Functions and Graphs | Precalculus

This precalculus provides a basic introduction into functions and graphs. It contains plenty of examples and multiple choice practice problems.

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[phunbaba]

For #10 the range starts up again at -1 not 1

[memesouls]

I like it when teachers explain stuff before hand and don't expect the students to remember everything. I find it quite annoying when teachers are like "oh yeah you guys should remember these concepts from LAST year." Its like sure, maybe a couple might remember but it doesn't hurt going over how the process works first. Teachers too often skim over certain subject matters thinking that "we already know." Its a stupid method of teaching and I really appreciate these videos existing that are quick and easy to follow. Straight to the point and very thorough.

[jordysavage]

learned more in 10 minutes than in a whole week at college algebra youre a G

[WheelzMayalls]

one if the best in youtube so far.. well done sir👏🏼👏🏼

[KS-iedv]

If you are wondering how to solve question 2

Here you go:

To determine possible values of x for which f(x) equals a given value, you need to substitute the value of f(x) into the function equation and solve for x. In this case, we are given that f(x) = 10, and we need to find potential values of x.

The function is given by f(x) = 2 | x - 5 | - 8. We can set this equation equal to 10:

2 | x - 5 | - 8 = 10

Next, we isolate the absolute value term by moving the constant terms to the other side:

2 | x - 5 | = 10 + 8
2 | x - 5 | = 18

Now, we can consider two cases: one where x - 5 is positive and another where it is negative.

Case 1: x - 5 is positive (x - 5 ≥ 0)
When x - 5 ≥ 0, the absolute value term simplifies to x - 5:

2 (x - 5) = 18
2x - 10 = 18
2x = 18 + 10
2x = 28
x = 14

So, x = 14 is a potential value.

Case 2: x - 5 is negative (x - 5 < 0)
When x - 5 < 0, the absolute value term becomes -(x - 5) or -x + 5:

2 (-x + 5) = 18
-2x + 10 = 18
-2x = 18 - 10
-2x = 8
x = -4

Therefore, x = -4 is another potential value.

In summary, the possible values of x for which f(x) = 10 are x = 14 and x = -4.

[mathsandsciencechannel]

THANK YOU SIR, YOUR VIDEOS HAS INSPIRED ME TO START MY MATHS AND SCIENCE CHANNEL. THANKS

[amh]

Thank u
This video better than school

[denisedattilo]

11:02 isn't the function supposed to begin at y=-1 rather than 1?🤔

[mzterzi]

Thanks. What software and tablet do you use

[sabaalsayyed]

i really cant handle it anymore! your voice is so soothing and relaxing man

[georgesadler]

MR. Organic Chemistry Tutor, thank you for a well-organized lecture/video on Functions and Graphs. The examples are easy to follow from beginning to end.

[elliebellie-xzeu]

ohhhh so im not stupid, my teacher just doesnt do their job 🤠🤠

[sayhenry]

Wait. How did you get number two if the question says f(x) =10 and you got 10= 2/x -5/-8

[EmpyreanLightASMR]

14:40 if you pause it immediately here, you get a bonus question that would otherwise go into the paid version of the video. Has anyone tried it?
Solve for h(x)

I took g(x) and plugged it into the x value of f(x). If f(x) is x^2 + 5x, and added g(x), I get:

(7x + 3)^2 + 5(7x + 3)

After foiling the first part, and distributing the 5 in the second part, I get:
49x^2 + 42x + 9 + 35x + 15

Combining like terms, I get:
49x^2 + 77x + 24

If he were to ask how to decompose this, I would have no idea.

[AishaAlHammadi-ex]

Thank you so much you saved my life. I have a calculus exam tomorrow and I understand everything. Wish me luck tomorrow on the exam.

[KELVINMWAISAKA-it]

@Question 10, i think you meant the range should be (-5, -3)U(-1, INF)

[jayburdeos]

It's like studying the power of (Gojo Saturo) infinite void.

[originalusername]

Of course you post this the day I have my test lol

[joseg.]

This guy is my teacher my teacher doesn’t teach us he legit read off a text book rather having him shows us how

[emmahilukilwa]

I didn't get question 11well please reexplain