SOLUTION: really need this answer

1)Graph f(x)=(x^2 – 4)/(x – 2) using a graphing calculator. Using a standard window with the trace feature, trace the graph to x=2. What happens?

2.

Algebra ->

Rational-functions

-> SOLUTION: really need this answer

1)Graph f(x)=(x^2 – 4)/(x – 2) using a graphing calculator. Using a standard window with the trace feature, trace the graph to x=2. What happens?

2.

Log On

Question 79627: really need this answer

1)Graph f(x)=(x^2 – 4)/(x – 2) using a graphing calculator. Using a standard window with the trace feature, trace the graph to x=2. What happens?

2. Why is there a “break” in the line at x=2? Why is the graph a line without a vertical asymptote at x=2? If x is “close to” 2, what is the y value “close to”?

Create a function that has either a hole, a break, or an asymptote in the graph.

You can put this solution on YOUR website! 1)Graph f(x)=(x^2 – 4)/(x – 2) using a graphing calculator. Using a standard window with the trace feature, trace the graph to x=2. What happens?

At x=2 you get an ERROR.

2. Why is there a “break” in the line at x=2?

The denominator cannot be zero; Because there is also a factor of

(x-2) in the numerator you get a “hole” in the graph.

———-

Why is the graph a line without a vertical asymptote at x=2?

If you cancel the (x-2) factor that is common to numerator and denominator

you get the function y=x+2 which graphs as a line.

———–

If x is “close to” 2, what is the y value “close to”?

y=4

———-

Create a function that has either a hole, a break, or an asymptote in the graph.

Asymptote: y=x/(x-2) will have a vertical asymptote at x=2.

Hole: y=[x^2-3x]/[x-3] will have a hole at x=3

=============

Cheers,

Stan H.