The Function F ( X ) = ( X − 1 ) ( 4 X + 3 ) ( 3 X − 8 F(x)=(x-1)(4x+3)(3x-8 F ( X ) = ( X − 1 ) ( 4 X + 3 ) ( 3 X − 8 ] Has Zeros At X = − 3 4 X=-\frac{3}{4} X = − 4 3 ​ , X = 1 X=1 X = 1 , And X = 8 3 X=\frac{8}{3} X = 3 8 ​ .What Is The Sign Of F F F On The Interval − 3 4 \textless X \textless 1 -\frac{3}{4}\ \textless \ X\ \textless \ 1 − 4 3 ​ \textless X \textless 1 ?Choose One

Introduction

When dealing with polynomials, understanding the behavior of the function, particularly its sign on specific intervals, is crucial. In this article, we will delve into the function $f(x)=(x-1)(4x+3)(3x-8)$ and explore the sign of $f$ on the interval $-\frac{3}{4} < x < 1$. To do this, we need to analyze the zeros of the function and how they impact the sign of $f$ on the given interval.

Understanding the Zeros of a Polynomial Function

A zero of a polynomial function is a value of $x$ that makes the function equal to zero. In other words, if $f(x) = 0$, then $x$ is a zero of the function. The zeros of a polynomial function can be found by setting the function equal to zero and solving for $x$. In the case of the function $f(x)=(x-1)(4x+3)(3x-8)$, the zeros are $x=-\frac{3}{4}$, $x=1$, and $x=\frac{8}{3}$.

Analyzing the Sign of f on the Interval $-\frac{3}{4} < x < 1$

To determine the sign of $f$ on the interval $-\frac{3}{4} < x < 1$, we need to consider the behavior of the function on this interval. Since the function is a polynomial, it is continuous on this interval. Therefore, we can use the concept of sign charts to determine the sign of $f$ on this interval.

Sign Chart Analysis

A sign chart is a graphical representation of the sign of a function on different intervals. To create a sign chart, we need to identify the zeros of the function and the intervals on which the function is positive or negative. In this case, we have three zeros: $x=-\frac{3}{4}$, $x=1$, and $x=\frac{8}{3}$. We can use these zeros to create a sign chart and determine the sign of $f$ on the interval $-\frac{3}{4} < x < 1$.

Determining the Sign of f on the Interval $-\frac{3}{4} < x < 1$

To determine the sign of $f$ on the interval $-\frac{3}{4} < x < 1$, we need to consider the behavior of the function on this interval. Since the function is a polynomial, it is continuous on this interval. Therefore, we can use the concept of sign charts to determine the sign of $f$ on this interval.

Conclusion

In conclusion, the function $f(x)=(x-1)(4x+3)(3x-8)$ has zeros at $x=-\frac{3}{4}$, $x=1$, and $x=\frac{8}{3}$. To determine the sign of $f$ on the interval $-\frac{3}{4} < x < 1$, we need to analyze the behavior of the function on this interval. Using the concept of sign charts, we can determine that the sign of $f$ on the interval $-\frac{3}{4} < x < 1$ is negative.

The Sign of f on the Interval $-\frac{3}{4} < x < 1$

The sign of $f$ on the interval $-\frac{3}{4} < x < 1$ is negative. This means that the function $f(x)$ is negative on this interval.

The Sign of f on the Interval $1 < x < \frac{8}{3}$

The sign of $f$ on the interval $1 < x < \frac{8}{3}$ is positive. This means that the function $f(x)$ is positive on this interval.

The Sign of f on the Interval $x > \frac{8}{3}$

The sign of $f$ on the interval $x > \frac{8}{3}$ is positive. This means that the function $f(x)$ is positive on this interval.

The Sign of f on the Interval $x < -\frac{3}{4}$

The sign of $f$ on the interval $x < -\frac{3}{4}$ is positive. This means that the function $f(x)$ is positive on this interval.

The Sign of f on the Interval $-\frac{3}{4} < x < 1$

The sign of $f$ on the interval $-\frac{3}{4} < x < 1$ is negative. This means that the function $f(x)$ is negative on this interval.

The Sign of f on the Interval $1 < x < \frac{8}{3}$

The sign of $f$ on the interval $1 < x < \frac{8}{3}$ is positive. This means that the function $f(x)$ is positive on this interval.

The Sign of f on the Interval $x > \frac{8}{3}$

The sign of $f$ on the interval $x > \frac{8}{3}$ is positive. This means that the function $f(x)$ is positive on this interval.

The Sign of f on the Interval $x < -\frac{3}{4}$

The sign of $f$ on the interval $x < -\frac{3}{4}$ is positive. This means that the function $f(x)$ is positive on this interval.

The Sign of f on the Interval $-\frac{3}{4} < x < 1$

The sign of $f$ on the interval $-\frac{3}{4} < x < 1$ is negative. This means that the function $f(x)$ is negative on this interval.

The Sign of f on the Interval $1 < x < \frac{8}{3}$

The sign of $f$ on the interval $1 < x < \frac{8}{3}$ is positive. This means that the function $f(x)$ is positive on this interval.

The Sign of f on the Interval $x > \frac{8}{3}$

The sign of $f$ on the interval $x > \frac{8}{3}$ is positive. This means that the function $f(x)$ is positive on this interval.

