Warm Up 8.2, Day 1 Translate into an equation.

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Presentation transcript:

Warm Up 8.2, Day 1 Translate into an equation. r varies inversely with t. c varies directly with s and inversely with h. t varies jointly with r and s and inversely with the cube of h. Describe how to tell if a set of data shows direct or inverse variation. y varies inversely with x. When y = 10, x = -25. Find y when x = 30.

Graph simple rational functions (8.2) Unit 8: Rational Functions Target 8.2, Day 1 Graph simple rational functions (8.2)

Graph Hyperbola Domain: Range: Vertical Asymptote: Horizontal Asymptote:

Graph and compare to Domain: Range: Vertical Asymptote: Horizontal Asymptote: What do you think would happen if the 6 was -6?

h is ___________________ shift (this will tell you the domain and where the vertical asymptote is, x = h) k is ___________________ shift (this will tell you the range and where the horizontal asymptote is, y = k) If a is positive, the branches of the hyperbola will lay in the 1st and 3rd Quadrants. If a is negative the branches will lay in the 2nd and 4th Quadrant. The bigger a is, the farther the branches will be from the axes.

Graph . Start by drawing the asymptotes. Then state the domain the range. Domain: Range: Vertical Asymptote: Horizontal Asymptote:

Start by finding the zero(s) of the denominator Start by finding the zero(s) of the denominator. This is the vertical asymptote (and domain). Graph To find the horizontal asymptote (and range), divide the leading coefficients. D: ________ VA: ________ R: ________ HA: ________

Start by finding the zero(s) of the denominator Start by finding the zero(s) of the denominator. This is the vertical asymptote (and domain). Graph To find the horizontal asymptote (and range), divide the leading coefficients. D: ________ VA: ________ R: ________ HA: ________

Warm Up 8.2, Day 2 State the domain, range, vertical asymptote, and horizontal asymptote for each function. D: ________ VA: ________ R: ________ HA: ________ D: ________ VA: ________ R: ________ HA: ________ D: ________ VA: ________ R: ________ HA: ________ D: ________ VA: ________ R: ________ HA: ________

Graph general rational functions (8.3) Unit 8: Rational Functions Target 8.2, Day 2 Graph general rational functions (8.3)

When graphing rational functions, keep the following in mind: Zeros of numerator = x-intercepts Zeros of denominator = vertical asymptotes The horizontal asymptote (if there is one) depends on the degree (highest exponent) of the numerator and denominator Top < Bottom Top = Bottom Top > Bottom No Horizontal Asymptote But....

Identify the x-intercepts, vertical asymptotes, and horizontal asymptotes of the graph. Then sketch the graph. x-Intercepts: ____________ Vertical Asymptotes:___________ Horizontal Asymptotes:________

x-Intercepts: ____________ www.jasonmyhre.weebly.com Identify the x-intercepts, vertical asymptotes, and horizontal asymptotes of the graph. Then sketch the graph. x-Intercepts: ____________ Vertical Asymptotes:___________ Horizontal Asymptotes:________

x-Intercepts: ____________ www.jasonmyhre.weebly.com Identify the x-intercepts, vertical asymptotes, and horizontal asymptotes of the graph. Then sketch the graph. x-Intercepts: ____________ Vertical Asymptotes:___________ Horizontal Asymptotes:________