Introduction to Functions - Algebra II
Card 0 of 1152
True or false: The graph of 
has as a horizontal asymptote the graph of the equation 
.
True or false: The graph of
is a rational function in simplest form whose denominator has a polynomial with degree greater than that of the polynomial in its numerator (2 and 1, respectively). The graph of such a function has as its horizontal asymptote the line of the equation 
.
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All inputs are valid. There is nothing you can put in for x that won't work.
All inputs are valid. There is nothing you can put in for x that won't work.
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All inputs are valid. There is nothing you can put in for x that won't work.
All inputs are valid. There is nothing you can put in for x that won't work.
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You cannot take the square root of a negative number.
You cannot take the square root of a negative number.
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The function includes all possible y-values (outputs). There is nothing you can put in for y that won't work.
The function includes all possible y-values (outputs). There is nothing you can put in for y that won't work.
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Squaring an input cannot produce a negative output.
Squaring an input cannot produce a negative output.
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The function includes all possible y-values (outputs). There is nothing you can put in for y that won't work.
The function includes all possible y-values (outputs). There is nothing you can put in for y that won't work.
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A number taken to a power must be positive.
A number taken to a power must be positive.
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The square root of any number cannot be negative.
The square root of any number cannot be negative.
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The absolute value of a number cannot be negative.
The absolute value of a number cannot be negative.
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Find the inverse of 
.
Find the inverse of
To create the inverse, switch x and y making the solution x=3y+3.
y must be isolated to finish the problem.
To create the inverse, switch x and y making the solution x=3y+3.
y must be isolated to finish the problem.
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Determine the domain of the following function:
Determine the domain of the following function:
The domain is all the possible values of 
. To determine the domain, we need to determine what values don't work for this equation. The only value that is not allowed for this equation is 5, since that would make the denominator have a value of 
, and you can not divide by 
. Therefore, the domain of this equation is:
and 
The domain is all the possible values of
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What is the domain and range of the following equation:
What is the domain and range of the following equation:
The domain of any quadratic function is always all real numbers.
The range of this function is anything greater than or equal to 5.
These written in the correct notation is:
Soft brackets are needed for infinity and a hard square bracket for 5 because it is included in the solution.
The domain of any quadratic function is always all real numbers.
The range of this function is anything greater than or equal to 5.
These written in the correct notation is:
Soft brackets are needed for infinity and a hard square bracket for 5 because it is included in the solution.
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Which of the following functions matches this domain: 
?
Which of the following functions matches this domain:
Because the domain is giving us a wide range of 
values, we can easily eliminate the fractional function 
as it only isolates a single 
value. We can eliminate 
as it means I am restricted to 
as my domain but I am looking for domain values greater than 
. This leaves us with the radical functions.
We have to remember the smallest possible value inside the radical is zero. Anything less means we will be dealing with imaginary numbers.
, 
This means the domain is 
which doesn't match our domain so this is wrong.
, 
. This means the domain is 
which doesn't match our domain since we want to EXCLUDE 
so this is wrong.
Since this is fractional expression with a radical in the denominator, we need to remember the bottom can't be zero and just set that denominator to equal 
. 
Square both sides to get 
. 
This actually means 
is not acceptable but any values greater than that is good. This is the correct answer.
Because the domain is giving us a wide range of
We have to remember the smallest possible value inside the radical is zero. Anything less means we will be dealing with imaginary numbers.
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What is the domain? 
What is the domain?
Notice that this is a parabolic function that will open downward. The domain refers to all possible x-values on the graph.
The parent function 
has a domain of all real numbers and a range from 
. The transformations of 
will not affect the domain, but the range of the graph since the y-values of the graph are affected.
There are no values of the x-variable that will make this function undefined, which means all real numbers can exist.
The answer is: 
Notice that this is a parabolic function that will open downward. The domain refers to all possible x-values on the graph.
The parent function
There are no values of the x-variable that will make this function undefined, which means all real numbers can exist.
The answer is:
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Solve for 
when 
.
Solve for
Plug 3 in for x:
Simplify:
= 
= 5
Plug 3 in for x:
Simplify:
=
= 5
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All inputs are valid. There is nothing you can put in for x that won't work.
All inputs are valid. There is nothing you can put in for x that won't work.
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All inputs are valid. There is nothing you can put in for x that won't work.
All inputs are valid. There is nothing you can put in for x that won't work.
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Find the domain:
Find the domain:
To find the domain, find all areas of the number line where the fraction is defined.
because the denominator of a fraction must be nonzero.
Factor by finding two numbers that sum to -2 and multiply to 1. These numbers are -1 and -1.
To find the domain, find all areas of the number line where the fraction is defined.
Factor by finding two numbers that sum to -2 and multiply to 1. These numbers are -1 and -1.
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What is the domain of the function 
?
What is the domain of the function
The domain is the set of x-values that make the function defined.
This function is defined everywhere except at 
, since division by zero is undefined.
The domain is the set of x-values that make the function defined.
This function is defined everywhere except at
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