Horizontal asymptote - Study guides, Class notes & Summaries

All rational functions can be expressed as f(x)=p(x)/q(x), where p and q are _______________ functions and q(x)=0 - CORRECT ANS polynomial The domain of every rational function is the set of all real numbers. - CORRECT ANS false The graph of the reciprocal function f(x)= 1/x has a break and is composed of two distinct branches. - CORRECT ANS true If the graph of a function f increases or decreases without bound as x approaches a, then the line x=a is __________________- of the graph of f....

AQA AS FURTHER MATHEMATICS 7366/1 Paper 1 Version: 1.0 Final G/LM/Jun23/E7 7366/1 (JUN) AS FURTHER MATHEMATICS Paper 1 Monday 15 May 2023 Afternoon Time allowed: 1 hour 30 minutes Materials  You must have the AQA Formulae and statistical tables booklet for A-level Mathematics and A-level Further Mathematics.  You should have a graphical or scientific calculator that meets the requirements of the specification. Instructions  Use black ink or black ball-point pen. Pencil...

Chapter 3: Polynomial and Rational Functions 1. Graph the given function. A) B) C) Larson/Hodgkins, College Algebra with Applications for Business and the Life Sciences, 2e Page 1 D) E) Ans: D 2. Find an equation of the parabola below. A) Larson/Hodgkins, College Algebra with Applications for Business and the Life Sciences, 2e 2 y–x–2 –3 Page 2 B) C) D) E) Ans: D 3. m(x)6x–62 +2 shifts right 6 units, shifts downward 2 units, and shrinks ...

College Algebra Questions Answered 100% correct 2023 quadratic formula compound interest formula simple interest formula distance formula D=R X T complex numbers discriminant formula if D> 0: 2 real solutions if D<0: 2 non-real solutions if D=0 : exactly 1 solution factor by grouping inequality signs when the inequality sign changes if you multiply or dividing both sides of the inequality by a negative number it changes the dire...

Asymptote correct answer: a horizontal, vertical, or slanted line that a graph approaches but never touches coefficient of determination correct answer: A statistic that measures how well a regression prediction approximates the real data points. An r^2 of 1 indicates that the regression prediction is a perfect fit for the data common ratio correct answer: The number by which each term in a sequence is multiplied to find the next number in the sequence; for example 4 is the common ratio...

Pure Maths A Level Questions and Answers 100% Pass Gradient y2-y1/x2-x1 Length of a line sqrt((x2-x1)^2+(y2-y1)^2) Midpoint (x1+x2/2, y1+y2/2) How do you know if two lines are perpendicular? When you multiply the gradients together they should equal -1. The general rule is perpendicular = -1/m. Or you could use Pythagoras to show there is a right angle How do you know if two lines are parallel? The gradients should be the same What should you always remember when finding the square roots? T...

Edexcel A Level Maths – Pure A+ Graded 100% Verified Natural Numbers ANS: The set of numbers 1, 2, 3, 4, ... Also called counting numbers. Integers ANS: The set of whole numbers and their opposites Z⁺ Z⁺₀ Rational Number ANS: set of all numbers that can be written as a fraction of two integers Q irrational numbers ANS: Numbers that can't be written as a fraction... examples √2 and π Universal Set ANS: A set that includes all the objects being discussed. - Ex...

Points of Inflection - ANSWER-If (c, f(c)) is a point of inflection of the graph of f, then either f"(c)=0 or f" is undefined at c Critical Value - ANSWER-Where first derivative is 0 or undefined Find absolute extrema - ANSWER-Use critical values and END POINTS in the function Horizontal Asymptote Rules - ANSWER-If m>n: NO HA If m=n: HA = co-eff of m/co-eff of n If m<n: HA: y = 0 Mean Value Theorem - ANSWER-if f(x) is continuous on [a,b] and differentiable on (a,b), there i...

MAT 101 MH V6 GRADED EXAM 4. COLLEGE ALGEBRA Question 1 Correct 8.75 points out of 8.75 Flag question Question text Determine the vertical asymptote(s) of the graph of the function. f (x) = xx2+81xx2+81 Select one: a. x = 9 and x = 0 b. x = 9 and x = -9 c. x = 9 d. None Question 2 Correct 8.75 points out of 8.75 Flag question Question text a. Identify the horizontal asymptote (if any). b. If the graph of the function has a horizontal asymptote, determine the point where the ...

Suppose that w and t vary inversely and that t=1/5 when w=4. Write a function that models the inverse variation, and find t when w=9. - t=4/5w; 4/45 Suppose that y varies directly with x and inversely with z, and y=18 when x=15 and z=5. Write the equation that models the relationship. Then find y when x=21 and z=7. - y=6x/z; 18 Graph the function y=13/6x - Graph C Sketch the asymptotes, and graph the function y= 5/(x-2) +3 - Graph C This graph of a function is translation of y=4/x. what is...