IB Mathematics Applications & Interpretation Topic SL…

An engineer models the cross-section of a reflector by $r(x)=\frac{3}{2}(x-6)^2+7$ , where and are measured in centimetres.

(a) the derivative $r'(x)$ .

(b) Find the slope of the tangent line at $x=8$ .

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 $f^{-1}(x)$ .

The height of an object is modelled by $h(t)=-t^2+6t+7,\qquad 0\leq t\leq7,$ where $t$ is in seconds and $h$ is in metres.

A dispatch program relabels five route codes in $D=\{-3,-1,0,2,4\}$ . The rule $f$ assigns each old code exactly one new code in $D$ , and each new code is used once. It is known that $f(-3)=2$ , $f(2)=4$ , $f(4)=-1$ and $f^{-1}(0)=-1$ . A fixed point means a code that is unchanged by the rule.

(a) Formulate an equation that relates $p$ and $q$ using the Pythagorean theorem.

(b) Express $q$ as a function of $p$ using the given ratio.

(d) the value of $x$ for which the slope of the tangent is $0$ .

(e) the domain and range of the function $r(x)$ .

(a) the range of $h$ and all times at which the height is 12 metres. Hence why the height model has no inverse function on its stated domain.

(b) The domain must be restricted to an interval on which $h$ is one-to-one while preserving the complete physical range found in part (a). the unique largest such interval.

(c) For this restricted function, $h^{-1}(7)$ and why the other algebraic time must be rejected even though it belongs to the original model.

(a) Reconstruct the complete mapping table for $f$ , explaining how the onto and one-to-one conditions the missing output.

(b) all fixed points of $f$ and find $f^{-1}(2)$ and $f^{-1}(-3)$ .

(c) One of the four displayed facts is replaced by $f^{-1}(0)=0$ . whether the resulting information can still a one-to-one function from $D$ onto $D$ .

A rectangular poster has a diagonal length of 65 cm. Its shape has a width of $p$ cm and a vertical height of $q$ cm.

rectangular poster with width p, height q, and diagonal 65 cm

The aspect ratio of height to width for this poster is 5:12.

IB Mathematics Applications & Interpretation SL 2.2—functions, Domains, Range, Graphs Questionbank

IB Mathematics Applications & Interpretation SL 2.2—functions, Domains, Range, Graphs Questionbank

IB Mathematics Applications & Interpretation SL 2.2—functions, Domains, Range, Graphs Questionbank

IB Mathematics Applications & Interpretation SL 2.2—functions, Domains, Range, Graphs Questionbank

IB Mathematics Applications & Interpretation (AI) Topic SL 2.2—functions, Domains, Range, Graphs Questionbank