Graphing Absolute Value Functions - 1

Graph f(x) = |x + 2| - 3

[wendygirl]

I learned more in this one video than in 2 years with my algebra teacher...

[bresaifullah]

Now...why couldn't my teacher have done that....plain and simple?! 4 days of studying (and brain frying) could have been narrowed down to almost 4 minutes of complete understanding! Lol, thanks you so much!

[lamyasms]

u helped me loads u are a math magician, i have an exam tomorrow wish me luck :)

[Onepieceblitz]

My math teacher doesn't teach us, rather she makes us watch pre-recorded lecture note videos. Instead of watching those I came here, you explain it more clearly thank you!

[breckett-]

Jesus. My teacher has been trying to teach this to me for a while and I come here, and you teach it flawlessly. Thank you so much :D

[rashelbee]

So I took Algebra 1 Honors when I was in the 8th grade, and I skipped Algebra 2 and am now taking College Algebra in the 10th grade. But I was moved into Algebra 1 about halfway through the course, so the rest of the year I was trying to catch up. My teacher was pretty bad anyways, so we only barely skimmed over graphing absolute value equations. I had entirely forgotten about them until one of the problems on my homework was {f(x)=|x+3| -5}. I Googled how to graph them, and your video was the easiest to understand. So thank you so very much! This will definitely help me throughout this year!

[mathman]

For absolute value functions, you can treat that coefficient as a slope. On either side of the vertex your graph would have a slope of 2 and you would be going down.

[mathman]

@ordude123 For absolute value functions, you can use the coefficient as though it were a slope. The negative two means that you would open down and be steeper than the normal function.

[mathman]

@theolivetree95 Yes, you would flip it vertically. It would be a reflection across the x-axis.

[cesaoreo]

Awesome video, really easy to understand and very straight forward explanation 👌

[mathman]

@f4iaz2010 The domain for a normal absolute value function is all real numbers. The range is determined by a couple things. If it opens up, the range is all numbers greater than or equal to the number "outside" the absolute values. In this case, the range is [-3, infinity). If the graph was upside-down, the range would be everything less than or equal to that number.

[himanshugediya]

Who else thinks people on YouTube are better then real teachers

[mathman]

Since the 4 is "outside" the main function, it indicates a vertical shift of +4 units. Just take the absolute value shape and move it up four units.

[lilmissy]

Thank you so much! What you taught me in 3 mins and 46 secs I understand more than what my teacher taught me in 50mins.! That's terrible!

[mathman]

You have to think about what value of x would "zero out" the inside of the function. Through observation, we find that that value indicates a horizontal shift.

[ShakeraSphere]

I wish I had u as teacher u explained it so simple if only other teachers had ur skills students lives would be easier

[sydriannevermore]

Thanks man you saved me since I missed a day of school when they taught this and got homework for the next day life saver man.

[theolivetree]

Thank you so much! One question though... If the coefficient were a negative one, would you flip the graph since the slope is negative???

[LobsterBackGaming]

thanks, my teacher didnt want to teach us the fast way to doing this with t charts since she wanted us to figure it out ourselves through a shifting pattern. But the way you explained it is way easier than her and now i can be ahead of my class mates who have no idea about this. :D THANK U

[mathman]

For one, your equation doesn't make sense. I assume you mean y=|2x+6|. If that is the case, we can simplify.

|2x+6| = |2(x+3)| = 2 |x+3|

So we really just have a vertical stretch. In either the original or simplified form, x = -3 will "zero out" the inside of the absolute value function. Hence, you would also have a horizontal shift of -3 units.