Question

For the piecewise function defined as:
(I'll attach an image below)
a.) Evaluate f(-2)
b.) graph f(x)

Answer 1

Hey Ria c: So which part we stuck on?
Both?\[\Large\rm f(x)=\cases{3x-2, &$x\le1$\\ \rm \frac{1}{2}x^3, &$x\gt1$}\]

Answer 2

Hi! ^.^
Yes... The fist one, I was thinking I plug in -2 for x, but I wasn't sure...

Answer 3

So your function is piece-wise.
It's two different functions, but never both at the same time.

f(-2) corresponds to x=-2.
When x is -2, which part should we use? The top line or the bottom?
(Read the restrictions to the right of each piece, after the commas)

Answer 4

-2 is `less than` 1.
Which inequality is going to hold true? :o

Answer 5

Uh... The first one?

Answer 6

Mmm good good \(\Large\rm -2\le1\).

Answer 7

\[\Large\rm f(-2)=\cases{\color{orangered}{3(-2)-2, }&$x\le1$\\ \rm \frac{1}{2}x^3, &$x\gt1$}\]

Answer 8

So what do we get for f(-2)? :o

Answer 9

Maybe it would make more sense to look at the first line instead of the entire function since we're dealing with x=-2:
\[\Large\rm f(x)=3(x)-2, \qquad \qquad x\le1\]\[\Large\rm f(-2)=3(-2)-2, \qquad \qquad x\le1\]

Answer 10

So whatchu get? :d

Answer 11

\[-8, x \le 1\]

Answer 12

f(-2)= -8

Ok good c:

Answer 13

Do you know how to graph y=3x-2?

Answer 14

3 is the slope and -2 is the y-intercept, right?

Answer 15

yes

Answer 16

s
Something like this? ;o

Answer 17

Woooooops :O
intercept is `-2` yah?
Not positive 2 silly ! :O

Answer 18

>o< Oh yea...

;o