### Concept (1)

We have rational functions whenever we have a fraction that has a polynomial in the numerator and/or in the denominator. An excluded value in the function is any value of the variable that would make the denominator equal to zero. To find the domain, list all the values of the variable that, when substituted, would result in a zero in the denominator.

### Sample Problems (8)

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Find the domain of

 f(x) = 4 x
###### Problem 1
How to find excluded values of a rational function where there are no sums or differences.

Find the domain of

 f(x) = 4 x − 3
###### Problem 2
How to find excluded values of a rational function where there is a sum or difference in the denominator.

Find the domain of

 f(x) = 4 2x² + 5x + 3
###### Problem 3
How to find excluded values of a rational function when the denominator is a factorable trinomial.
###### Problem 4
Vertical and horizontal translations on the parent graph of a rational function.
###### Problem 5
Reflecting the parent graph of a rational function across the x axis
###### Problem 6
Vertical translations on the parent graph of a rational function.
###### Problem 7
Domain restrictions and excluded values of rational expressions.
###### Problem 8
Sketching rational functions and asymptotes using horizontal transformations.