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IB Maths AA SL 2.4 Key Graph Features

IB Maths AA SL 2.4 Key Graph Features
IB Mathematics: analysis and approaches guide, first assessment 2021

Practise determining intercepts, roots, vertices, extrema, symmetry, range and asymptotes algebraically or with technology, including intersections of curves and lines.

How this is tested

  • solve f(x) = 0 and evaluate f(0) to state intercepts as complete coordinate pairs
  • read or calculate vertices, extrema, symmetry and asymptotes while respecting the stated domain
  • use a graphical intersection or distance condition to determine a required point or parameter

Question 9

[Maximum number: 7]

The function f is defined by f(x)=5ex−e2xex+1f(x)=\frac{5 \mathrm{e}^{x}-\mathrm{e}^{2 x}}{\mathrm{e}^{x}+1}. The following diagram shows part of the graph of f. The graph intersects the y-axis at point P and intersects the x-axis at point R . Point Q is a local maximum point with coordinates (q,7−26)(q, 7-2 \sqrt{6}).

Figure for Question 9 — IB Maths AA SL

Question 9(a)(i)

(a)

Find the coordinates of point P .

Question 9(a)(ii)

(b)

Find the coordinates of point R .

[ 6 ]

Question 9(b)

(c)

State the range of f.

[ 1 ]