Math Problem Statement

Find the x-intercept of the function represented by the graph. Responses A 10 B 20 C 25 D 50

Find the x-intercept of the function represented by the graph.

Solution

To find the xx-intercept of the function represented in this graph, we look for the point where the curve crosses the xx-axis (where y=0y = 0).

Observing the graph:

  1. The curve appears to be asymptotic near x=0x = 0, approaching the yy-axis from the left as yy \to -\infty.
  2. The graph crosses the xx-axis at a point around x=10x = 10.

Answer:

The xx-intercept is approximately at x=10x = 10, so the correct answer is: A) 10

Would you like more detailed steps or further analysis?


Here are five related questions to deepen understanding:

  1. How do you determine the xx-intercept of a function given its equation?
  2. What does it mean for a function to be asymptotic to the yy-axis?
  3. How would you find the yy-intercept if the function has one?
  4. Can the slope of the graph near the xx-intercept give any insights into the function's behavior?
  5. What kind of functions typically have asymptotes, like the one seen near x=0x = 0?

Tip: For functions that seem to diverge near the axes, look for vertical or horizontal asymptotes as clues about their behavior.

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Math Problem Analysis

Mathematical Concepts

Algebra
Graph Analysis
Intercepts
Asymptotes

Formulas

x-intercept: f(x) = 0

Theorems

Intercept Theorem

Suitable Grade Level

Grades 8-10