Math Problem Statement

Use the graph of the function f shown to the right to answer parts​ (a)-(n). Question content area bottom left Part 1 ​(a) Find ​f(negative 14​) and ​f(negative 6​). f left parenthesis negative 14 right parenthesis equals    negative 2 f left parenthesis negative 6 right parenthesis equals    3 Part 2 ​(b) Find ​f(12​) and ​f(0​). f left parenthesis 12 right parenthesis equals    2 f left parenthesis 0 right parenthesis equals    negative 1 Part 3 ​(c) Is ​f(4​) positive or​ negative? Positive Positive Negative Negative Your answer is correct. Part 4 ​(d) Is ​f(negative 4​) positive or​ negative? Positive Positive Your answer is correct.Negative Negative Part 5 ​(e) For what​ value(s) of x is ​f(x)equals​0? xequals    enter your response here ​(Use a comma to separate answers as​ needed.)

Solution

To solve part (e), we need to find the values of xx where f(x)=0f(x) = 0, which represents the points where the graph crosses the x-axis.

These are the x-values where the function equals 0, or where the graph intersects the horizontal axis (y = 0).

Let’s summarize what we need:

  • Look for the points where f(x)=0f(x) = 0 by identifying the x-intercepts on the graph.

Since the graph is not provided in text form, I cannot see it directly. Could you describe the graph or provide the x-values where the graph intersects the x-axis? These x-values are the solutions for part (e).

Once you provide those details, I can give a complete answer.

Do you have any further questions about the previous parts, or would you like more details? Here are five related questions to expand on the information:

  1. What is the behavior of f(x)f(x) near x=14x = -14 and x=12x = 12?
  2. How do you determine whether a function is positive or negative using its graph?
  3. What is the significance of finding f(x)=0f(x) = 0 in terms of the function's real-world applications?
  4. How can we find the maximum and minimum points of a function using its graph?
  5. What does the slope of a graph tell us about the rate of change of the function?

Tip: Remember, the x-intercepts of a function are the points where the function's output is zero (y = 0), and these are crucial for solving many algebraic problems.

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Math Problem Analysis

Mathematical Concepts

Function Analysis
Graph Interpretation

Formulas

f(x) = 0 (finding x-intercepts)
Determining the sign of a function from a graph

Theorems

Basic properties of functions and their graphs

Suitable Grade Level

Grades 9-11