Question

Write an inequality for the graph.

Answer 1

first off, notice the vertex, and also that's an absolute value function graph
what would be your vertex?

Answer 2

Could you explain more? I don't understand

Answer 3

Hello?

Answer 4

Please can somebody help?

Answer 5

@jdoe0001 ? @oscar1997flores

Answer 6

woops, sorry, was a bit .. .caught up

Answer 7

notice the coordinates for the vertex , what can you see as the vertex coordinates?

Answer 8

I don't understand that, can you explain what that is?

Answer 9

the vertex.... you know is an absolute value expression, right?
based on the graph, the graph of absolute value expressions look like http://education-portal.com/cimages/multimages/16/transformations.jpg

Answer 10

Alright, I understand I see that the vertex is hitting (5,1) right?

Answer 11

right, the vertex is (5, 1) the lines are SOLID, that means is going to be either \(\bf \le \ or \ \ge\ \) when is > or < is a DASHED LINE

the absolute parent expression will be |x| simple enough
it's SHIFTED HORIZONTALLY by 5 units, that means | x - 5 |
it's SHIFTED VERTICALLY by 1 unit UP, that means | x -5 | + 1

so that's our left side... so our right side will be "y"
so \(\bf \large | x - 5 | +1 \quad \square ? \quad y \)

what goes between it? we dunno
but we have a shaded area, which is the area that's TRUE for the inequality

so pick a point in the shaded area, or TRUE for the inequality, that we can test :)

Answer 12

shifted horizontally by 5units to the right that is, which is |x -5 |, anyhow, pick a point in the TRUE or shaded are

Answer 13

2?

Answer 14

(2, ? )

Answer 15

Lets say 5?

Answer 16

ok, (2, 5) is in the TRUE or shaded area, so our inequality must yield true
so let's test it

x = 2, y = 5

\(\bf | x - 5 | +1 \quad \square ? \quad y \\ \quad \\
| (2) - 5 | +1 \quad \square ? \quad (5) \implies |-3| +1 \quad \square ? \quad (5)\\\quad\\
\implies -3 +1 \quad \square ? \quad (5) \implies -2 \quad \square ? \quad 5\\
\textit{well, -2 is clearly less than 5, recall we have to use} \le \ or \ \ge\\
-2 \quad \square ? \quad 5 \implies -2 \le 5\\
\textit{so our sign is } \le\\
| x - 5 | +1 \quad \square ? \quad y \implies \color{blue}{| x - 5 | +1 \quad \le \quad y }\)

Answer 17

Ah so |x−5|+1≤y
would be the answer?

Answer 18

hhhmm one sec.... I have an error :(

Answer 19

|-3| = 3

Answer 20

ok

Answer 21

\(\bf | x - 5 | +1 \quad \square ? \quad y \\ \quad \\
| (2) - 5 | +1 \quad \square ? \quad (5) \implies |-3| +1 \quad \square ? \quad (5)\\ \quad \\
\implies 3 +1 \quad \square ? \quad (5) \implies 4 \quad \square ? \quad 5\\
\textit{well, 4 is clearly less than 5, recall we have to use} \le \ or \ \ge\\
4 \quad \square ? \quad 5 \implies 4 \le 5\\
\textit{so our sign is } \le\\
| x - 5 | +1 \quad \square ? \quad y \implies \color{blue}{| x - 5 | +1 \quad \le \quad y} \)

still less than 5 anyhow

Answer 22

So that's the answer?

Answer 23

yeap, that's the inequality

Answer 24

Thank you!

Answer 25

yw