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Example Questions
Example Question #1 : Introduction To Functions
Which analysis can be performed to determine if an equation is a function?
Vertical line test
Calculating zeroes
Horizontal line test
Calculating domain and range
Vertical line test
The vertical line test can be used to determine if an equation is a function. In order to be a function, there must only be one (or
) value for each value of
. The vertical line test determines how many
(or
) values are present for each value of
. If a single vertical line passes through the graph of an equation more than once, it is not a function. If it passes through exactly once or not at all, then the equation is a function.
The horizontal line test can be used to determine if a function is one-to-one, that is, if only one value exists for each
(or
) value. Calculating zeroes, domain, and range can be useful for graphing an equation, but they do not tell if it is a function.
Example of a function:
Example of an equation that is not a function:
Example Question #2 : Introduction To Functions
Which graph depicts a function?
Example Question #1 : Introduction To Functions
The graph below is the graph of a piece-wise function in some interval. Identify, in interval notation, the decreasing interval.
As is clear from the graph, in the interval between (
included) to
, the
is constant at
and then from
(
not included) to
(
not included), the
is a decreasing function.
Example Question #1 : Functions As Graphs
Without graphing, determine the relationship between the following two lines. Select the most appropriate answer.
Intersecting
Supplementary
Perpendicular
Parallel
Complementary
Perpendicular
Perpendicular lines have slopes that are negative reciprocals. This is the case with these two lines. Although these lines interesect, this is not the most appropriate answer since it does not account for the fact that they are perpendicular.
Example Question #4 : Introduction To Functions
Find the slope from the following equation.
To find the slope of an equation first get the equation in slope intercept form.
where,
represents the slope.
Thus
Example Question #1 : Functions As Graphs
3 spaces right, 2 spaces down
3 spaces right, 2 spaces up
3 spaces left, 2 spaces down
3 spaces up, 2 spaces left
3 spaces left, 2 spaces down
When determining how a the graph of a function will be translated, we know that anything that happens to x in the function will impact the graph horizontally, opposite of what is expressed in the function, whereas anything that is outside the function will impact the graph vertically the same as it is in the function notation.
For this graph:
The graph will move 3 spaces left, because that is the opposite sign of the what is connected to x directly.
Also, the graph will move down 2 spaces, because that is what is outside the function and the 2 is negative.
Example Question #3 : Introduction To Functions
Define a function .
Is this function even, odd, or neither?
Odd
Even
Neither
Odd
To identify a function as even odd, or neither, determine
by replacing
with
, then simplifying. If
, the function is even; if
is odd.
,
so
By the Power of a Product Property,
,
so is an odd function
Example Question #7 : Introduction To Functions
Define a function .
Is this function even, odd, or neither?
Neither
Even
Odd
Neither
To identify a function as even odd, or neither, determine
by replacing
with
, then simplifying. If
, the function is even; if
is odd.
so
By the Power of a Product Property,
, so
is not an even function.
,
, so
is not an odd function.
Example Question #8 : Introduction To Functions
Define a function .
Is this function even, odd, or neither?
Even
Odd
Neither
Even
To identify a function as even, odd, or neither, determine
by replacing
with
, then simplifying. If
, the function is even; if
is odd.
, so
is an even function.
Example Question #1 : Introduction To Functions
Define a function .
Is this function even, odd, or neither?
Odd
Even
Neither
Odd
To identify a function as even, odd, or neither, determine
by replacing
with
, then simplifying. If
, the function is even; if
is odd.
Since ,
is an odd function.
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