IB Mathematics Analysis and Approaches Topic AHL…

Let $a$ be a positive real number.

(a) Solve the inequality $|x-3| < 2x$ .

(b) Show that the solution of $|x-a| < 2x$ is $x > \frac{a}{3}$ .

(e) On a separate set of axes, the graph of $y = f(|x|)$ , indicating all $x$ -intercepts, the $y$ -intercept and any turning points.

The function $f$ is defined by $f(x) = x^2 - 4x$ for $x \in \mathbb{R}$ .

(a) Find the $x$ -intercepts and the coordinates of the vertex of $y = f(x)$ .

(d) Solve the equation $[f(x)]^2 = 4f(x)$ algebraically.

Solve the inequality $|2x - 1| > x + 3$ for $x \in \mathbb{R}$ .

The function $f$ is defined by $f(x) = x^3 - 3x$ for $x \in \mathbb{R}$ .

(a) Find the $x$ -intercepts and the coordinates of the stationary points of $y = f(x)$ .

(c) why $|x-a| < 2x$ has no negative solutions, and verify the general result of part (b) against your answer to part (a).

(b) On the same set of axes, the graphs of $y = f(x)$ and $y = [f(x)]^2$ , indicating clearly the $x$ -intercepts and the $y$ -coordinate of the local maximum of $y = [f(x)]^2$ .

(c) the coordinates of the local minima of $y = [f(x)]^2$ and why these points coincide with the $x$ -intercepts of $f$ .

(b) the graph of $y = |f(x)|$ , clearly showing the $x$ -intercepts and the coordinates of all turning points.

IB Mathematics Analysis and Approaches AHL 2.16—graphing Modulus Equations and Inequalities Questionbank

IB Mathematics Analysis and Approaches AHL 2.16—graphing Modulus Equations and Inequalities Questionbank

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IB Mathematics Analysis and Approaches AHL 2.16—graphing Modulus Equations and Inequalities Questionbank

IB Mathematics Analysis and Approaches AHL 2.16—graphing Modulus Equations and Inequalities Questionbank

IB Mathematics Analysis and Approaches (AA) Topic AHL 2.16—graphing Modulus Equations and Inequalities Questionbank

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