How do I prove this?

Question

This is a proof question that I don't know how to do other than to plug in numbers, however, the second part of the question says to do that...

Anyway, here is the question.

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1. Determine whether the following functions are linear:

a) y=5x

b) y=x^2

c) y=log(x)

2. Verify the above proofs using x=3 and x= 4

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Obviously a) is the only linear one, however how do I show that? Especially since the latter portion of the question instructs you to use the numbers

This is just a practice theory question, no test.

Answer 1

Look a linear fn. is one in which power of x is 1 and it is under no mathematical operation like log x, sin x etc.

Ok what u can do is put x=3 and x=4 in the above equations and plot the points on a graph paper. If by joining the 2 points(or more points, if any) u obtain a straight line then the function is linear otherwise not

Hope I answered the question  

Answer 2

only (a) is linear function because for any value of 'x' there a exists a unique 'y' such that y=5x.

but same can't be applied to (c) though the above stated is true.Basically, its said to be a logarithmic function.

Answer 3

because y=5x. If y were to equal say... 2, then you'd just go up two on your graph and make a horizontal line at y=2. In your linear equation, we have y=5x. since x is a variable, we can assume that it is taking the place of all real numbers, so if x were 1 then... y=5(1) or just y=5, so then you could draw a horizontal line at y=5. say x was 56, then we would have y=5(56) or just y=280, so we would draw a horizonal (linear line) at y=280. I hope this all helped!

Answer 4

Graph y =5x, and then plug in 3 and 4 for x. y=15 and y=20 should cross or atleast be tangent to y=5x

:D hope this helps!

Answer 5

Its very simple. You are basically stuck up with ´what should I do so that I can show these are linear?´

The answer is that u just transform the equations in the form of standard equations of line which are:

y=mx+c where y and x are variables x is slope of the line and c is just another constant.

there are many other standard line equations, Check your textbook for them...

I m sure this willl help...

Answer 6

1)For a linear function,its has a general equation which is

y= mx + c

From the equation above, only a) is fitted to y = mx + c.The answer is a)

2)You substitute x into each equation and see its fitted or not.

   But at here, you don't have enough evidence to proof using those x.