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 [tex]f[/tex] from a set [tex]A[/tex] to a set [tex]B[/tex] is a relation that assigns to each element [tex]x[/tex] in the set [tex]A[/tex] exactly one element [tex]y[/tex] in the set [tex]B[/tex]. The set [tex]A[/tex] is the domain (also called the set of inputs) of the function and the set [tex]B[/tex] contains the range (also called the set of outputs).
Therefore, the right option is [tex]f(x)=x[/tex] as illustrated in the Figure below.
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
[tex]f(x) =x[/tex]
Differentiate to find the slope
Slope =1 = constant
Hence this is a straight line
2 function
[tex]f(x) = x^ 2\\f'(x) =2x[/tex]
Thus slope depends on the value of x and not a constant. This cannot be a straight line
3 function
[tex]f(x) =|x|\\i.e. f(x) = -x, x<0\\ f(x) = x, x\geq 0[/tex]
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
