
for
is used, and
Since
, then
Example Question #1 : Solving Piecewise And Recusive Functions
Define functions and
as follows:
Evaluate Evaluate .
Undefined
Undefined
First, evaluate using the definition of
for
:
Therefore,
However, is not in the domain of
.
Therefore, is an undefined quantity.
Example Question #2 : Solving Piecewise And Recusive Functions
Define functions and
as follows:
Evaluate .
Undefined
First, evaluate using the definition of
for
:
Therefore,
Evaluate using the definition of
for
:
Example Question #3 : Solving Piecewise And Recusive Functions
Define functions and
as follows:
Evaluate .
Undefined
First we evaluate . Since
, we use the definition of
for the values in the range
:
Therefore,
Since , we use the definition of
for the range
:
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