5. Rational Functions

Graph each rational function. See Examples 5–9. ƒ(x)=5x/(x^2-1)

Graph each rational function. See Examples 5–9. ƒ(x)=[(x+6)(x-2)]/[(x+3)(x-4)]

Graph each rational function. See Examples 5–9. ƒ(x)=[(x+3)(x-5)]/[(x+1)(x-4)]

Graph each rational function. See Examples 5–9. ƒ(x)=(x^2+8x+16)/(x^2+4x-5)

Graph each rational function. See Examples 5–9. ƒ(x)=(x^2+2x+1)/(x^2-x-6)

Graph each rational function. See Examples 5–9. ƒ(x)=(20+6x-2x^2)/(8+6x-2x^2)

Graph each rational function. See Examples 5–9. ƒ(x)=(18+6x-4x^2)/(4+6x+2x^2)

Provide a short answer to each question. What is the domain of the function ƒ(x)=1/x^2? What is its range?

Graph each rational function. See Examples 5–9. ƒ(x)=(9x^2-1)/(x^2-4)

Graph each rational function. See Examples 5–9. ƒ(x)=(16x^2-9)/(x^2-9)

Provide a short answer to each question. What is the equation of the vertical asymptote of the graph of y=1/(x-3)+2? Of the horizontal asymptote?

Work each problem. Which function has a graph that does not have a vertical asymptote?A. ƒ(x)=1/(x^2+2) B. ƒ(x)=1/(x^2-2) C. ƒ(x)=3/x^2 D. ƒ(x)=(2x+1)/(x-8)

Identify any vertical, horizontal, or oblique asymptotes in the graph of y=ƒ(x). State the domain of ƒ.

Find a rational function ƒ having a graph with the given features. x-intercepts: (-1, 0) and (3, 0)y-intercept: (0, -3)vertical asymptote: x=1horizontal asymptote: y=1

Find a rational function ƒ having a graph with the given features.x-intercepts: (1, 0) and (3, 0)y-intercept: none vertical asymptotes: x=0 and x=2horizontal asymptote: y=1