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

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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:

f(x)=-2x^2(x+1)(x-2)(x+2)

$f(x)=\frac{x+1}{x+2}$

f(x)=-2(x+1)(x-2)(x+2)

$f(x)=x^2x^{-2}$

f(x)=(x+1)^3(x-2)^2

Correct answer:

f(x)=-2(x+1)(x-2)(x+2)

Explanation:

Use the zeroes of the graph to determine the matching function. Zeroes are values of x where f(x)=0 . 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 x=-2 , x=-1 , and x=2 . Therefore, you need to look for a function that will equal zero at these x values.

A function with a factor of (x+2) will equal zero when x=-2 , because the factor of (x+2) will equal zero. The matching factors for the other two zeroes, x=-1 and x=2 , are (x+1) and (x-2) , respectively.

The answer choice f(x)=-2x^2(x+1)(x-2)(x+2) 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 x^2 , which results in a zero at x=0 . This additional zero that isn't present in the graph indicates that this cannot be matching function.

f(x)=-2(x+1)(x-2)(x+2) 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.

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

Graph zeroes

Which of the functions below best matches the graphed function?

Possible Answers:

f(x)= x(3x-5)(x+2)

f(x)= x(3x+5)(x-2)

f(x)= (3x+5)(x+2)

f(x)= x(3x-5)(x-2)

f(x)= x(x+2)^2

Correct answer:

f(x)= x(3x-5)(x+2)

Explanation:

First, look at the zeroes of the graph. Zeroes are where the function touches the x-axis (i.e. values of where f(x)=0 ).

The graph shows the function touching the x-axis when x=-2 , x=0 , 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 f(x)=0 when x=0 ), a factor of (x+2) to make f(x)=0 when x=-2 , and a factor which will make f(x)=0 when is at a value between 1.5 and 2.

f(x)= x(3x-5)(x+2)

This function fills the criteria; it has an and an (x+2) factor. Additionally, the third factor, (3x-5) , will result in f(x)=0 when $x=\frac{5}{3}$ , which fits the image. It also does not have any extra zeroes that would contradict the graph.

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

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

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