IB Mathematics Analysis and Approaches Topic SL…

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

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

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

The function $f$ is defined by $f(x)=\ln(4x)$ , where $x>0$ .

(e) The graph of $y=f\left(\frac{e^3}{4}x^5\right)$ can be generated through a sequence of a vertical stretch and a vertical translation of the graph of $y=\ln x$ . these two transformations, clearly stating the order in which they should be performed.

The basic function is $f(x)=\sqrt{x}$ for $x\ge 0$ . Define the transformed function $g(x)=3\sqrt{x-4}+1,\quad x\ge 4.$

The graph of $y = \cos x$ is transformed by the following sequence of four transformations.

A horizontal stretch with scale factor $0.8$ , then a translation of $1.6$ units in the positive $x$ -direction.

A vertical stretch with scale factor $2.5$ , then a translation of $3.1$ units in the positive $y$ -direction.

(a) Find the equation of the resulting graph in the form $y = a\cos\left(b(x+c)\right) + d$ .

(b) Write down the period of this graph and the range of the corresponding function.

(d) Find the smallest positive value of $x$ at which this graph meets the line $y = x$ .

The basic function is $f(x)=\sqrt{x}$ for $x\ge 0$ . Define $g(x)=1.5\sqrt{x-8}+2,\quad x\ge 8.$

(a) the exact value of $f\left(\frac{e^4}{4}\right)$ .

(b) the exact value of $f\left(\frac{1}{4}\right)$ .

(d) Using your result from part 3, or otherwise, the value of $f^{-1}(-2)$ .

(a) the transformations that map $y=f(x)$ to $y=g(x)$ .

(b) the domain and range of $g$ .

(d) $k(x)=|g(x)|,\ x\ge 4$ . Using technology, solve $k(x)=x-2$ for $4\le x\le 13$ . Give all solutions correct to 3 d.p.

(a) the transformations mapping $y=f(x)$ to $y=g(x)$ .

(b) the domain and range of $g$ .

IB Mathematics Analysis and Approaches SL 2.11—transformation of Functions Questionbank

IB Mathematics Analysis and Approaches SL 2.11—transformation of Functions Questionbank

IB Mathematics Analysis and Approaches SL 2.11—transformation of Functions Questionbank

IB Mathematics Analysis and Approaches SL 2.11—transformation of Functions Questionbank

IB Mathematics Analysis and Approaches (AA) Topic SL 2.11—transformation of Functions Questionbank