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Functions - IB Questionbank | RevisionDojo

Practice Functions with authentic IB Mathematics Analysis and Approaches (AA) exam questions for both SL and HL students. This question bank mirrors Paper 1, 2, 3 structure, covering key topics like functions and equations, calculus, complex numbers, sequences and series, and probability and statistics. Get instant solutions, detailed explanations, and build exam confidence with questions in the style of IB examiners.

Paper

Level

Question 1

SLPaper 1

The function is defined as $f(x)=3^{x}+1$ . The graph of $f(x)$ passes through points $A(0, a)$ , $B(1, b)$ , and $C(-1, c)$ .

Find the values of $a, b$ , and $c$ .

[3]

Sketch the graph of $f(x)$ . Indicate the y-intercept, the horizontal asymptote, and the points $A, B$ , and $C$ on the graph.

[3]

Question 2

SLPaper 1

Let $f(x)=\sqrt{x}$ , defined for $x \geq 0$ . The graph of $g$ is obtained from the graph of $f$ by a horizontal stretch by a factor of 2 , followed by a vertical translation of 3 units up.

Express $g(x)$ in terms of $x$ .

[1]

Write down the domain and range of $g$ .

[2]

The point $B(4,2)$ lies on the graph of $f$ . Find the coordinates of the corresponding point on the graph of $g$ .

[2]

Question 3

HLPaper 1

Solve the inequality:

$\sqrt{3 x+4} \leq 4-x, x \geq-\frac{4}{3}$ .

[6]

Question 4

HLPaper 1

Consider the function $f(x)=\frac{3-x}{x+1}$ , where $x \in \mathbb{R}, x \neq-1$ .

Find the coordinates of the points where the graph of $y=f(x)$ intersects the axes.

[3]

Sketch the graph of $y=f(x)$ , clearly showing the asymptotes and the points found in part (a).

[4]

Question 5

SLPaper 1

Let $g(x)=\frac{3 x-6}{x+2}$ , for $x \neq-2$ .

For the graph of $g$ , find the $y$ -intercept.

[2]

Hence or otherwise, write down $\lim _{x \rightarrow \infty}\left(\frac{3 x-6}{x+2}\right)$ .

[2]

Question 6

SLPaper 1

The function $g$ is defined by $g(x)=\frac{4}{x+1}$ , where $x \in \mathbb{R}, x \neq-1$ .

Write down the equation of the vertical asymptote of the graph of $g$ .

[1]

Write down the equation of the horizontal asymptote of the graph of $g$ .

[1]

(i) Find the coordinates where the graph of $g$ crosses the $y$ -axis.

[1]

Find the coordinates where the graph of $g$ crosses the $x$ -axis.

[1]

Sketch the graph of $g$ on the axes below.

[1]

Question 7

SLPaper 1

The function $f$ is defined by $f(x)=\frac{3}{x-2}$ , where $x \in \mathbb{R}, x \neq 2$ .

Write down the equation of the vertical asymptote of the graph of $f$ .

[1]

Write down the equation of the horizontal asymptote of the graph of $f$ .

[1]

Find the coordinates where the graph of $f$ crosses the $y$ -axis.

[1]

Find the coordinates where the graph of $f$ crosses the $x$ -axis.

[1]

Sketch the graph of $f$ on the axes below.

[1]

Question 8

SLPaper 1

Consider the function $f(x)=1-x^{2}$ , for $-2 \leq x \leq 2$ .

Find the values of $x$ for which $f(x)=0$ .

[2]

Sketch the graph of $f$ on the grid provided below.

[3]

Question 9

SLPaper 1

The function j is defined for all x ∈ ℝ. The line with equation y = 6x - 1 is the tangent to the graph of j at x = 4.

Write down the value of j'(4).

[1]

Find j(4).

[1]

The function k is defined for all x ∈ ℝ where k(x) = x² - 3x and m(x) = j(k(x)). Find m(4).

[2]

Hence find the equation of the tangent to the graph of m at x = 4.

[3]

Question 10

SL & HLPaper 1

Consider the quadratic function $f(x) = 2(x - 2)^2 + 4$ .

Describe the transformations applied to the function $y = x^2$ to obtain the function $f(x)$ .

[3]

Given that $x^2\geq f(x)$ under the interval $[2,4]$ , find the area between the curves $y = x^2$ and $f(x) = 2(x - 2)^2 + 4$ within that interval.

[5]

Functions Questionbank