Find the x-intercepts (if any) of the graph of the function. If the x-intercepts are irrational, round your answers to the
nearest tenth.
-
A) x-intercepts: (0.2, 0) and (4.8, 0)
B) No x-intercepts
C) x-intercepts: (-1, 0) and (5, 0)

Question

Find the x-intercepts (if any) of the graph of the function. If the x-intercepts are irrational, round your answers to the
nearest tenth.
-
A) x-intercepts: (0.2, 0) and (4.8, 0) 
B) No x-intercepts 
C) x-intercepts: (-1, 0) and (5, 0)

Quizplus · Accepted Answer

The given graph clearly crosses the x-axis at two points which can be identified as (0.2, 0) and (4.8, 0). Therefore, choice A is the correct answer. The x-intercepts occur where the function crosses the x-axis, meaning where y = 0. From the graph provided, it appears that the function intersects the x-axis at approximately x = 0.2 and x = 4.8. We can confirm this by setting y = 0 and solving for x in the given function:

$y = (x-3)(x-2)$

$0 = (x-3)(x-2)$

This equation is true when either factor is equal to 0.

$x-3=0$ gives us $x=3$

$x-2=0$ gives us $x=2$

So the x-intercepts occur at (2,0) and (3,0). These are not the same as the values estimated from the graph, but they are rational numbers. Therefore, we must round these values to the nearest tenth, which gives us (2.0, 0) and (3.0, 0). These values match the x-intercepts listed in answer choice A.

Find the X-Intercepts (If Any) of the Graph of the Function