Math Problem Statement

Given the graph of f(x), find the function values for the provided x-values in problems 18 and 19.

Solution

The problem asks us to determine function values f(x)f(x) for specific xx values using the graphs provided in questions 18 and 19.

Analysis of Graph 18:

  1. For f(3)f(-3):

    • Locate x=3x = -3 on the graph. The function value corresponds to the yy-coordinate at this xx.
    • The point appears to be at y=2y = -2, so f(3)=2f(-3) = -2.
  2. For f(1)f(1):

    • At x=1x = 1, find the corresponding yy-value.
    • It appears to be y=4y = 4, so f(1)=4f(1) = 4.
  3. For f(0)f(0):

    • At x=0x = 0, the function appears to intersect the yy-axis at y=2y = 2.
    • Thus, f(0)=2f(0) = 2.
  4. For f(2)f(2):

    • At x=2x = 2, find the corresponding yy-value.
    • The graph shows y=0y = 0, so f(2)=0f(2) = 0.

Analysis of Graph 19:

  1. For f(4)f(-4):

    • Locate x=4x = -4. The yy-value there appears to be around y=3y = 3.
    • Thus, f(4)=3f(-4) = 3.
  2. For f(0)f(0):

    • At x=0x = 0, the function intersects the yy-axis around y=0y = 0.
    • So, f(0)=0f(0) = 0.
  3. For f(2)f(2):

    • At x=2x = 2, find the corresponding yy-value.
    • It seems to be around y=2y = -2, so f(2)=2f(2) = -2.
  4. For f(5)f(5):

    • At x=5x = 5, find the corresponding yy-value.
    • It appears to be at y=3y = 3, so f(5)=3f(5) = 3.

Final Answers:

  • Graph 18:
    • a) f(3)=2f(-3) = -2
    • b) f(1)=4f(1) = 4
    • c) f(0)=2f(0) = 2
    • d) f(2)=0f(2) = 0
  • Graph 19:
    • a) f(4)=3f(-4) = 3
    • b) f(0)=0f(0) = 0
    • c) f(2)=2f(2) = -2
    • d) f(5)=3f(5) = 3

Would you like further details or explanations on any of these values?

Related Questions:

  1. What is the significance of a function's roots, such as f(2)=0f(2) = 0 in Graph 18?
  2. How do you find the maximum or minimum values from a function's graph?
  3. What is the relationship between a graph's intercepts and its equation?
  4. How does the slope of a curve change at turning points?
  5. How can you determine the domain and range from a function's graph?

Tip: When analyzing graphs, always identify key points like intercepts, turning points, and end behaviors to understand the function’s behavior.

Ask a new question for Free

By Image

Drop file here or Click Here to upload

Math Problem Analysis

Mathematical Concepts

Graph Interpretation
Function Values
Coordinates

Formulas

-

Theorems

Graph interpretation of function values at specific points

Suitable Grade Level

Grades 8-10