|
A rational function R(x) is a function of the formshown, where P(x) and Q(x) are polynomials, and Q(x) is not the zero polynomial. R(x) = Q(x) P(x) A rational function is a function of the formshown, where Q(x) is not the zero polynomial. h(x) = True or False: The function shown below is a rational function: x + 3 5x False True P(x) Q(x) A rational function is a function of the formshown, where Q(x) is not the zero polynomial. True or False: The function shown below is a rational function: g(x) = x – 1 6 False True Q(x) P(x) A rational function is a function of the formshown, where Q(x) is not the zero polynomial. True or False: The function shown below is a rational function: f(x) = x – 1 0 True False Q(x) P(x) A rational function is a function of the formshown, where Q(x) is not the zero polynomial. The domain of a rational function is all real numbers except for the zeros of Q(x). g(x) = x + 3 x – 2 What is the domain of g(x)? x ≠ -3 x ≠ -2 x ≠ 2 x ≠ 3 P(x) Q(x) A rational function is a function of the formshown, where Q(x) is not the zero polynomial. The domain of a rational function is all real numbers except for the zeros of Q(x). h(x) = x(x+1) x+1 What is the domain of h(x)? x ≠ -1 x ≠ 0 x ≠ 1 All real numbers Q(x) P(x) h(x) = The vertical asymptotes of R(x) will occur at the zeros of Q(x). So, if r is a zero for Q(x), then x = r will be a vertical asymptote. x(x+1) x+2 Identify a vertical asymptote of h(x). x = 1 x = 0 x = -1 x = -2 R(x) = Q(x) P(x) k(x) = The vertical asymptotes of R(x) will occur at the zeros of Q(x). So, if r is a zero for Q(x), then x = r will be a vertical asymptote. -3x+9 2x Identify a vertical asymptote of k(x). x = 3 x = 2 x = 0 x = 1/2 R(x) = Q(x) P(x) If the degree of the numerator = denominator, then thereis a horizontal asymptote at y = k, where k is the quotientof the leading coefficient of the numerator ÷ the leadingcoefficient of the denominator. If the degree of the numerator > denominator, then thereis no horizontal asymptote. Finding a horizontal asymptote: If the degree of the numerator < denominator,then y = 0 is the horizontal asymptote. R(x) = Q(x) P(x) Finding a horizontal asymptote: If the degree of the numerator < denominator,then y = 0 is the horizontal asymptote. True or False: For the Rational Function given below, the horizontal asymptote is y = 0. f(x) = 5x2+ 3x 2x3 False True Finding a horizontal asymptote: If the degree of the numerator < denominator,then y = 0 is the horizontal asymptote. True or False: For the Rational Function given below, the horizontal asymptote is y = 0. f(x) = (2x + 3)(x – 5) (x + 1)2 False True True or False: For the Rational Function given below, the horizontal asymptote is y = 0. Finding a horizontal asymptote: If the degree of the numerator < denominator,then y = 0 is the horizontal asymptote. f(x) = (2x+3)(x–5) 4x + 1 True False True or False: For the Rational Function given below, the horizontal asymptote is y = 2. Finding a horizontal asymptote: If the degree of the numerator = denominator, then thereis a horizontal asymptote at y = k, where k = the leading coefficient of the numerator ÷ the leading coefficient of the denominator. f(x) = 6x2 – 7x – 15 3x + 1 False True True or False: For the Rational Function given below, the horizontal asymptote is y = -8. Finding a horizontal asymptote: If the degree of the numerator = denominator, then thereis a horizontal asymptote at y = k, where k = the leading coefficient of the numerator ÷ the leading coefficient of the denominator. g(x) = –12x2 + 3x +1 4x2 - 3x + 2 False True True or False: For the Rational Function given below, the x-intercept is x = -5 Finding an x-intercept To find the x-intercept, set y = 0. Because it is a rational function, set the numerator = 0 and solve for x. g(x) = (x + 1)2 x + 5 True False True or False: For the Rational Function given below, the x-intercept is x = -2. Finding an x-intercept To find the x-intercept, set y = 0. Because it is a rational function, set the numerator = 0 and solve for x. g(x) = (x – 2)(x – 3) (x – 3)2 True False True or False: For the Rational Function given below, the y-intercept is -1/5. Finding a y-intercept To find the y-intercept, set x = 0. Because it is a rational function, set the numerator = 0 and solve for x. g(x) = 2x – 1 3x + 5 True False Finding a y-intercept To find the y-intercept, set x = 0. True or False: For the Rational Function given below, the y-intercept is 2/3. y = x – 2 x + 3 True False |