Use the a, b, and c-sliders to graph the function.f(x)= (x-1)/(x^2-4x+3) (a=-1, b=-4,c=3) . Note that the denominator factors to (xminus−3)(xminus−1). Complete parts 1 and 2 below.
Use the interactive figure to find your answer. Use the left and right arrow keys to move along a slider as needed.
1. Domain: The function is defined for all real numbers except for the values of x that make the denominator equal to zero.
x^2 - 4x + 3 = 0
(x - 3)(x - 1) = 0
x = 3 or x = 1
Therefore, the domain of the function is all real numbers except x = 1 and x = 3.
2. As x approaches 1 from the left, the function approaches positive infinity. As x approaches 1 from the right, the function approaches negative infinity.
As x approaches 3 from the left, the function approaches negative infinity. As x approaches 3 from the right, the function approaches positive infinity.