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Horizontal translation - MYP Questionbank | RevisionDojo

Practice Horizontal translation with authentic MYP MYP Extended Mathematics 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 MYP examiners.

Type

Difficulty

Question 1

Let $g(x) = f(x-2)$ . If the point $(5, 10)$ lies on the graph of $y = g(x)$ , which point must lie on the graph of $y = f(x)$ ?

Question 2

Given the parent exponential function $f(x) = 2^x$ , which of the following describes the graph of the function $g(x) = 2^{x-3}$ ?

Question 3

If the graph of ${y = f(x)}$ is symmetric about the line ${x = 0}$ (indicating an even function), what is the equation of the line of symmetry for the transformed graph ${y = f(x - 5)}$ ?

Question 4

Given that $f(3) = 10$ , for which value of $x$ does the function

g(x) = f(x-5)+2

produce an output of $12$ ?

Question 5

Which of the following transformations of the coordinate axes is equivalent to translating the graph of $y = f(x)$ by 3 units to the right while keeping the graph stationary?

Question 6

The function $f(x) = \frac{1}{x}$ has a vertical asymptote at $x = 0$ . If the graph is transformed into $y = f(x+4)$ , determine the equation of the new vertical asymptote.

Question 7

Describe the transformations required to move the graph of $y=f(x)$ to the graph of

$y = f(x + 3) - 2$

Question 8

The vertex of the parabola $y = a(x - h)^2 + k$ is located at $(h, k)$ . What are the coordinates of the vertex for the transformed parabola $y = a(x - h + 3)^2 + k$ ?

Question 9

If the point $(a, b)$ lies on the graph of $y = f(x)$ , which coordinates represent the corresponding point on the graph of $y = f(x + h) - k$ ?

Question 10

A quadratic function is defined as $f(x) = (x-2)^2 + 5$ . A horizontal translation is applied to create the function

g(x) = (x+3)^2 + 5

Describe the translation that occurred.

Type

Difficulty

Question 1

Let $g(x) = f(x-2)$ . If the point $(5, 10)$ lies on the graph of $y = g(x)$ , which point must lie on the graph of $y = f(x)$ ?

Question 2

Given the parent exponential function $f(x) = 2^x$ , which of the following describes the graph of the function $g(x) = 2^{x-3}$ ?

Question 3

If the graph of ${y = f(x)}$ is symmetric about the line ${x = 0}$ (indicating an even function), what is the equation of the line of symmetry for the transformed graph ${y = f(x - 5)}$ ?

Question 4

Given that $f(3) = 10$ , for which value of $x$ does the function

g(x) = f(x-5)+2

produce an output of $12$ ?

Question 5

Which of the following transformations of the coordinate axes is equivalent to translating the graph of $y = f(x)$ by 3 units to the right while keeping the graph stationary?

Question 6

The function $f(x) = \frac{1}{x}$ has a vertical asymptote at $x = 0$ . If the graph is transformed into $y = f(x+4)$ , determine the equation of the new vertical asymptote.

Question 7

Describe the transformations required to move the graph of $y=f(x)$ to the graph of

$y = f(x + 3) - 2$

Question 8

The vertex of the parabola $y = a(x - h)^2 + k$ is located at $(h, k)$ . What are the coordinates of the vertex for the transformed parabola $y = a(x - h + 3)^2 + k$ ?

Question 9

If the point $(a, b)$ lies on the graph of $y = f(x)$ , which coordinates represent the corresponding point on the graph of $y = f(x + h) - k$ ?

Question 10

A quadratic function is defined as $f(x) = (x-2)^2 + 5$ . A horizontal translation is applied to create the function

g(x) = (x+3)^2 + 5

Describe the translation that occurred.

Type

Difficulty

Question 1

Let $g(x) = f(x-2)$ . If the point $(5, 10)$ lies on the graph of $y = g(x)$ , which point must lie on the graph of $y = f(x)$ ?

Question 2

Given the parent exponential function $f(x) = 2^x$ , which of the following describes the graph of the function $g(x) = 2^{x-3}$ ?

Question 3

If the graph of ${y = f(x)}$ is symmetric about the line ${x = 0}$ (indicating an even function), what is the equation of the line of symmetry for the transformed graph ${y = f(x - 5)}$ ?

Question 4

Given that $f(3) = 10$ , for which value of $x$ does the function

g(x) = f(x-5)+2

produce an output of $12$ ?

Question 5

Which of the following transformations of the coordinate axes is equivalent to translating the graph of $y = f(x)$ by 3 units to the right while keeping the graph stationary?

Question 6

The function $f(x) = \frac{1}{x}$ has a vertical asymptote at $x = 0$ . If the graph is transformed into $y = f(x+4)$ , determine the equation of the new vertical asymptote.

Question 7

Describe the transformations required to move the graph of $y=f(x)$ to the graph of

$y = f(x + 3) - 2$

Question 8

The vertex of the parabola $y = a(x - h)^2 + k$ is located at $(h, k)$ . What are the coordinates of the vertex for the transformed parabola $y = a(x - h + 3)^2 + k$ ?

Question 9

If the point $(a, b)$ lies on the graph of $y = f(x)$ , which coordinates represent the corresponding point on the graph of $y = f(x + h) - k$ ?

Question 10

A quadratic function is defined as $f(x) = (x-2)^2 + 5$ . A horizontal translation is applied to create the function

g(x) = (x+3)^2 + 5

Describe the translation that occurred.

Horizontal translation Questionbank