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I CAN :

I CAN :. Find the x, y intercepts, vertex, domain and range of quadratics and some even powered functions. x 2. x.

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I CAN :

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  1. I CAN: Find the x, y intercepts, vertex, domain and range of quadratics and some even powered functions. x2 x This IMPLIES that I can successfully : factor, used the QF, employ the graph translation patterns (left, right, up, down etc) and use –b/2a to find the x coordinate of the vertex.

  2. I CAN: Find the x, y intercepts, IP, domain and range of cubics and odd powered functions. x This IMPLIES that I can successfully : factor, used the QF, employ the graph translation patterns (left, right, up, down etc), Remainder Thm, Intermediate Value thm (p/q, long division) and use –b/2a to find the x coordinate of the vertex.

  3. I CAN: Find the x, y intercepts of rational functions f(x) = f(x) = f(x) = f(x) = f(x) = This IMPLIES that I can successfully : factor, used the QF, employ the graph translation patterns (left, right, up, down etc), Remainder Thm, Intermediate Value thm (p/q, long division) and use –b/2a to find the x coordinate of the vertex.

  4. I CAN: Find the vertical asymptotes and domain of a rational function. f(x) = f(x) = f(x) = f(x) = This IMPLIES that I can successfully : factor, used the QF, employ the graph translation patterns (left, right, up, down etc), Remainder Thm, Intermediate Value thm (p/q, long division) and use –b/2a to find the x coordinate of the vertex.

  5. I CAN: Find the horizontal asymptotes and range of a rational function. f(x) = f(x) = f(x) = f(x) = This IMPLIES that I can successfully implement the 3 patterns that help determine the horizontal asymptote which rely on the degree of the numerator and the degree of the denominator. (check last note sheet)

  6. I CAN: Find the slant asymptotes and/or hole of a rational function. I don’t have to worry about range if the function has a slant asymptote. f(x) = f(x) = f(x) = This IMPLIES that I can successfully factor and complete long division and graph a line.

  7. FINDING A SLANT ASYMPTOTE AND/OR HOLE: f(x) = Divided numerator by denominator x – 1/3 YES, there is a remainder but we ignore it! The slant asymptote is y =x – 1/3 THERE IS NO HORIZONTAL ASYMPTOTE! We MUST factor numerator and denominator to find the VA and possible holes, etc.

  8. FINDING A SLANT ASYMPTOTE AND/OR HOLE: f(x) = Factor numerator by grouping x2 x2 (x2-1) (x

  9. FINDING A SLANT ASYMPTOTE AND/OR HOLE: f(x) = Factor denominator. Use trial and error or whatever method you learned in AA This is my method…. 3 time -2 = - 6 -1 and 6 multiply to -6 and add to 5 Multiply the 3 and -2. Factor -6 so that you get two factors that ADD to 5. Replace 5x as follows: x Factor by grouping.

  10. FINDING A SLANT ASYMPTOTE AND/OR HOLE: Because there are NO factors that cancel between the numerator and the denominator there is NO hole in this rational function. f(x) = (x IF we had and example that looked like this: (x We would have a hole (open little circle) on the graph at x = -1 and then cancel out the x+1 factors because they would not be VA nor x intercepts.

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