Math Problem Statement

A 2-column table with 6 rows. The first column is labeled x with entries negative 2, negative 1, 0, 1, 2, 3. The second column is labeled f of x with entries negative 10, negative 8, negative 6, negative 4, negative 2, 0. Which is an x-intercept of the continuous function in the table?

Solution

The x-intercept of a function is the point where the function crosses the x-axis, meaning f(x)=0f(x) = 0. From the table, we need to find where f(x)=0f(x) = 0.

Given the table:

\hline x & f(x) \\ \hline -2 & -10 \\ -1 & -8 \\ 0 & -6 \\ 1 & -4 \\ 2 & -2 \\ 3 & 0 \\ \hline \end{array}$$ We can see that at $$x = 3$$, $$f(3) = 0$$. Thus, the x-intercept is at **$$x = 3$$**. Would you like more details or have any questions? Here are 5 related questions: 1. What is the y-intercept of this function? 2. How do we calculate the slope between two points in the table? 3. Is this function linear based on the given data? 4. How can you determine if a function is continuous from a table? 5. What happens if a function has multiple x-intercepts? **Tip:** An x-intercept occurs where the function value equals zero; always check for this when interpreting tables of functions.

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Math Problem Analysis

Mathematical Concepts

Functions
X-Intercept
Continuous Functions

Formulas

f(x) = 0

Theorems

X-Intercept Theorem: A function crosses the x-axis when f(x) = 0

Suitable Grade Level

Grades 6-8