Math Problem Statement

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Find f(1) and one value of x for which f(x) = 0 based on the graph of a function f.

Solution

Let's solve the problem step by step by analyzing the graph and the given questions:

(a) Find f(1)f(1):

To find f(1)f(1), look at the graph where x=1x = 1 and find the corresponding yy-value. On the graph, when x=1x = 1, the yy-value is approximately 3. Hence:

f(1)=3f(1) = 3

(b) Find one value of xx for which f(x)=0f(x) = 0:

We are looking for the xx-value where the graph intersects the xx-axis, which is when f(x)=0f(x) = 0. From the graph, the function intersects the xx-axis at x=3x = -3.

Thus:

x=3x = -3

Final answers:

  • f(1)=3f(1) = 3
  • One value of xx for which f(x)=0f(x) = 0 is x=3x = -3.

Let me know if you need any more details!


Here are 5 related questions for further practice:

  1. What is f(0)f(0) based on the graph?
  2. Find the slope of the line represented by the graph.
  3. How would you find the yy-intercept of the function?
  4. What is the domain and range of this function?
  5. How can you express this linear function algebraically?

Tip: To find where a function equals zero (i.e., its roots), always check where it crosses the x-axis.

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Math Problem Analysis

Mathematical Concepts

Linear Functions
Graph Analysis

Formulas

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Theorems

Linear Graphs and their intercepts

Suitable Grade Level

Grades 8-10