If the graph of y=|x| is compressed vertically by a factor of 1/3, reflected about the x-axis and translated 3 unit(s) left and 5 unit(s) up, what is the equation of the new graph?

Y= -1/3 |x+3| +5

Step-by-step explanation:

An absolute value will always make a V line.

In your particular problem it wants you to reflect it over the x axis, and to do this you simply need to place a negative.

A negative in the beginning of the problem is only there to say whether you flip your line or not, and this means you don't have to worry about it any more.

What it looks like so far: Y= -

Next it wants you to compress the line vertically by 1/3

A number that causes your line to compress is always less than one

A number that stretches your line would be 1 or more

This number is always placed right next to the left of the parenthesis or absolute value.

What it looks like so far: Y= - 1/3

Now we want the line to move left 3 units.

We are now inside of the absolute value because this is where we move the line left or right. This can get a little confusing, but once you get it then you don't forget it.

Inside the line.. a -# moves right and a +# moves left.

This number should be placed inside the absolute value and to the right of the x.

What it should look like: Y= - 1/3 |x + 3|

Now they want us to move the line up by 5 points.

To the outer right side of the absolute value is where we move things up or down.

To move a number up you need to place a + sign with however many places it wants you to move to the right of the sign, but to move the line down you need to place a - sign with however many places it wants you to move to the right of the sign.

To move this up you simply need to place a +5 to the outer right side of the absolute value.

What you should end up with: Y= - 1/3 |x+3| +5

5   1/4   miles per hour

step-by-step explanation:

15   3/4 / 3 = 5   1/4