Texas Algebra II
Don't mess with Texas…EOC.
Algebra I just wasn't challenging enough for you? Shmoop's guide to the Texas Algebra II End-of-Course Assessment will open the door to the fabulous world of quadratic functions, square root functions, rational functions, and—well, let's just say we hope you're really into functions. As if that's not enough, we'll cover how to actually use these functions to do useful things. Everyone wins! Except for Algebra I; it misses you.
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Where the Deer, Antelope, and Cartesian Coordinates Play
Domain and range always go together, but they deal with opposite things. Think of them like height and width, or contrast and brightness: two related descriptions of the same thing. Domain describes a function's possible x-values, and range is all of the possible y's. For many functions (especially linear ones) domain and range can be described as "all real numbers" since any input gives a real output.
However, that isn't true in all cases.
Say we're given the function and asked to find the domain and range. We can start by making a quick graph to help visualize our deliberations.
First, think about the domain, or all the possible x's for this function. Recalling, of course, that the line extends beyond the boundaries of our mere mortal representation of a graph, there doesn't seem to be anything stopping those x-values from going as high or as low as they like. Looking at the equation confirms that. Any x we put in, whether it's huge, irrational, negative, will give us a real y output. Therefore, the domain is all real values of x.
Now we'll tackle the range. The lowest value of y visible on our graph is at x = 0, where y = 5. We know based on the shape of the parent function that the graph never curves back lower that that minimum point, so we can say that the range is y ≥ 5. When we check back with our equation, it makes perfect sense. If y was 4 and we tried to solve for x, something horrible would happen.
-4 = x2
Taking the square root of a negative is the mathematical equivalent of a party foul. Let's avoid that.