# Thread: Step function Graphing issue

1. ## Step function Graphing issue

Okay, I'm slightly confused. I'm currently in the beginning of my course Algebra 2 /Trig and I can't seem to figure out how to graph this step function

2[[x+5]]

I'm comfortable with rigid transformations, but this seems to be nonrigid?

Help. Thanks.

2. Originally Posted by Skynt
Okay, I'm slightly confused. I'm currently in the beginning of my course Algebra 2 /Trig and I can't seem to figure out how to graph this step function

2[[x+5]]

I'm comfortable with rigid transformations, but this seems to be nonrigid?

Help. Thanks.

I'm afraid your notation means nothing to me. Please explain what [[z]] is
meant to denote. Presumably from the title of this thread it is supposed
to denote the Heaviside unit step function.

RonL

3. Well. it's the Greatest Integer notation I think. I know a function that uses it forms steps on a graph.

4. The greatest integer function is also known as the floor function.

5. i'll try to explain it with this..
consider the graph of
$\displaystyle y = [|x|]$, i assume you know the graph of this basic function..

now, the effects on that graph when you have the general form of the greatest integer function
$\displaystyle y = a[|bx - c|] + d$ is this..

$\displaystyle \frac{1}{b}$ is the length of each step

$\displaystyle \frac{c}{b}$ horizontal shift of the graph

$\displaystyle a$ is the distance between steps.. (because of the effect of this part, the "slope" of the "ladder" is more positive if $\displaystyle a>1$, while the slope approaches to 0 when $\displaystyle 0<a<1$)

$\displaystyle d$ is the value of y when on the interval $\displaystyle \left[ \frac{c}{b},\frac{c + 1}{b} \right)$

thus, from your given $\displaystyle 2[|x + 5|]$,

the graph of $\displaystyle y=[|x|]$ shifts 5 units to the left and the distance between steps is 2..

6. Originally Posted by Skynt
Well. it's the Greatest Integer notation I think. I know a function that uses it forms steps on a graph.
This is the floor function usually written $\displaystyle \lfloor x \rfloor$.

RonL