Question

Absolute value function has the form of this:
f(x)=|ax+b|

The x-intercept is (3/2,0) and y-intercept is (0,6)

Find the value of a and b.

Answer 1

\[{x \epsilon R}\]

Answer 2

That is the domain and our range is {yI y> or equal to 0, y is also real number}
Find the value of a and b

Answer 3

can you help?

Answer 4

We know this is in the form of Y=mx + b

Answer 5

m and a are the same. These two indicate the slope. b is the y-intercept. I know how to find b, but not a

Answer 6

It's not actually of the form mx+b.

Answer 7

ok

Answer 8

Let's consider an example.
Help me graph this function: f(x) = |2x +6|

Answer 9

What is y when x =0?
What is x when y =0?

Answer 10

Ok first we find the x and y intercepts

Answer 11

y= (0,6)
x= (-3,0)

Answer 12

Then we graph

Answer 13

Good.

Answer 14

How about y when x = -6?

Answer 15

x= (-6,0)?

Answer 16

No, I mean if you plug in x = -6, what is f(x)?
f(-6) = |2(-6)+6|

Answer 17

oh I am sorry
y= 6
absolute value of a negative number is postive number

Answer 18

\(\large {
f(x)={\color{blue}{ y}}=|a{\color{brown}{ x}}+b|\qquad
\begin{cases}
(\frac{3}{2}&,0)\\
{\color{brown}{ x}}&{\color{blue}{ y}}
\\\hline\\
(0&,6)\\
{\color{brown}{ x}}&{\color{blue}{ y}}
\end{cases}\implies
\begin{cases}
{\color{blue}{ 0}}=\left|a\cdot {\color{brown}{ \frac{3}{2}}}+b\right|
\\

\\\hline\\
{\color{blue}{ 6}}=|a\cdot {\color{brown}{ 0}}+b|
\end{cases}
\\ \quad \\
6=|a\cdot 0+b|\implies 6=|b|
\\ \quad \\
\textit{keep in mind that }|a+b|\iff |a|+|b|
}\)

Answer 19

Good! So we get those three points and we can graph it from that.
(-6,6), (-3,0), (0, 6)

Answer 20

ok @jdoe0001 then how do you find a using that way?

Answer 21

Now my question is this: What did the +3 in our equation do? And what did the 2 in our equation do?

Answer 22

@SmoothMath I do not understand what do you mean exactly by +3 and 2 ?

Answer 23

Our function was f(x) = |2x+3|
what did the +3 do to the graph?

Answer 24

3 is the y-intercept? 2 is the slope?

Answer 25

Close. But look at the y-axis. Does it cross at 3? No, it crosses at 6. The y-intercept is 6.

Answer 26

@korosh23 well... does it matter how you're meant to get it? graphicaly, or usnig a system of equations?

if graphically, then SmoothMath way would work

Answer 27

You're correct about the slope. 2 made the graph have a steepness of 2.

Answer 28

@korosh23 anyhow, in my case, I'm using a system of equations, but either method will do, just a matter of what is it the exercise is covering

Answer 29

No I want it algebrically. Well I know the answer, just can I explain to you guys and see if it is correct or not?

Answer 30

well, post what you have, or take a screenshot of it on paper, and post it away :)

Answer 31

ok wait a moment

Answer 32

Absolute value function has the form of this:
f(x)=|ax+b|

The x-intercept is (3/2,0) and y-intercept is (0,6)

b is 6 since it is the y-intercept.

a is the slope and I found it this way.

Answer 33

@jdoe0001 @SmoothMath

Answer 34

You should have stuck with me on my explanation =)

Answer 35

b is not the y-intercept, as I showed you in my example.

Answer 36

Go look at it again. b is not the y- intercept. What is it?

Answer 37

but math can be applied differently, In my textbook it says b is the y-intercept and also my teacher admit that too.

Answer 38

I'm afraid I'm biased towards the algebraic approach

but the graphic one will do @korosh23 :)

Answer 39

@jdoe0001 that means I am correct?

Answer 40

Haha it's not a question of bias. It's a question of fact.

Answer 41

hmmm not sure what you got for "a" or "b" @korosh23

so.... can't say is wrong or right