Question

Find f(-3) of the function, f(x) = {x^3 + 2x^2 - x + 6, x < -3
|-3x - 3|, x >= -3

Answer 1

Hey frog :)
\[\Large f(x)=\cases{x^3+2x^2-x+6, &$x\lt-3$\\ |-3x-3|, &$x\ge-3$}\]

Answer 2

With a piece-wise function we only use ONE PIECE at a time.
So based on which x value they give us, that will tell us which part to use.

Example:
If we wanted to evaluate this function at -4,\[\Large f(x)=\cases{\color{orangered}{x^3+2x^2-x+6,} &$x\lt-3$\\ |-3x-3|, &$x\ge-3$}\]We would use this piece, `because this is the piece we use when our x value is less than -3`

Answer 3

So in that example we would get:\[\Large\rm f(-4)=(-4)^3+2(-4)^2-(-4)+6\]Which simplifies to something..

Answer 4

If we want to evaluate this function at -3,
which piece do you think we should use?
Which part has an "or equal to" for the point -3?

Answer 5

The second part?

Answer 6

So: |-3(-3) - 3| = |9 - 3| = |6| = 6
?

Answer 7

@zepdrix

Answer 8

Yayyyy good job \c:/

Answer 9

thanks!