Question

Anyone wanna help with calc?

Answer 1

which calc?

Answer 2

@Thatonegirl_ Do you need help?

Answer 3

if the function f defined by
f(x)={cx+3, x<2
{3x^2-1, x>=2
is continuous everywhere on (-∞,∞), what is the value of f(1)?

Answer 4

Calc BC and yes please

Answer 5

I'm guessing i have to solve for c, but how?

Answer 6

This function is defined with 2 parts: for x values to the left of 2 and for x values to the right of or equal to 2. In which interval does x=1 lie?

Answer 7

to the left

Answer 8

OK. Which function pertains to x values to the left of 2? type it out.

Answer 9

cx+3

Answer 10

Yes. You need to label that function. Would you mind doing so?

Answer 11

What do you mean label it?

Answer 12

You have a name; this function has a name. The function's name is f(x).

Write out this function, the one for x values to the left of 2.

Answer 13

ohh f(x)=cx+1 for x<2

Answer 14

Cool. Perfect.
Now replace x with '1' since we are evaluating f(1).

Answer 15

gotcha
f(1)=c+1

Answer 16

Since we don't have a value for c, your statement, above, is the best we can do. You're done.

Answer 17

Just regard "c" as a constant.

Answer 18

okay so now what?

Answer 19

Hold: You first defined that function as f(x) = cx+3. What happened to the 3?

Start over; it'll only take a minute.

Find f(1).

Answer 20

oops
f(1)=c+3

Answer 21

Right. We have no way to evaluate c, so just leave it there as a constant coeffficient of x.

f(x)=cx+3

So your f(1)=c+3 is correct and complete.

Answer 22

Okay cool.

Answer 23

Happy to be of help. Good luck to you!

Answer 24

Wait so what is the answer then??

Answer 25

my options are..
7, 10, 11, 9, 8

Answer 26

I've already told you that:

Right. We have no way to evaluate c, so just leave it there as a constant coeffficient of x.

f(x)=cx+3

So your f(1)=c+3 is correct and complete.

Answer 27

You still have not provided any clue regarding how one would find the value of c.

If the answer is contained in {7, 10, 11, 9, 8}, then something's missing from what you have shared with me.

Answer 28

this is everything :/ @mathmale

Answer 29

so heres the second equation.. and the whole function is continuous so does this help somehow?

Answer 30

force the left and right sided limits at x = 2 to be equal.

Answer 31

nvm that graph should b part of a parabola lol and ohh okay thank you so much

Answer 32

cx+3=11
cx=8
c(2?)=8
c=4
@irishboy123

Answer 33

i got that too

key thing is you agree with the idea, continuity.

Answer 34

Sorry I missed the significance of "continuity" earlier.

For the overall function to be continuous, the function defined on x<2 must equal the function defined on x equal to or greater than 2.

Thus: Let x=2 and equate cx+3 to 3x^2 - 1.

Answer 35

since x is no longer an unknown quantity, you now have all the info you need to solve for c. What is it?

Answer 36

The overall answer i got to be 7 with c=4 @mathmale thank you both so much :) @irishboy123