then reload this page.
In this lesson, you will learn about functions: rules which assign
outputs to inputs.
A function is a rule which assigns a
single output ($y$-value) to each of its inputs ($x$-values). Not every number needs to be
a possible input.
The table below gives an example of a function. The $(x,y)$ values shown in the table
are also plotted on the grid to the left.
Click . Now the $(x,y)$ values shown in the
next table below are plotted on the grid to the left.
In table-qn, you looked at a function where the rule was
given by a table. You can also use a graph to give the rule for a function. The graph plotted
on the grid to the left is an example of this.
You can click inside the grid and drag the vertical bar around to see the $y$-value
corresponding to each $x$-value, under the words “Trace at:” to the right of the grid. For
example, you can set the vertical bar to $x=2$. Then the information to the right of the grid
will tell you that the function assigns the output 4 to the input 2.
Click to see another graph plotted on the
grid to the left.
Another way to give a rule is to use a
formula. For example, there is a function that takes each input $x$
and assigns to it the output $2x-3$. If you give it the input $1$, it produces the output
Each row of the table below gives an input to this function. Enter the corresponding
Click to see the entire graph of this
function. This is the graph of $y=2x-3$, so it is a straight line.
The function which assigns the output $-x+2$ to the input $x$ is
graphed on the grid to the left.
A function whose output always increases as its input increases is called an
increasing function. A function whose output always decreases as its
input increases is called a decreasing function.
A function whose graph is a straight line (that is, a function given by a formula
of the form $mx+b$) is called a linear function.
A function is increasing whenever its graph goes up and to the right.
It is decreasing whenever its graph goes down and to the right.
A linear function is increasing whenever the slope of its graph is positive. It is decreasing
whenever the slope of its graph is negative.
A ball is dropped from a window 30 meters above the ground. We will study the
function whose input is the number of seconds $t$ since the ball was dropped, and whose output
is the height of the ball $\cl"red"h$ above the ground (in meters). This function is graphed on
the grid to the left.
A catapult shoots a pumpkin into the air. The function whose input is the number
of seconds $t$ since the pumpkin was released, and whose output is the height of the pumpkin
$\cl"red"h$ above the ground in meters, is graphed on the grid to the left.