What is the range of a function?

The set of all outputs the function produces (y-values).

How is \{x\in\mathbb{R}:x2\} read?

All real numbers x such that x is greater than 2.

Does x\geq3 include 3?

Yes. \geq includes the end value; does not.

Range of the mapping 1\to3,\ 2\to5,\ 3\to3?

\{3,5\}, because a repeated output is listed once.

How do you find the range of f(x)=3x+1 on 0\leq x\leq2?

Evaluate at both ends: f(0)=1 and f(2)=7, so 1\leq f(x)\leq7.

Why check the vertex when finding a quadratic's range on a restricted domain?

The vertex may lie inside the domain and give the greatest or least value.

How do you find the vertex of a quadratic?

Complete the square, or find the point halfway between the roots.

Domain and rangeIB MYP Maths Extended: Flashcards

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What is the domain of a function?

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What is the domain of a function?: The set of all allowed inputs ( $x$ -values).
What is the range of a function?: The set of all outputs the function produces ( $y$ -values).
How is $\{x\in\mathbb{R}:x>2\}$ read?: All real numbers $x$ such that $x$ is greater than $2$ .
What does $\mathbb{R}$ stand for?: The set of real numbers.
Does $x\geq3$ include $3$ ?: Yes. $\geq$ includes the end value; $>$ does not.
Range of the mapping $1\to3,\ 2\to5,\ 3\to3$ ?: $\{3,5\}$ , because a repeated output is listed once.
Domain of $\frac{1}{x+4}$ ?: All real $x$ except $x=-4$ .
Domain of $\sqrt{x-1}$ ?: $x\geq1$
Range of $\sqrt{x}$ ?: $y\geq0$
Range of $f(x)=x^2+2$ for all real $x$ ?: $f(x)\geq2$
How do you find the range of $f(x)=3x+1$ on $0\leq x\leq2$ ?: Evaluate at both ends: $f(0)=1$ and $f(2)=7$ , so $1\leq f(x)\leq7$ .
Why check the vertex when finding a quadratic's range on a restricted domain?: The vertex may lie inside the domain and give the greatest or least value.
How do you find the vertex of a quadratic?: Complete the square, or find the point halfway between the roots.

Exam questions on Domain and range

A function is defined by $f(x)=2x-3$ , where $x$ is a real number and $-1\leq x\leq4$ .
The domain of $f$ is restricted so that $f(x)\geq0$ . Find the new domain.2 marks
Consider the functions $h(x)=\sqrt{x+3}$ and $k(x)=\dfrac{4}{x-5}$ . Each function has the largest possible domain of real numbers.
State the range of $h$ and give a reason.2 marks
A quadratic function is defined by $f(x)=x^2-6x+5$ .
By completing the square, find the coordinates of the lowest point of the graph, and hence state the range of $f$ when its domain is all real numbers.3 marks

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Written by the Exaim team, led by Shaun Daswani (Head of Upper Secondary, Improve ME Institute; MSc Financial Mathematics, Imperial College London; BSc, UCL) and Jason Daswani (operational lead, Improve ME Institute; LSE).