Question

the function f(x) = |2x-4| is not a one-to-one function. graph the part of the function that is one-to-one and extends to positive infinity.

Answer 1

Here, we want to graph the part of the graph that is one-to-one

What we have to do here is to remove the absolute value signs and plot the graph of the line that it normally looks like

Generally, we have the equation of a straight line as;

$y\text{ = mx + b}$

where m is the slope and b is the y-intercept

Looking at the function f(x) = 2x-4; -4 is simply the y-intercept value

So, we have a point at (0,-4)

To get the second point, set f(x) = 0

$\begin{gathered} 2x-\text{ 4 = 0} \\ 2x\text{ = 4} \\ x\text{ =}\frac{4}{2}\text{ = 2} \end{gathered}$

So, we have the second point as (2,0)

By joining (2,0) to (0,-4) ; we have the plot of the part of the function that extends to infinity