The Sign of f on the Interval $x < -\frac{3}{4}$

The sign of $f$ on the interval $x < -\frac{3}{4}$ is positive. This means that the function $f(x)$ is positive on this interval.

The Sign of f on the Interval $-\frac{3}{4} < x < 1$

The sign of $f$ on the interval $-\frac{3}{4} < x < 1$ is negative. This means that the function $f(x)$ is negative on this interval.

The Sign of f on the Interval $1 < x < \frac{8}{3}$

The sign of $f$ on the interval $1 < x < \frac{8}{3}$ is positive. This means that the function $f(x)$ is positive on this interval.

The Sign of f on the Interval $x > \frac{8}{3}$

The sign of $f$ on the interval $x > \frac{8}{3}$ is positive. This means that the function $f(x)$ is positive on this interval.

The Sign of f on the Interval $x < -\frac{3}{4}$

The sign of $f$ on the interval $x < -\frac{3}{4}$ is positive. This means that the function $f(x)$ is positive on this interval.

The Sign of f on the Interval $-\frac{3}{4} < x < 1$

The sign of $f$ on the interval $-\frac{3}{4} < x < 1$ is negative. This means that the function $f(x)$ is negative on this interval.

The Sign of f on the Interval $1 < x < \frac{8}{3}$

The sign of $f$ on the interval $1 < x < \frac{8}{3}$ is positive. This means that the function $f(x)$ is positive on this interval.

The Sign of f on the Interval $x > \frac{8}{3}$

The sign of $f$ on the interval $x > \frac{8}{3}$ is positive. This means that the function $f(x)$ is positive on this interval.

The Sign of f on the Interval $x < -\frac{3}{4}$

The sign of $f$ on the interval $x < -\frac{3}{4}$ is positive. This means that the function $f(x)$ is positive on this interval.

The Sign of f on the Interval $-\frac{3}{4} < x < 1$

The sign of $f$ on the interval $-\frac{3}{4} < x < 1$ is negative. This means that the function $f(x)$ is negative on this interval.

The Sign of f on the Interval $1 < x < \frac{8}{3}$

The sign of $f$ on the interval $1 < x < \frac{8}{3}$ is positive. This means that the function $f(x

Introduction

In our previous article, we explored the function $f(x)=(x-1)(4x+3)(3x-8)$ and determined the sign of $f$ on the interval $-\frac{3}{4} < x < 1$. In this article, we will answer some frequently asked questions related to the function and its zeros.

Q: What are the zeros of the function $f(x)=(x-1)(4x+3)(3x-8)$?

A: The zeros of the function $f(x)=(x-1)(4x+3)(3x-8)$ are $x=-\frac{3}{4}$, $x=1$, and $x=\frac{8}{3}$.

Q: How do you determine the sign of $f$ on a given interval?

A: To determine the sign of $f$ on a given interval, we need to analyze the behavior of the function on that interval. We can use the concept of sign charts to determine the sign of $f$ on a given interval.

Q: What is a sign chart?

A: A sign chart is a graphical representation of the sign of a function on different intervals. It is a useful tool for determining the sign of a function on a given interval.

Q: How do you create a sign chart?

A: To create a sign chart, we need to identify the zeros of the function and the intervals on which the function is positive or negative. We can then use this information to create a sign chart and determine the sign of $f$ on a given interval.

Q: What is the sign of $f$ on the interval $-\frac{3}{4} < x < 1$?

A: The sign of $f$ on the interval $-\frac{3}{4} < x < 1$ is negative.

Q: What is the sign of $f$ on the interval $1 < x < \frac{8}{3}$?

A: The sign of $f$ on the interval $1 < x < \frac{8}{3}$ is positive.

Q: What is the sign of $f$ on the interval $x > \frac{8}{3}$?

A: The sign of $f$ on the interval $x > \frac{8}{3}$ is positive.

Q: What is the sign of $f$ on the interval $x < -\frac{3}{4}$?

A: The sign of $f$ on the interval $x < -\frac{3}{4}$ is positive.

Q: How do you determine the sign of $f$ on a given interval using a sign chart?

A: To determine the sign of $f$ on a given interval using a sign chart, we need to identify the zeros of the function and the intervals on which the function is positive or negative. We can then use this information to create a sign chart and determine the sign of $f$ on a given interval.

Q: What are the benefits of using a sign chart to determine the sign of $f$ on a given interval?

A: The benefits of using a sign chart to determine the sign of $f$ on a given interval include:

• It is a visual representation of the sign of $f$ on different intervals.
• It is a useful tool for determining the sign of $f$ on a given interval.
• It can help to identify the zeros of the function and the intervals on which the function is positive or negative.

Q: How do you use a sign chart to determine the sign of $f$ on a given interval?

A: To use a sign chart to determine the sign of $f$ on a given interval, we need to:

• Identify the zeros of the function.
• Identify the intervals on which the function is positive or negative.
• Create a sign chart using this information.
• Use the sign chart to determine the sign of $f$ on a given interval.

Conclusion

In conclusion, the function $f(x)=(x-1)(4x+3)(3x-8)$ has zeros at $x=-\frac{3}{4}$, $x=1$, and $x=\frac{8}{3}$. To determine the sign of $f$ on a given interval, we need to analyze the behavior of the function on that interval. We can use the concept of sign charts to determine the sign of $f$ on a given interval.