Math Problem Statement

Use the given graph of the function f to answer parts (a)-(e).

Solution

Let's go over the parts one by one based on the provided graph of the function f(x)f(x):

  1. Part (a)

    • f(12)=8f(12) = 8
    • f(0)=4f(0) = -4
  2. Part (c): Is f(4)f(4) positive or negative?

    • From the graph, at x=4x = 4, the function value f(4)=8f(4) = -8, so it is negative.
  3. Part (d): Is f(6)f(-6) positive or negative?

    • At x=6x = -6, the function value f(6)=12f(-6) = 12, so it is positive.
  4. Part (e): For what value(s) of xx is f(x)=0f(x) = 0?

    • The points where f(x)=0f(x) = 0 are the x-intercepts of the graph. These points are at x=12,2,8,12x = -12, -2, 8, 12.

Thus, for part (e), the values of xx are: x=12,2,8,12x = -12, -2, 8, 12

Let me know if you would like further details or explanations on any part!

Here are some related questions for further understanding:

  1. How do you find the x-intercepts of a function graphically?
  2. What does it mean when f(x)=0f(x) = 0?
  3. How would you determine whether a function is increasing or decreasing from a graph?
  4. How can you tell if a function is positive or negative from its graph?
  5. What does it mean when the function has multiple points where f(x)=0f(x) = 0?

Tip: To determine if a function is positive or negative at a given point, look at whether the function lies above or below the x-axis at that point!

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Math Problem Analysis

Mathematical Concepts

Graph Interpretation
Function Evaluation
Positive and Negative Values
X-Intercepts

Formulas

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Theorems

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Suitable Grade Level

Grades 9-11