HiSET: Math : Use the zeros to construct a rough graph of a function

Study concepts, example questions & explanations for HiSET: Math

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Example Questions

Example Question #1 : Use The Zeros To Construct A Rough Graph Of A Function

The graph of a function is shown below, with labels on the y-axis hidden.

Graph zeroes 2

Determine which of the following functions best fits the graph above.

Possible Answers:

Correct answer:

Explanation:

Use the zeroes of the graph to determine the matching function. Zeroes are values of x where . In other words, they are points on the graph where the curve touches zero. 

Visually, you can see that the curve crosses the x-axis when , and . Therefore, you need to look for a function that will equal zero at these x values. 

A function with a factor of  will equal zero when  , because the factor of  will equal zero. The matching factors for the other two zeroes,  and , are  and , respectively.  

The answer choice  has all of these factors, but it is not the answer because it has an additional zero that would be visible on the graph. Notice it has a factor of , which results in a zero at . This additional zero that isn't present in the graph indicates that this cannot be matching function.  

 is the answer because it has all of the required factors and, as a result, the required zeroes, while not having additional zeroes. Notice that the constant coefficient of negative 2 does not affect where the zeroes are. 

Example Question #1 : Zeroes Of Polynomials

Graph zeroes

Which of the functions below best matches the graphed function?

Possible Answers:

Correct answer:

Explanation:

First, look at the zeroes of the graph. Zeroes are where the function touches the x-axis (i.e. values of  where ). 

The graph shows the function touching the x-axis when , , and at a value in between 1.5 and 2.

Notice all of the possible answers are already factored. Therefore, look for one with a factor of  (which will make  when ), a factor of  to make  when , and a factor which will make  when  is at a value between 1.5 and 2.

This function fills the criteria; it has an  and an  factor. Additionally, the third factor, , will result in  when , which fits the image. It also does not have any extra zeroes that would contradict the graph.

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