Mathematics Dictionary Dr. K. G. Shih

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Rational Functions and Numbers

Questions

Read Symbol defintion Q01 | - Rational Function : y = 1/(a*x + b) Q02 | - Rational Function : y = 1/(a*x^2 + b*x + c) Q03 | - y = ((x - 1)^m)/(2*x) Q04 | - Q05 | - Q06 | - Q07 | - Q08 | - Q09 | - Q10 | -

Answers

Q01. Rational Function : y = 1/(a*x + b) Find asymptote by (a*x + b) = 0. Hence asymptote is x = -b/a. Sketch graph of y = 2*x + 3 Clcik Start after entering application program. Click subjection Rational Function in upper box. Click y = a*x + b in lowe box. Type in coefficients 2, 3. Quick sketch Draw asymptote x = -3/2. Draw y-intercept, that is x = 0 and y = 3. For x < -3/2, y = 0 as x = -infinite and y = -infinite as x = -2/3. The curve is concave downward. For x > -3/2, y = +infinite as x = -2/3 and y = 0 as x = +infinite. The curve is concave upward. Hence we can draw the curve quickly with few points. Go to Begin Q02. Rational Function : y = 1/(a*x^2 + b*x + c) Find asymptote by (a*x^2 + b*x + c) = 0. It has no vertical asymptote if b^2 - 4*a*c < 0. It has one vertical asymptote if b^2 - 4*a*c = 0. It has two vertical asymptotes if b^2 - 4*a*c > 0. Sketch graph of y = x^2 - 6*x + 8 Clcik Start after entering application program. Click subjection Rational Function in upper box. Click y = 1/(a*x^2 + b*x + c) in lowe box. Type in coefficients 1, -6, 8. Quick sketch Draw asymptotes x = 2 and x = 4. Draw y-intercept, that is x = 0 and y = 8. For x < 2, y = 0 as x = -infinite and y = -infinite as x = 2. The curve is concave downward. For 2 < x < 4, y = +infinite as x = 2 and y = +infinite as x = 4. The curve is concave upward. For x > 4, y = -infinite as x = 4 and y = 0 as x = +infinite The curve is concave downward. Hence we can draw the curve quickly with few points. Go to Begin Q03. y = ((x - 1)^m)/(2*x) Find asymptote of ((x-1)^2)/(2*x). Find asymptote of ((x-1)^3)/(2*x). Find asymptote of ((x-1)^4)/(2*x). Sketch graph of y = ((x-1)^m)/(2*x) Clcik Start after entering application program. Click subjection Rational Function in upper box. Click y = ((x-1)^m)/(x^n) in lowe box. Type in data m = 2, 3 or 4. Go to Begin Q04. y = ((x - 1)^m)/(a*x^2 + b*x + c) Find asymptote of ((x-1)^3)/(x^2). Find asymptote of ((x-1)^4)/(x^2). Find asymptote of ((x-1)^5)/(x^2). Sketch graph of y = ((x-1)^m)/(a*x^2 + b*x + c) Clcik Start after entering application program. Click subjection Rational Function in upper box. Click y = ((x-1)^m)/(a*x^2 + b*x + c) in lowe box. Type in data m = 2, 3 or 4. then coefficients a, b, c. Go to Begin Q05. Answer Go to Begin Q06. Answer Go to Begin Q07. Answer Go to Begin Q08. Answer Go to Begin Q09. Answer Go to Begin Q10. Answer Go to Begin

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