Domain and Range - Algebra 2
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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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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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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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is a sine curve. What are the domain and range of this function?
The domain includes the values that go into a function (the x-values) and the range are the values that come out (the 
or y-values). A sine curve represent a wave the repeats at a regular frequency. Based upon this graph, the maximum 
is equal to 1, while the minimum is equal to –1. The x-values span all real numbers, as there is no limit to the input fo a sine function. The domain of the function is all real numbers and the range is 
.
The domain includes the values that go into a function (the x-values) and the range are the values that come out (the
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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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If 
, which of these values of 
is NOT in the domain of this equation?
If
Using 
as the input (
) value for this equation generates an output (
) value that contradicts the stated condition of 
.
Therefore 
is not a valid value for 
and not in the equation's domain:
Using
Therefore
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