SOLUTION: My question comes from the pre-calculus CLEP study guide from collegeboard.com. It is an Algebra problem and a graph, but I am unable to paste the graph into this box. <p> <p>

Question 135958: My question comes from the pre-calculus CLEP study guide from collegeboard.com. It is an Algebra problem and a graph, but I am unable to paste the graph into this box.

Here is the question and a verbal explanation of the graph. I can send it to an email address if that is a possibility.

The figure above shows the complete graphs of the functions f and g. Based on the graphs, the equation f(x) - g(x) = 0 has how many roots?

The graph is on a cartesian plane. The y=f(x) graph is a slope with a y-intercept of about 2 and an x intercept of about -4, and is upward sloping to the right. The y=g(x) is a curvy graph. Please excuse my description, I am unaware of the actual graphing equation used for it so bare with me. It begins down at -4,-4 curves upward and hits a mzxima at around 1,3 curves back down to a minima of 3,-2 curves back upward to a maxima of about 5,1, and then makes a final curve down to a stopping point at about 7,-3.

My question is: what is the process for finding these roots when there are no numbers to guide you. What do plug in, or utilize to find the answer? I am stuck on this one, and it is the first question on the study guide. There was a similar question on the College Algebra CLEP study guide. Thank you for all of your help. If you need me to email you the graph, please send me a link of where I can send it.

Thanks again.

Cheryl
Answer by Fombitz(32388) (Show Source): You can put this solution on YOUR website!
The specific values of the points for each of the curves is not important.
This is more of a "think-about-it" question.
What can you say about f(x) and g(x) when f(x)-g(x)=0?

Whenever the two curves intersect (when f=g), the difference function has a zero.
Add up the number of intersections, that's the number of zeros for the difference function.

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