All College Algebra Resources
Example Questions
Example Question #81 : Graphs
Define a function
.Which statement correctly gives
?
The inverse function
of a function can be found as follows:Replace
with :
Switch the positions of
and :
or
Solve for
. This can be done as follows:Square both sides:
Add 9 to both sides:
Multiply both sides by
, distributing on the right:
Replace
with :
Example Question #1 : Miscellaneous Functions
Refer to the above diagram, which shows the graph of a function
.True or false:
.True
False
False
The statement is false. Look for the point on the graph of
with -coordinate by going right unit, then moving up and noting the -value, as follows:, so the statement is false.
Example Question #1 : Miscellaneous Functions
The above diagram shows the graph of function
on the coordinate axes. True or false: The -intercept of the graph isFalse
True
False
The
-intercept of the graph of a function is the point at which it intersects the -axis (the vertical axis). That point is marked on the diagram below:The point is about one and three-fourths units above the origin, making the coordinates of the
-intercept .Example Question #3 : Miscellaneous Functions
A function
is defined on the domain according to the above table.Define a function
. Which of the following values is not in the range of the function ?
This is the composition of two functions. By definition,
. To find the range of , we need to find the values of this function for each value in the domain of . Since , this is equivalent to evaluating for each value in the range of , as follows:
Range value: 3
Range value: 5
Range value: 8
Range value: 13
Range value: 21
The range of
on the set of range values of - and consequently, the range of - is the set . Of the five choices, only 45 does not appear in this set; this is the correct choice.Example Question #91 : Graphs
Evaluate:
Evaluate the expression
for , then add the four numbers:
Example Question #2 : Miscellaneous Functions
Evaluate:
Evaluate the expression
for , then add the five numbers:
Example Question #2 : Miscellaneous Functions
refers to the floor of , the greatest integer less than or equal to .
refers to the ceiling of , the least integer greater than or equal to .
Define
andWhich of the following is equal to
?
, so, first, evaluate by substitution:
, so evaluate by substitution.
,
the correct response.
Example Question #3 : Miscellaneous Functions
refers to the floor of , the greatest integer less than or equal to .
refers to the ceiling of , the least integer greater than or equal to .
Define
and .Evaluate
, so first, evaluate using substitution:
, so evaluate using substitution:
,
the correct response.
Example Question #172 : College Algebra
Consider the polynomial
,
where
is a real constant. For to be a zero of this polynomial, what must be?None of the other choices gives the correct response.
By the Factor Theorem,
is a zero of a polynomial if and only if . Here, , so evaluate the polynomial, in terms of , for by substituting 2 for :
Set this equal to 0: