Functions Toolkit Flashcards

All 5 cards in this deck

What is a function?

A rule that assigns exactly one output to each input value of $x$.
e.g. $f(x) = x^2 - 9$

What is the domain of a function?

The set of input values $x$ that the function is defined for.
e.g. $f(x)=\frac{1}{x}$ has domain all $x$ except $x=0$

What are the steps to evaluate a function at a given value?
e.g. $f(x) = x^2 - 9$, work out $f(4)$

1. Replace every $x$ with the value: $4^2 - 9$
2. Work it out: $16 - 9 = 7$

What are the steps to solve $f(x) = k$ for $x$?
e.g. $f(x) = 2x + 1$, solve $f(x) = -5$

1. Set the expression equal to the value: $2x + 1 = -5$
2. Solve the equation: $2x = -6$, so $x = -3$

What are the steps to work out the range of a function over a given domain?
e.g. $f(x) = x^2 + 1$ for $1 \le x \le 7$

1. Substitute the endpoints of the domain: $f(1) = 2$, $f(7) = 50$
2. Check if a turning point lies inside the domain ($x = 0$ is not in $1 \le x \le 7$)
3. State the range, smallest value first: $2 \le f(x) \le 50$