Give the values of A and B for the function f(x)={Ax-B when x

Question

Give the values of A and B for the function f(x)={Ax-B when x<=1, -24x when 1<x<5, Bx^2-A when x>= 5} to be continuous at both x = 1 and x = 5.

misty1212 · Answer

HI!!

misty1212 · Answer

this is  not as hard as it may look
replace $x$ by $1$ in both expressions 
$$Ax-B$$ and $$-24x$$

misty1212 · Answer

if $x=1$the first one is $A-B$ and the second is $-24$ so you have on equation 
$$A-B=-24$$

misty1212 · Answer

then put in $x=5$ in both $-24x$ and $Bx^2-A$

misty1212 · Answer

this time you get 
$$-120=25B-A$$ as a second equation

misty1212 · Answer

solve the system 
$$A-B=-24\25B-A=-120$$ to find $A$ and $B$

clara1223 · Answer

Thanks so much! I got that A= -30 and B=-6. I'm just going to plug them back in to make sure they work! ti
jhj

misty1212 · Answer

i didn't do it, but i can check if you like

misty1212 · Answer

yeah i get the same thing

clara1223 · Answer

Don't worry about it, plugging it in will tell me if it's right or not.

clara1223 · Answer

oh, thanks!

misty1212 · Answer

$$f(x) = \left\{\begin{array}{rcc}
Ax-B & \text{if}  & x <1 \
-24x& \text{if}  & 1\leq x\leq5\
Bx^2-A&\text{if} &x>5
\end{array}
\right.
$$

misty1212 · Answer

just seeing if i could write it 
$$\color\magenta\heartsuit$$