+0  
 
+3
872
3
avatar+2533 

\(if\:\:m\ne 0,\:m\ne 1, and\:\;f(x)=mx+b,\:\text{then which of}\\ \text{the following statements concering the graphs whose}\\ \text{are} \;y=f(x)+3\;\;and\;y=f(x+3)\;\text{must be true?}\)

 

(A) the graph don't intersect

(B) the graphThe graph intersect in one point

(C) the graph intersect in two points

(D) the graphin more than two points

 

I get

 

\(\begin{array}{rcll} m(x-3)+b &=&mx+b+3 \\ mx-3m &=& mx+3\\ m&=&-1 \end{array}\)

 

I think D because their slopes are the same but (x-3) is tricking

 Mar 18, 2016

Best Answer 

 #2
avatar+21972 
+20

Let's take a particular example; let's say that f(x)  =  7x + 29.

y  =  f(x) + 3  =  (7x + 29) + 3  =  7x + 32

y  =  f(x + 3)  =  7(x + 3) + 29  =  7x + 21 + 29  =  7x + 50

This shows that, for this case, the two lines are parallel because they have the same slope but different y-intercepts.

This says that the answer is (A).

 

f(x) + 3  takes the original function, f(x), and moves it up 3 spaces but leaves the slope alone.

f(x + 3)  makes the y-value of f(x) the y-value of f(x + 3); it moves it 3 spaces down the line but leaves the slope alone. 

 

My suggestion to doing problems like this:  take a particular example but don't use values for m and b that are special numbers, such as 0, 1 or -1. Then, analyze what happens to the particular beginning example.

 Mar 18, 2016
 #1
avatar+2533 
0

yes D is need to be answer

 Mar 18, 2016
 #2
avatar+21972 
+20
Best Answer

Let's take a particular example; let's say that f(x)  =  7x + 29.

y  =  f(x) + 3  =  (7x + 29) + 3  =  7x + 32

y  =  f(x + 3)  =  7(x + 3) + 29  =  7x + 21 + 29  =  7x + 50

This shows that, for this case, the two lines are parallel because they have the same slope but different y-intercepts.

This says that the answer is (A).

 

f(x) + 3  takes the original function, f(x), and moves it up 3 spaces but leaves the slope alone.

f(x + 3)  makes the y-value of f(x) the y-value of f(x + 3); it moves it 3 spaces down the line but leaves the slope alone. 

 

My suggestion to doing problems like this:  take a particular example but don't use values for m and b that are special numbers, such as 0, 1 or -1. Then, analyze what happens to the particular beginning example.

geno3141 Mar 18, 2016
 #3
avatar+2533 
0

Yes i wanted to say exactly the opposite but i mixed them supid me :/

Thanks Geno ! :)

Solveit  Mar 18, 2016

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