IB Mathematics Applications & Interpretation Topic SL…

The function $f$ is defined by $f(x) = 2x^3 + 5$ , $-2 \le x \le 2$ .

(a) Write down the range of $f$ .

(b) Find an expression for $f^{-1}(x)$ .

Over one day, harbour water depth $h$ is modelled linearly between $(0,10)$ , $(6,16)$ , $(14,8)$ and $(24,14)$ , where time is in hours after midnight and depth is in metres. A vessel needs sufficient depth and clearance below a bridge; it can pass only when $11\leq h\leq13$ .

(a) the piecewise linear graph, labelling every turning point and the gradient of each segment.

An actuator uses a signed input $x\in[-3,3]$ and returns response $r(x)$ in response units according to

$r(x)=\begin{cases}2x+4,&-3\leq x\lt-1,\\x^2-2,&-1\leq x\leq1,\\4-2x,&1\lt x\leq3.\end{cases}$

A production model expresses two cost components, in thousands of dollars, as $f(x)=\frac2x$ and $g(x)=x$ , where $x$ is production in hundreds of units and $0\lt x\leq5$ . Total cost is $s(x)=f(x)+g(x)$ .

A parking garage charges $\text{＄}3$ for each started hour. Thus $C(0)=0$ and $C(t)=3n$ for $n-1\lt t\leq n$ , where $n=1,2,3,4$ and $t$ is measured in hours.

(b) every time at which the depth is $12$ m and hence why “time as a function of depth” fails on the complete day.

(a) $y=r(x)$ on a set of axes, showing all open and closed endpoints and both jumps.

(b) the range of $r$ and all inputs that produce response $-1$ .

(c) A domain restriction must be a closed interval containing $x=0$ and one endpoint of the original domain. whether such a restriction can both preserve the complete range and make $r$ one-to-one.

(a) $f$ and $g$ , and their point of intersection.

(b) the graph of $s(x)=f(x)+g(x)$ and its minimum point using technology.

(c) Hence all production settings $x$ for which the total cost is at most 3 thousand dollars. why multiplying the inequality by $x$ does not reverse its direction.

(a) the graph of $C$ for $0\leq t\leq4$ on a set of axes, showing every open and closed endpoint.

(b) A rival charges continuously according to $L(t)=3t$ . Add its graph and all times at which the two charges are equal.

IB Mathematics Applications & Interpretation SL 2.3—graph of a Function Questionbank

IB Mathematics Applications & Interpretation SL 2.3—graph of a Function Questionbank

IB Mathematics Applications & Interpretation SL 2.3—graph of a Function Questionbank

IB Mathematics Applications & Interpretation SL 2.3—graph of a Function Questionbank

IB Mathematics Applications & Interpretation (AI) Topic SL 2.3—graph of a Function Questionbank