unit circle quadrants all students take calculus

If we graph this equation we get a graph that looks like:Īs we can see from the graph the domain and range are indeed what we found algebraically. Now that we have solved the domain and range algebraically we can verify our answers using a graphical approach. Therefore, there is not a possible way to every achieve y = 0 because 3 divided by anything will never by 0. Once again we must take into consideration that the x is in the denominator. To solve for the range we must consider all of the y values that are possible for the function. This is the only value for x that is not possible so the domain is. Therefore, x = 0 is not a possible value for the function.

If x = 0 then the function would be undefined because 0 cannot be in the denominator. The x is in the denominator which means some values of x will not be possible. To solve for the domain algebraically we need to consider what x values are possible for this function. The range of a function is the set of all possible outputs, or dependent variables, for the function.ĭomain and range can be found algebraically or by graphing.Įxample: Find the domain and range for the function The domain of a function is the set of all possible inputs, or independent variables, for the function. If there is any point at which the vertical line passes through the graph of the equation more than once, then it is not a function. Imagine moving a vertical line back and forth across the graph (You can use your pencil or the edge of a ruler for this.).

You can tell if an equation is a function by performing the vertical line test. To solve this we will substitute x = 2 into our function. To find the function value given the value of the function, plug in the value of the function given for x.Įxample: Let, find the function values of.

Where is the value of the function, y is the dependent variable, and x is the independent variable. A function is relationship between two variables such that each independent variable has only one dependent variable.

Unit circle quadrants all students take calculus