IB Mathematics Analysis and Approaches Functions

Question Type 1: Finding the equation of a straight line using a point and a y-intercept

Question Type 2: Finding the equation of a straight line using a point and a gradient

Question Type 3: Converting between different forms

Question Type 4: Finding the gradient using two points

Question Type 5: Using two points to find the equation of a line and the y-intercept

Question Type 6: Identifying whether two lines are perpendicular, parallel or none

Question Type 7: Finding a parallel line and perpendicular line passing through specific point for a given line

Question Type 1: Finding the value of a function

Question Type 2: Determining if a specific relation is a function

Question Type 3: Finding the domain of different simple functions

Question Type 4: Finding the domain of more complex functions

Question Type 5: Finding the range of different simple functions

Question Type 6: Finding the range of more complex functions

Question type 7: Determining whether the function has an inverse in the respective domains

Question Type 8: Solving questions with the values of inverses

Question Type 1: Graphing functions

Question Type 1: Finding x- and y-intercepts

Question Type 2: Finding points of intersection of two straight lines

Question Type 3: Finding points of intersection of two more difficult functions

Question Type 1: Finding composite functions given two simple functions

Question Type 2: Finding composite functions of two more complex functions

Question Type 3: Finding inverses for simple functions

Question Type 4: Finding inverses for functions that require multiple manipulations

Question Type 1: Computing the vertex and the y-intercept for quadratics

Question Type 2: Factorizing to get from ax^2 + bx + c to a(x-p)(x-q)

Question Type 3: Using vertex to factorize ax^2+bx+c into vertex form

Question Type 4: Finding roots of quadratics by converting into a(x-p)(x-q) and equating to 0

Question Type 5: Finding roots of quadratics by converting into vertex form and solving for square root

Question Type 1: Finding solutions to quadratic equations by turning into ax^2+bx+c=0 and solving for x

Question Type 2: Finding solutions to quadratic inequalities by converting into ax^2+bx+c > or < 0 and checking intervals

Question Type 3: Finding how many roots the quadratic has

Question Type 4: For a quadratic dependent on a parameter, finding the value of the parameter that results in either situation of roots

Question Type 1: Finding the horizontal and vertical asymptotes of simple rational functions

Question Type 2: Given asymptotes and relations between variables, coming up with the rational equation

Question Type 3: Graphing different rational functions, including the intercepts and the asymptotes

Question Type 1: Drawing exponential functions and indicating their asymptotes

Question Type 2: Drawing logarithmic functions as inverses of the exponential functions

Question Type 3: Finding domain and range of logarithmic and exponential functions

Question Type 4: Finding the inverses of logarithmic and exponential functions

Question Type 1: Constructing simple graphs to solve equations

Question Type 2: Solving for x more difficult equations

Question Type 3: Solving using solver mode

Question Type 4: Solving using graph function

Question Type 1: Drawing the effect of single transformations on a graph

Question Type 2: Determining whether two transformations are the same effect wise

Question Type 3: Given a description of transformations, finding the appropriate transformed function

Question Type 4: Creating a description explaining function transformations

Question Type 5: Drawing the effect of multiple transformations on a graph

Question Type 1: Finding factors of a polynomial using factor theorem

Question Type 2: For small polynomials, given a remainder or factor, finding a parameter's value

Question Type 3: Finding several parameter values given remainder and/or factors

Question Type 4: Given a polynomial, finding the sum and products of roots

Question Type 5: Finding possible values of parameters given the sum and product of roots

Question Type 1: Finding the asymptotes and intercepts of rational functions of the form f(x)=(ax+b)/(cx^2+dx+e)

Question Type 2: Graphing functions for different pairs of a,b,c in (x+a)/(x+b)(x+c) to test different looks of graphs

Question Type 3: Applying polynomial division for rational functions

Question Type 4: Finding the asymptotes and intercepts of rational functions of the form f(x)=(ax^2+bx+c)/(dx+e)

Question Type 1: Verifying whether some simple functions are odd or even or neither

Question Type 2: Finding parameter values such that a function is odd or even or neither

Question Type 3: Graphing odd, even or neither functions

Question Type 4: Finding the inverse with domain restriction

Question Type 5: Finding the inverse of more complex equations and restrictions on the domain

Question Type 6: Showing whether a function is self-inverse or not

Question Type 7: Finding for what value of a given parameter is a function self-inverse

Question Type 1: Graphing simple polynomials up to the 3rd degree

Question Type 2: Solving polynomial inequalities analytically

Question Type 3: Using calculator to graph equations and find solutions to inequalities

Question Type 1: Graphing equations with the absolute value of the whole function

Question Type 2: Solving equations with the absolute value of the whole function

Question Type 3: Graphing equations with the absolute values on the x only

Question Type 4: Solving absolute value equations by considering all possible conditions