2. True or false: A rational function as a vertical asymptote at x = c every time c is a zero of the denominator. If the statement is false justify your answer using mathematical terminology learned in class and examples of at least 2 functions that make this statement false.
True
3. Describe how the graph of a nonzero rational function f(x) = (ax+b)/(cx+d) can be obtained from the graph y = 1/x.
You can determine the y-int, x-int, the vertical asymptote, and horizontal asymptote. The graph is shifted left ax = -b units and down cx = -d units. The y-int is b/d. For the x-int, you cross multiply, where the denominator is canceled out, and you solve 0 = ax + b.
4. Write a rational function with the following properties:
2. True or false: A rational function as a vertical asymptote at x = c every time c is a zero of the denominator. If the statement is false justify your answer using mathematical terminology learned in class and examples of at least 2 functions that make this statement false.
True3. Describe how the graph of a nonzero rational function f(x) = (ax+b)/(cx+d) can be obtained from the graph y = 1/x.
You can determine the y-int, x-int, the vertical asymptote, and horizontal asymptote. The graph is shifted left ax = -b units and down cx = -d units. The y-int is b/d. For the x-int, you cross multiply, where the denominator is canceled out, and you solve 0 = ax + b.4. Write a rational function with the following properties:
(a) Vertical asymptotes: x = -5 and x = 2
1/x2+3x-10(b) Horizontal asymptote: y = -3
(1/x2-9) -3(c) y-intercept 1
1/x+1