How is the graph of y = |x| − 1 different from the parent function f(x) = |x|?

We can define transformations as operators that act over functions and modify them in some way. One of these transformations is the family of translations, who translate the whole graph of the function in some given direction.

Here we will find that the graph of y = |x| - 1 is a translation of 1 unit downwards of y = |x|.

To see this, we first need to know the vertical translation.

For a given function f(x), a vertical translation of N units is written as:

g(x) = f(x) + N

If N is positive the translation is upwards

if N is negative the translation is downwards,

So if here we have:

f(x) = |x|

then:

g(x) = |x| - 1 = f(x) - 1

So we can see that this is a translation of one unit down. This moves the whole graph of |x| one unit downwards, the graphs can be seen in the image below.

Where the blue graph is the one of y = |x| - 1

If you want to learn more, you can read:

link

Step-by-step explanation:

the graph moves down one unit

if you add/subtract outside the parent function the graph moves up/down

the ratio of white tiles to blue tiles is 48: 16. the ratio in it's simplest form is 3: 1.

step-by-step explanation:

ratio: take the first number and add a colon next to it, then add the second number after that. make sure the ratio order matches up with the written problem!

simplest form: we can simplify the ratio 48 : 16 by dividing both terms by the greatest common factor (gcf).

the gcf of 48 and 16 is 16.

divide both terms by 16:

48 ÷ 16 = 3

16 ÷ 16 = 1

reducing to simplest form:

48 : 16 = 3 : 1

the least common denominatore of 7 and 2 is 9

step-by-step explanation:

7+2=9