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Rational functions - MYP Questionbank | RevisionDojo

Practice Rational functions 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

Which of the following best describes a rational function $R(x)$ ?

Question 2

True or False: For a rational function $f(x) = \frac{a}{x-h} + k$ , if $a > 0$ , the function is strictly decreasing on both of its disjoint domain intervals $(-\infty, h)$ and $(h, \infty)$ .

Question 3

True or False: The lines $y - k = x - h$ and $y - k = -(x - h)$ are lines of symmetry for the graph of the rational function $$ f(x) = \frac{a}{x-h} + k

Question 4

Find the $x$ -intercept of the rational function

f(x) = \frac{6}{x-2} + 3

Question 5

For the rational function $f(x) = \frac{a}{x-h} + k$ where $a \neq 0$ , which condition ensures that the graph has no $x$ -intercept?

Question 6

For the function $f(x) = \frac{5}{x-1} + 2$ , at which value of $x$ does the graph intersect its own horizontal asymptote?

Question 7

The rational function $f(x) = \frac{2x+5}{x-1}$ can be rewritten in the form $f(x) = \frac{a}{x-h} + k$ . Determine the value of the parameter $a$ .

Question 8

For the transformed reciprocal function $f(x) = \frac{a}{x-h} + k$ , where $a, h, k \in \mathbb{R}$ and $a \neq 0$ , identify the value that is excluded from the range of the function.

Question 9

Consider the following statement:

"Increasing the value of the parameter $a$ in the function $f(x) = \frac{a}{x-h} + k$ will cause the vertical asymptote to shift to the right."

Determine whether the statement is true or false and identify the correct reasoning.

Question 10

Determine the domain of the inverse function $f^{-1}(x)$ for the function defined by $f(x) = \frac{1}{x-4} + 2$ .

Type

Difficulty

Question 1

Which of the following best describes a rational function $R(x)$ ?

Question 2

True or False: For a rational function $f(x) = \frac{a}{x-h} + k$ , if $a > 0$ , the function is strictly decreasing on both of its disjoint domain intervals $(-\infty, h)$ and $(h, \infty)$ .

Question 3

True or False: The lines $y - k = x - h$ and $y - k = -(x - h)$ are lines of symmetry for the graph of the rational function $$ f(x) = \frac{a}{x-h} + k

Question 4

Find the $x$ -intercept of the rational function

f(x) = \frac{6}{x-2} + 3

Question 5

For the rational function $f(x) = \frac{a}{x-h} + k$ where $a \neq 0$ , which condition ensures that the graph has no $x$ -intercept?

Question 6

For the function $f(x) = \frac{5}{x-1} + 2$ , at which value of $x$ does the graph intersect its own horizontal asymptote?

Question 7

The rational function $f(x) = \frac{2x+5}{x-1}$ can be rewritten in the form $f(x) = \frac{a}{x-h} + k$ . Determine the value of the parameter $a$ .

Question 8

For the transformed reciprocal function $f(x) = \frac{a}{x-h} + k$ , where $a, h, k \in \mathbb{R}$ and $a \neq 0$ , identify the value that is excluded from the range of the function.

Question 9

Consider the following statement:

"Increasing the value of the parameter $a$ in the function $f(x) = \frac{a}{x-h} + k$ will cause the vertical asymptote to shift to the right."

Determine whether the statement is true or false and identify the correct reasoning.

Question 10

Determine the domain of the inverse function $f^{-1}(x)$ for the function defined by $f(x) = \frac{1}{x-4} + 2$ .

Type

Difficulty

Question 1

Which of the following best describes a rational function $R(x)$ ?

Question 2

True or False: For a rational function $f(x) = \frac{a}{x-h} + k$ , if $a > 0$ , the function is strictly decreasing on both of its disjoint domain intervals $(-\infty, h)$ and $(h, \infty)$ .

Question 3

True or False: The lines $y - k = x - h$ and $y - k = -(x - h)$ are lines of symmetry for the graph of the rational function $$ f(x) = \frac{a}{x-h} + k

Question 4

Find the $x$ -intercept of the rational function

f(x) = \frac{6}{x-2} + 3

Question 5

For the rational function $f(x) = \frac{a}{x-h} + k$ where $a \neq 0$ , which condition ensures that the graph has no $x$ -intercept?

Question 6

For the function $f(x) = \frac{5}{x-1} + 2$ , at which value of $x$ does the graph intersect its own horizontal asymptote?

Question 7

The rational function $f(x) = \frac{2x+5}{x-1}$ can be rewritten in the form $f(x) = \frac{a}{x-h} + k$ . Determine the value of the parameter $a$ .

Question 8

For the transformed reciprocal function $f(x) = \frac{a}{x-h} + k$ , where $a, h, k \in \mathbb{R}$ and $a \neq 0$ , identify the value that is excluded from the range of the function.

Question 9

Consider the following statement:

"Increasing the value of the parameter $a$ in the function $f(x) = \frac{a}{x-h} + k$ will cause the vertical asymptote to shift to the right."

Determine whether the statement is true or false and identify the correct reasoning.

Question 10

Determine the domain of the inverse function $f^{-1}(x)$ for the function defined by $f(x) = \frac{1}{x-4} + 2$ .

Rational functions Questionbank