Verified Answer :

danielmaduroh

Right answer:

f(x)=x


In geometry, a line is straight (no curves) and has no thickness,. This extends in both directions without end, that is, infinitely. We need to find from the options the graph of a line, recall that a function \(f\) from a set \(A\) to a set \(B\) is a relation that assigns to each element \(x\) in the set \(A\) exactly one element \(y\) in the set \(B\). The set \(A\) is the domain (also called the set of inputs) of the function and the set \(B\) contains the range (also called the set of outputs).


Therefore, the right option is \(f(x)=x\) as illustrated in the Figure below.

View image danielmaduroh

Answer:

f(x) =x

Step-by-step explanation:

Given are three functions of x

We have to find the function whose graph is a straight line

We know that a straight line has constant slope throughout its domain

Let us check with this

I function

\(f(x) =x\)

Differentiate to find the slope

Slope =1 = constant

Hence this is a straight line

2 function

\(f(x) = x^ 2\\f'(x) =2x\)

Thus slope depends on the value of x and not a constant.  This cannot be a straight line

3 function

\(f(x) =|x|\\i.e. f(x) = -x, x<0\\      f(x) = x, x\geq 0\)

This function has slope 1 for positive x and -1 for negative x

Since not constant cannot be a straight line

So answer is option A

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