IB Mathematics Analysis and Approaches Topic…

Consider the function $f(x)=\ln (2 x-1)-\sin (x)$ , where $x>\frac{1}{2}$ .

(a) the graph of $y=f(x)$ for $0.5<x \leq 4$ , showing the intercepts and the behavior at $x=\frac{1}{2}$ .

(b) Solve the inequality $\ln (2 x-1)<\sin (x)$ .

(e) Solve the inequality $\frac{6|x|^{2}-5|x|-4}{2|x|^{2}-8} \geq \frac{3}{2}$ , for .

A line through $A(-4,3)$ with gradient $m$ intersects the curve $C:y=x^2+8x$ at points $P$ and $Q$ .

(a) Show the $x$ -coordinates of the intersections satisfy:

x^2+(8-m)x+(-4m-3)=0.

(b) Show that the line intersects $C$ at two distinct points for every real value of $m$ .

(d) Given that $PQ=11$ , find the possible values of $m$

The graph of $y=f(x)$ is shown below. The points $(-1,0)$ and $(3,0)$ lie on the graph, with a minimum at $(1,-2)$ .

(b) The point $B(-1,0)$ is on the graph of $f$ . Find the coordinates of the corresponding point on the graph of $y=f(x+3)$ .

Consider the rational function $f(x)=\frac{6 x^{2}-5 x-4}{2 x^{2}-8}$ , where $x \in \mathbb{R}, x \neq \pm 2$ . The graph of $y=f(x)$ has a local minimum at point P and a local maximum at point Q.

(a) Express $f(x)$ in the form $\frac{a(x-b)(x-c)}{(x-d)(x-e)}$ , where $a, b, c, d, e \in \mathbb{R}$ .

(a) the graph of $y=\frac{1}{2}f(x)$ on the diagram below.

(b) the equations of the vertical and horizontal asymptotes of the graph of $y=f(x)$ .

(d) Using a graphical calculator, find the coordinates of the local minimum at P and the local maximum at Q, and hence the range of $f(x)$ .

IB Mathematics Analysis and Approaches Functions Questionbank

IB Mathematics Analysis and Approaches Functions Questionbank

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IB Mathematics Analysis and Approaches Functions Questionbank

IB Mathematics Analysis and Approaches Functions Questionbank

IB Mathematics Analysis and Approaches (AA) Topic Functions Questionbank

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