use the a, b, and c - sliders to graph the function ( f(x)=\frac{x - 1}{x^{2}-4x + 3}(a=-1,b=-4,\text{ and…

use the a, b, and c - sliders to graph the function ( f(x)=\frac{x - 1}{x^{2}-4x + 3}(a=-1,b=-4,\text{ and }c = 3) ). note that the denominator factors to ( (x - 3)(x - 1) ). complete parts 1 and 2 below.\nuse the interactive figure to find your answer. use the left and right arrow keys to move along a slider as needed.\nclick here to launch the interactive figure.\npart 1: what is the equation of the vertical asymptote?\na. ( y = 3x )\nb. ( x = 3 )\nc. ( x = y )\nd. ( y = 0 )

use the a, b, and c - sliders to graph the function ( f(x)=\frac{x - 1}{x^{2}-4x + 3}(a=-1,b=-4,\text{ and }c = 3) ). note that the denominator factors to ( (x - 3)(x - 1) ). complete parts 1 and 2 below.\nuse the interactive figure to find your answer. use the left and right arrow keys to move along a slider as needed.\nclick here to launch the interactive figure.\npart 1: what is the equation of the vertical asymptote?\na. ( y = 3x )\nb. ( x = 3 )\nc. ( x = y )\nd. ( y = 0 )

Answer

Explanation:

Step1: Recall the definition of vertical asymptote

A vertical asymptote occurs at the value of (x) that makes the denominator of a rational function equal to zero (provided the numerator is not also zero at that value).

Step2: Set the denominator equal to zero

The function is (f(x)=\frac{x - 1}{x^{2}-4x + 3}), and the denominator (x^{2}-4x + 3=(x - 3)(x - 1)). Set (x^{2}-4x + 3 = 0), so ((x - 3)(x - 1)=0).

Step3: Solve for (x)

Using the zero - product property (ab = 0) implies (a=0) or (b = 0). So (x-3=0) gives (x = 3) and (x - 1=0) gives (x = 1). But when (x = 1), the numerator (x-1=0). So the vertical asymptote is at (x = 3) (since the numerator is non - zero at (x = 3)).

Answer:

B. (x = 3)