Match The Graph Of F With The Correct Sign Chart
Introduction
Mathematics is a subject that has always been feared by many students. There are many concepts that students find difficult to understand. One such concept is matching the graph of f with the correct sign chart. In this article, we will explore this concept and learn how to match the graph of f with the correct sign chart.
What is f?
f is a function that is represented by a graph. A graph is a visual representation of the function. It shows the relation between the input and output values of the function. The graph of f can be used to determine the behavior of the function.
What is a sign chart?
A sign chart is a table that is used to determine the sign of a function in different intervals. It is used to analyze the behavior of the function. The sign chart is divided into intervals based on the roots of the function. The sign of the function is determined in each interval.
How to match the graph of f with the correct sign chart?
To match the graph of f with the correct sign chart, we need to follow the following steps:
- Determine the roots of the function
- Divide the number line into intervals based on the roots
- Determine the sign of the function in each interval
- Compare the sign chart with the graph of f
Example
Let's consider the function f(x) = (x-2)(x+3)(x-5).
Step 1: Determine the roots of the function.
The roots of the function are x=2, x=-3, and x=5.
Step 2: Divide the number line into intervals based on the roots.
We have three intervals: (-∞,-3), (-3,2), and (2,5), and (5,∞).
Step 3: Determine the sign of the function in each interval.
In the interval (-∞,-3), all three factors of the function are negative, so the sign of the function is negative.
In the interval (-3,2), the factor (x+3) is positive, and the factors (x-2) and (x-5) are negative. So, the sign of the function is positive.
In the interval (2,5), all three factors of the function are positive, so the sign of the function is positive.
In the interval (5,∞), the factors (x-2) and (x+3) are positive, and the factor (x-5) is negative. So, the sign of the function is negative.
Step 4: Compare the sign chart with the graph of f.
From the graph of f, we can see that the function is negative in the interval (-∞,-3), positive in the interval (-3,2), positive in the interval (2,5), and negative in the interval (5,∞). This matches with the sign chart we have obtained.
Conclusion
Matching the graph of f with the correct sign chart is an important concept in mathematics. It helps us to analyze the behavior of the function. By following the steps mentioned in this article, we can easily match the graph of f with the correct sign chart.