Building blocks

## Problem

For some of the following functions, work out the values of $f(1)$, $f(-1)$, $f(2)$, $f(-2)$, and so on.

• $f(x)=x^2$

• $f(x)=2$

• $f(x)=1-x^2$

• $f(x)=x^4+2$

• $f(x)=1-\dfrac{1}{x^2}$

• $f(x)=x^2-2x+2$

What did you notice as you worked out these values?

Now carefully sketch the graphs of the functions on the same set of axes.

On a new set of axes, carefully sketch graphs of the following functions. Again, for some of the functions you may find it helpful to work out $f(1)$, $f(-1)$, $f(2)$, $f(-2)$, and so on. Note down your ideas as you sketch each graph.

• $f(x)=x$

• $f(x)=-\dfrac{1}{x}$

• $f(x)=x^3$

• $f(x)=\dfrac{x^3}{10}$

• $f(x)=x(x-1)(x+1)$

• $f(x)=1+\dfrac{1}{x}$

What did you notice this time?