Zeros of Functions

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What are the zeros of a function?

Back

The zeros of a function are the values of x for which the function f(x) = 0.

Tags

CCSS.HSF-IF.C.7D

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How can you find the zeros of a function using a graphing calculator?

Back

You can find the zeros by entering the function into the calculator, using the 'y=' button, and then pressing 'graph' to visualize where the function crosses the x-axis.

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What does it mean if a function has two zeros?

Back

It means that the graph of the function intersects the x-axis at two distinct points.

Tags

CCSS.HSF-IF.C.7C

Front

How do you determine the number of zeros a polynomial function has?

Back

The number of zeros can be determined by the degree of the polynomial; a polynomial of degree n can have up to n real zeros.

Front

What is the zero of the function f(x) = 3x + 9?

Back

The zero is x = -3, found by setting f(x) to 0 and solving for x.

Tags

CCSS.HSF-IF.C.7D

Front

What is the significance of the x-intercepts of a graph?

Back

The x-intercepts represent the zeros of the function, indicating where the function's value is zero.

Tags

CCSS.HSF-IF.C.7C

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How do you find the zeros of the function f(x) = x^3 - 7x^2?

Back

You can find the zeros by factoring the polynomial or using a graphing calculator to identify where the function equals zero.

Tags

CCSS.HSF-IF.C.7C

Front

What is the relationship between the degree of a polynomial and its zeros?

Back

The degree of a polynomial indicates the maximum number of zeros it can have, but not all zeros need to be real.

Front

What does it mean for a function to have complex zeros?

Back

Complex zeros occur when the function does not intersect the x-axis, resulting in solutions that include imaginary numbers.

Tags

CCSS.HSN.CN.C.9

Front

How can you verify the zeros of a function?

Back

You can verify the zeros by substituting the values back into the function and checking if f(x) equals zero.

Tags

CCSS.HSF-IF.C.7C