Four Functions

[nycmathguy]

Section 1.4
Questions
81, 82, 83, 84

How is this done?

 

[MathLover1]

hint:
given functions:
f(x)=c*x
g(x)=c*x^2
h(x)=c*sqrt(x)
r(x)=c/x

go to first table, use one value of x and one of y, plug in one of the given functions,
calculate value of c, then try another value of x and y to see if they satisfy equation. I not, do same using second equation.

Or, you can use two points (x,y) from each table and find a function that passes through.

 

[nycmathguy]

hint:
given functions:
f(x)=c*x
g(x)=c*x^2
h(x)=c*sqrt(x)
r(x)=c/x

go to first table, use one value of x and one of y, plug in one of the given functions,
calculate value of c, then try another value of x and y to see if they satisfy equation. I not, do same using second equation.

Or, you can use two points (x,y) from each table and find a function that passes through.

Can you do 82? I will then use your work on 82 to do the rest.

 

[MathLover1]

81.
use two ordered pairs from given table

(0,0)
(1,-2)

slope is
c=(-2-0)/(1-0)=-2

use slope point formula

y-y[1]=m(x-x[1]) ..........since c=-2, and point (1,-2)
y-(-2)=-2(x-1)
y+2=-2x+2
y=-2x+2-2
y=-2x
or
f(x)=-2x

check if it is f(x)=cx

check another point: (-4,-32)
-32=-2(-4)=
-32=8=> false

so, f(x)=-2x is not solution for f(x)=cx

check if solution is g(x)=cx^2

use x=-4 and y=-32
-32=c(-4)^2
-32=c(16)
c=-32/16
c=-2

use x=1 and y=-2
-2=c(1)^2
-2=c(1)
c=-2


so,
g(x)=-2x^2
-32=-2(-4)^2
-32=-2(16)
-32=-32 => true

or another ordered pair
-2=-2(1)^2
-2=-2(1)
-2=-2 => true

so, function g(x)=cx^2 fits the data in the table 81

 

[nycmathguy]

81.
use two ordered pairs from given table

(0,0)
(1,-2)

slope is
c=(-2-0)/(1-0)=-2

use slope point formula

y-y[1]=m(x-x[1]) ..........since c=-2, and point (1,-2)
y-(-2)=-2(x-1)
y+2=-2x+2
y=-2x+2-2
y=-2x
or
f(x)=-2x

check if it is f(x)=cx

check another point: (-4,-32)
-32=-2(-4)=
-32=8=> false

so, f(x)=-2x is not solution for f(x)=cx

check if solution is g(x)=cx^2

use x=-4 and y=-32
-32=c(-4)^2
-32=c(16)
c=-32/16
c=-2

use x=1 and y=-2
-2=c(1)^2
-2=c(1)
c=-2


so,
g(x)=-2x^2
-32=-2(-4)^2
-32=-2(16)
-32=-32 => true

or another ordered pair
-2=-2(1)^2
-2=-2(1)
-2=-2 => true

so, function g(x)=cx^2 fits the data in the table 81

This is tedious. I will work out the rest on paper using your solution steps for 81. I will continue our discussion here if needed. More questions coming later or tomorrow.

 

[nycmathguy]

81.
use two ordered pairs from given table

(0,0)
(1,-2)

slope is
c=(-2-0)/(1-0)=-2

use slope point formula

y-y[1]=m(x-x[1]) ..........since c=-2, and point (1,-2)
y-(-2)=-2(x-1)
y+2=-2x+2
y=-2x+2-2
y=-2x
or
f(x)=-2x

check if it is f(x)=cx

check another point: (-4,-32)
-32=-2(-4)=
-32=8=> false

so, f(x)=-2x is not solution for f(x)=cx

check if solution is g(x)=cx^2

use x=-4 and y=-32
-32=c(-4)^2
-32=c(16)
c=-32/16
c=-2

use x=1 and y=-2
-2=c(1)^2
-2=c(1)
c=-2


so,
g(x)=-2x^2
-32=-2(-4)^2
-32=-2(16)
-32=-32 => true

or another ordered pair
-2=-2(1)^2
-2=-2(1)
-2=-2 => true

so, function g(x)=cx^2 fits the data in the table 81

I will do the other questions in like manner and show my work here when time allows. Good job with 81.

 

[nycmathguy]

81.
use two ordered pairs from given table

(0,0)
(1,-2)

slope is
c=(-2-0)/(1-0)=-2

use slope point formula

y-y[1]=m(x-x[1]) ..........since c=-2, and point (1,-2)
y-(-2)=-2(x-1)
y+2=-2x+2
y=-2x+2-2
y=-2x
or
f(x)=-2x

check if it is f(x)=cx

check another point: (-4,-32)
-32=-2(-4)=
-32=8=> false

so, f(x)=-2x is not solution for f(x)=cx

check if solution is g(x)=cx^2

use x=-4 and y=-32
-32=c(-4)^2
-32=c(16)
c=-32/16
c=-2

use x=1 and y=-2
-2=c(1)^2
-2=c(1)
c=-2


so,
g(x)=-2x^2
-32=-2(-4)^2
-32=-2(16)
-32=-32 => true

or another ordered pair
-2=-2(1)^2
-2=-2(1)
-2=-2 => true

so, function g(x)=cx^2 fits the data in the table 81

Question 82

I selected points (4, 1) and (0, 0).

Let c = slope

c = (0 - 1)/(0 - 4)

c = 1/4

Does f(x) = cx apply to table 82?

Pick point (4, 1).

Let f(x) = y

y = cx

1 = (1/4)(4)

1 = 1

It checks to be true.

So, f(x) = cx applies to table 82.

I then did the same math work for question 83. I found out that h(x) does not apply to table 83.
I took a slight pause and asked myself
this question: DO I NEED TO CONTINUE TO FIND THE CORRECT FORMULA FOR QUESTIONS 83 AND 84?

No need to do anymore math here. Since h(x) does not apply to table 83, it must then apply to table 84.
This means that r(x) applies to table 83, without the need for further calculations.

You say?

 

[MathLover1]

perfect

 

[nycmathguy]

perfect

It's good exercise.