Thread: True/False : 2 Questions

1- The following function is one-to-one

f(x)= -x if x belongs to [-1,0]
f(x)=3x+2 if x belongs to [0,1]

2- The following parametric curve represents a line segment from (0,3) to (2,0) :

and where

For (1): I think its false, if we draw the function on the interval [-1,1] we will get a graph which is similar to the graph of f(x)=|x| (the v-shape). clearly there are horizontal lines intersect the curve of f in more than one point, so its not 1-1 function, so the statement is false.

For (2): I do not have any idea!

Its ok for number1.
Its true
sorry, I made mistake when i draw
its one-to-one

I need number 2 please.

Originally Posted by Miss

1- The following function is one-to-one

f(x)= -x if x belongs to [-1,0]
f(x)=3x+2 if x belongs to [0,1]

2- The following parametric curve represents a line segment from (0,3) to (2,0) :

and where

For (1): I think its false, if we draw the function on the interval [-1,1] we will get a graph which is similar to the graph of f(x)=|x| (the v-shape). clearly there are horizontal lines intersect the curve of f in more than one point, so its not 1-1 function, so the statement is false.

For (2): I do not have any idea!

I see you already figured out (1), but try to be careful about writing intervals like [a,b] or (a,b) or (a,b] or [a,b). The f(x) you wrote above is not a function because the first part gives f(0) = 0 and the second part gives f(0) = 2.

For (2), first check start and end points.

x(0) = 0 and y(0) = 3

and .

So we can't conclude whether it's true or false yet.

Now express y in terms of x:



This is an equation of a line, so the answer to (2) is True.

Originally Posted by Miss

1- The following function is one-to-one

f(x)= -x if x belongs to [-1,0]
f(x)=3x+2 if x belongs to [0,1]

2- The following parametric curve represents a line segment from (0,3) to (2,0) :

and where

For (1): I think its false, if we draw the function on the interval [-1,1] we will get a graph which is similar to the graph of f(x)=|x| (the v-shape). clearly there are horizontal lines intersect the curve of f in more than one point, so its not 1-1 function, so the statement is false.

For (2): I do not have any idea!

(1) agree

(2)





now calculate and ATQ.



btw ... not to cramp your style, but the pink type is difficult to read.

Hello, Miss!

2. The following parametric curve represents a line segment from (0,3) to (2,0)

. . . . This is true.

We have: .




So we have: .

The graph would be a straight line (infinitely long).


However, ranges from 0 to

Then: .


Therefore, the graph is the line segment from (0.3) to (2,0).