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AHL 2.8—Transformations of graphs, composite transformations - IB Questionbank | RevisionDojo

Practice AHL 2.8—Transformations of graphs, composite transformations with authentic IB Mathematics Applications & Interpretation (AI) exam questions for both SL and HL students. This question bank mirrors Paper 1, 2, 3 structure, covering key topics like core principles, advanced applications, and practical problem-solving. Get instant solutions, detailed explanations, and build exam confidence with questions in the style of IB examiners.

Paper

Level

Question 1

HLPaper 2

The point $A(-1,3)$ lies on the curve $y=f(x)$ .

Find the coordinates of the corresponding point under $y=2 f(x-3)+4$ .

[4]

Question 2

HLPaper 1

The point $A(1,0.5)$ lies on the curve $y=f(x)$ . Write down the coordinates of the corresponding point under the following transformations.

$y=f(x)+5$

[1]

$y=5 f(x)$

[1]

$y=f(x+5)$

[1]

$y=f(5 x)$

[1]

Question 3

HLPaper 2

The quadratic function $f$ is defined by $f(x)=3 x^{2}-12 x+11$

Draw the graph of $f(x)$ for $0 \leq x \leq 4$

[1]

Write function $f$ in the form $f(x)=3(x-h)^{2}+k$

[2]

The graph of $f$ is translated 3 units in the positive $x$ - direction and 5 units in the positive $y$ - direction. Find the function $g$ for the translated graph, giving you answer in the form $f(x)=3(x-p)^{2}+q$

[2]

Question 4

HLPaper 1

Let function $f(x)=\frac{x^{3}}{3}-x^{2}-3 x$ . Part of the graph of $f$ is shown below.

There is a maximum point at $A$ and a minimum point at $B(3,-9)$ . Write down the coordinates of:

The image of $B$ after reflection in the $y$ - axis.

[1]

The image of $B$ after translation by the vector $\binom{-2}{5}$

[1]

The image of $B$ after reflection in the $x$ -axis followed by a horizontal stretch with scale factor $\frac{1}{2}$ .

[1]

Question 5

HLPaper 2

Let $f(x)=3 x^{2}$ . The graph of $f$ is translated 1 units to the right and 2 units down.

The graph of $g$ is the image of the graph of $f$ after this translation.

Write down the coordinates of the vertex of the graph of $g$ .

[2]

Express $g$ in the form $g(x)=3(x-p)^{2}+q$

[1]

Write down the coordinates of the vertex of the graph of $h$ .

[1]

Question 6

HLPaper 2

Let function $f(x)=2 x+1$

Draw the graph of $f(x)$ for $0 \leq x \leq 2$

[1]

Let $g(x)=f(x+3)-2$ , draw the graph of $g(x)$ for $-3 \leq x \leq-1$

[2]

Question 7

HLPaper 2

The graph of the function $y=f(x), 0 \leq x \leq 4$ , is shown below.

Find the value of $f(1)$ and $f(3)$

[2]

Sketch the graph of $y=3 f(-x)$

[1]

Sketch the graph of $y=f(2 x)$

[1]

Write down domain and range of $y=3 f(-x)$ and $y=f(2 x)$ .

[4]

Question 8

HLPaper 2

Let $f(x)=x^{2}$ and $g(x)=2(x-1)^{2}$ .

The graph of $g$ can be obtained from the graph of $f$ using two transformations. Give a full geometric description of each of the two transformations.

[2]

The graph of $g$ is translated by the vector $\binom{3}{-2}$ to give the graph of $h$ The point ( $-1,1$ ) on the graph of $f$ is translated to the point $P$ on the graph of $h$ . Find the coordinates of $P$ .

[3]

Question 9

HLPaper 2

The graph of a function $f$ is shown in the diagram below.

On the same diagram, sketch the graph of $y=-f(x)$

[1]

Find $g(-3)$

[2]

Describe fully the transformation that maps the graph of $f$ to the graph of $g$ .

[1]

Question 10

HLPaper 2

Let $f(x)=x^{2}+4$ and $g(x)=x-1$

Find $(f \circ g)(x)$

[1]

The vector $\binom{3}{-1}$ translates the graph of $(f \circ g)(x)$ to the graph of $h$ Find the coordinates of the vertex of the graph of $h$ .

[3]

Show that $h(x)=x^{2}-8 x+19$

[1]

The line $y=2 x-6$ is a tangent to the graph of $h$ at the point $P$ . Find the $x$ -coordinate of $P$ .

[2]

The line $y=2 x-5$ intersects the graph of $h$ at two points. Find the coordinates of the two points of intersection.

[3]

AHL 2.8—Transformations of graphs, composite transformations Questionbank