Question

find the minimum and maximum value of \(y\) if

Answer 1

\(\large \color{black}{\begin{align}

y=\text{max}(2x+3,x-1),\ -10\leq x\leq 10\hspace{.33em}\\~\\
\end{align}}\)

Answer 2

Since it is a linear function you can test the endpoints.

Answer 3

how is defined:
\[\Large \max \left( {f\left( x \right),g\left( x \right)} \right)\]?

Answer 4

is it a metric?

Answer 5

sorry, I remember now!

Answer 6

we can write this:
\[\max \left( {f\left( x \right),g\left( x \right)} \right) = \frac{1}{2}\left\{ {f\left( x \right) + g\left( x \right) + \left| {f\left( x \right) - g\left( x \right)} \right|} \right\}\]

Answer 7

I am with @jayzdd

Answer 8

well answer given is

\(\large \color{black}{\begin{align}

& y_{\text{max}} =23\hspace{.33em}\\~\\

& y_{\text{min}} =-11\hspace{.33em}\\~\\
\end{align}}\)

Answer 9

I used a wrong formula

Answer 10

It must be\[y=\frac{3x+2+|x+4|}{2}\]

Answer 11

@Michele_Laino 's formula looks correct.

Answer 12

yeah, that's the correct formula

Answer 13

just for the record

https://www.desmos.com/calculator/a9klmgww5t

Answer 14

so we just need to plug three values for finding max and min, -10, -4 and 10

Answer 15

yes -10 and 10