Math Problem Statement

Evaluate g(0) and find the value(s) of x where g(x) = 3 using the graph of the function g(x).

Solution

Let's analyze the graph to solve the given questions:

  1. Evaluate g(0)g(0):

    • To find g(0)g(0), locate the point on the graph where x=0x = 0. The y-coordinate at this point represents g(0)g(0).
    • From the graph, when x=0x = 0, g(0)=1g(0) = -1.
  2. For what value(s) of xx does g(x)=3g(x) = 3?

    • To find the value of xx where g(x)=3g(x) = 3, look for the point on the graph where the y-coordinate is 3.
    • From the graph, g(x)=3g(x) = 3 when x=2x = 2.

Answers:

  • g(0)=1g(0) = -1
  • x=2x = 2 when g(x)=3g(x) = 3

Would you like more details on how to interpret such graphs or any other questions?

Here are 5 related questions:

  1. What is the slope of the given linear function?
  2. How would you find the x-intercept of the graph?
  3. How can you express this linear function algebraically?
  4. For what value of xx does g(x)=3g(x) = -3?
  5. What is the domain and range of this function?

Tip: When interpreting a graph, remember that the x-values represent the input to the function, and the y-values represent the output.

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Math Problem Analysis

Mathematical Concepts

Algebra
Linear Functions
Graph Interpretation

Formulas

y = mx + b

Theorems

Slope-Intercept Form
Linear Function Theorem

Suitable Grade Level

Grades 6-8