All Precalculus Resources
Example Questions
Example Question #53 : Pre Calculus
What is the domain of the following function?

The denominator becomes zero whenever cos(x) becomes 1 and this happens when x is an odd multiple of . To avoid division by zero, we exclude all these numbers. Therefore the domain is:
Example Question #1 : Algebra Of Functions
Simplify the following expression:
When multiplying polynomials, add their exponents.
Example Question #22 : Functions
Simplify this polynomial:
When dividing polynomials, you must subtract corresponding exponents.
Thus, our answer is
.
Example Question #23 : Functions
Simplify the following:
When dividing, we must subtract the exponents.
Thus, our answer is .
Example Question #1 : Piecewise Functions
Let
What does equal when ?
Because 3>0 we plug the x value into the bottom equation.
Example Question #2 : Piecewise Functions
Let
What does equal when ?
Because we use the first equation.
Therefore, plugging in x=0 into the above equation we get the following,
.
Example Question #26 : Functions
Determine the value of if the function is
In order to determine the value of of the function we set
The value comes from the function in the first row of the piecewise function, and as such
Example Question #1 : Piecewise Functions
Determine the value of if the function is
In order to determine the value of of the function we set
The value comes from the function in the first row of the piecewise function, and as such
Example Question #28 : Functions
For the function defined below, what is the value of when ?
8
0
2
7
3
8
Evaluate the function for . Based on the domains of the three given expressions, you would use , since is greater than or equal to .
Example Question #29 : Functions
If is the greatest integer function, what is the value of ?
The greatest integer function takes an input and produces the greatest integer less than the input. Thus, the output is always smaller than the input and is an integer itself. Since our input was , we are looking for an integer less than this, which must be since any smaller integer would by definition not be "greatest".