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Example Questions
Example Question #133 : Advanced Geometry
Give the -coordinate of the
-intercept of the graph of the function
The -intercept of the graph of
is the point at which it intersects the
-axis. Its
-coordinate is 0; its
-coordinate is
, which can be found by substituting 0 for
in the definition:
Example Question #134 : Advanced Geometry
Give the -coordinate of the
-intercept of the graph of the function
.
The graph of has no
-intercept.
The -intercept of the graph of
is the point at which it intersects the
-axis. Its
-coordinate is 0; its
-coordinate is
, which can be found by substituting 0 for
in the definition:
,
the correct choice.
Example Question #135 : Advanced Geometry
Give the -coordinate of the
-intercept of the graph of the function
.
The graph of has no
-intercept.
The graph of has no
-intercept.
The -intercept(s) of the graph of
are the point(s) at which it intersects the
-axis. The
-coordinate of each is 0,; their
-coordinate(s) are those value(s) of
for which
, so set up, and solve for
, the equation:
Subtract 7 from both sides:
Divide both sides by 2:
The next step would normally be to take the natural logarithm of both sides in order to eliminate the exponent. However, the negative number does not have a natural logarithm. Therefore, this equation has no solution, and the graph of
has no
-intercept.
Example Question #51 : Coordinate Geometry
Give the -coordinate of the
-intercept of the graph of the function
The -intercept(s) of the graph of
are the point(s) at which it intersects the
-axis. The
-coordinate of each is 0,; their
-coordinate(s) are those value(s) of
for which
, so set up, and solve for
, the equation:
Add 8 to both sides:
Divide both sides by 2:
Take the common logarithm of both sides to eliminate the base:
Example Question #51 : Graphing
Give the domain of the function .
The set of all real numbers
The set of all real numbers
Let . This function is defined for any real number
, so the domain of
is the set of all real numbers. In terms of
,
Since is defined for all real
, so is
; it follows that
is as well. The correct domain is the set of all real numbers.
Example Question #52 : Graphing
Give the range of the function .
The set of all real numbers
Since a positive number raised to any power is equal to a positive number,
Applying the properties of inequality, we see that
,
and the range of is the set
.
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