How can I find the Domain and Range for y=1/-x -2 And y=-4/x-4 +4
they also ask me to compare these 2 problems with graph of y=1/x
please help me solve these algebra problems.
polynomials have a domain of all reals numbers.
rational functions, being the quotient of two polynomials, do also, with the exception of values where the denominator is zero.
So, 1/-x has a domain of all reals except x=0
rational functions with linear denominators always have a range of all reals.
See the graphs at
http://www.wolframalpha.com/input/?i=plot+y%3D1%2F-x-2%2Cy%3D-4%2F%28x-4%29+%2B4+
To find the domain and range of each equation, we need to analyze the variables and restrictions involved.
1. For the equation y = 1/(-x) - 2:
The denominator (-x) cannot be zero because division by zero is undefined. So, the domain is any real number except x = 0.
As for the range, the value of -x can be any real number except zero. Therefore, the range is also any real number except y = 0.
2. For the equation y = -4/(x - 4) + 4:
Similar to the previous equation, the denominator (x - 4) cannot be zero, as division by zero is undefined. So, the domain is any real number except x = 4.
The range is the set of all real numbers, as there are no restrictions on the numerator.
Now, let's compare these two equations with the graph of y = 1/x.
1. Domain and Range Comparison:
The domain of y = 1/x is any real number except x = 0, which is similar to the first equation.
The range of y = 1/x is any real number except y = 0, which is also similar to the first equation.
2. Graphical Comparison:
The graph of y = 1/x is a hyperbola. It approaches the x and y axes but never touches them.
For the first equation, the graph will be a reflection of the graph of y = 1/x along the y-axis and shifted downward by 2 units.
For the second equation, the graph will be a reflection of the graph of y = 1/x along the x-axis, shifted right by 4 units, and then shifted upward by 4 units.
You can plot these graphs on a graphing calculator or online tool to visualize the comparisons further.