Introduction to Functions Flashcards

All 6 cards in this deck

In function notation, what does $f(3)$ mean?

The output of the function $f$ when the input $x$ is $3$.
e.g. if $f(x)=2x+1$ then $f(3)=7$.

How do you evaluate $f(-3)$ for a given function?

e.g. $f(x)=2x^2$

Substitute $-3$ in place of every $x$, keeping the negative in brackets.
$f(-3)=2\times(-3)^2=18$

What are the steps to solve $f(x)=k$ for $x$?

e.g. solve $f(x)=11$ where $f(x)=2x+3$

1. Write the equation: $2x+3=11$
2. Solve using inverse operations: $2x=8$
3. Give $x$: $x=4$

For which value of $x$ is a function of the form $f(x)=\frac{a}{x-b}$ undefined?

e.g. $f(x)=\frac{5}{x-2}$

$x=b$, because the denominator would be $0$.
Here $x=2$.

True or false? $f(x+2)$ means the same as $f(x)+2$.

False. $f(x+2)$ means substitute $x+2$ as the input; $f(x)+2$ means add $2$ to the output.

True or false? In $f(x)=3x^2$, writing $f(4)$ means $f$ multiplied by $4$.

False. $f(4)$ means the value of the function when the input is $4$, not a multiplication.