All HiSET: Math Resources
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 they-axis hidden.
Determine which of the following functions best fits the graph above.
Use the zeroes of the graph to determine the matching function. Zeroes are values ofxwhere.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.因此,需要寻找一个函数will equal zero at thesexvalues.
A function with a factor ofwill equal zero when, because the factor ofwill equal zero. The matching factors for the other two zeroes,and, areand, respectively.
The answer choicehas 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 :Use The Zeros To Construct A Rough Graph Of A Function
Which of the functions below best matches the graphed function?
First, look at the zeroes of the graph. Zeroes are where the function touches the x-axis (i.e. values ofwhere).
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 makewhen), a factor ofto makewhen, and a factor which will makewhenis at a value between 1.5 and 2.
This function fills the criteria; it has anand anfactor. Additionally, the third factor,, will result inwhen, which fits the image. It also does not have any extra zeroes that would contradict the graph.
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