domain of (5x+4)/(4x-7)

Question

what is the domain

Answer 1

The domain is the set of x values in which the expression is defined.  To find it, we set the denominator equal to zero.

 

4x - 7 = 0

 

Solve for x.  The x value is the restricted value and is not in the domain. 

 

If you were to graph this, the restricted x value would be a vertical asymptote.

 

 

 

 

The range is the set of output values in which expression is defined.  To find it, we examine the degree of the numerator and denominator.  Since the degree of both numerator and denominator are the same, we divide the coefficients.

 

Range is all output values from negative infinity to positive infinity, excluding 5/4.

 

If you were to graph this,   y=5/4  would be a horizontal asymptote.

Answer 2

The domain for this function is all numbers that do not make the denominator zero because a fraction with a zero in the denominator is undefined.  For this function, you would set the denominator, 4x - 7, equal to zero and solve for x:

 

4x - 7 = 0

4x = 7

x = 7/4

 

The domain is all real numbers excluding 7/4.