Math Problem Statement

Identify the x- and y-intercepts of the functions graphed below.

Solution

To solve this, let's identify the x-intercepts and y-intercepts of the graphs one by one.

  1. Graph 1:

    • x-intercept(s): The graph crosses the x-axis at approximately x=1x = 1.
    • y-intercept: The graph crosses the y-axis at approximately y=1y = 1.
  2. Graph 2:

    • x-intercept(s): The graph crosses the x-axis at two points, approximately at x=1x = -1 and x=1x = 1.
    • y-intercept: The graph crosses the y-axis at y=2y = 2.
  3. Graph 3:

    • x-intercept(s): No x-intercept, the graph does not touch or cross the x-axis.
    • y-intercept: The graph crosses the y-axis at approximately y=0.5y = 0.5.
  4. Graph 4:

    • x-intercept(s): The graph crosses the x-axis at x=2x = -2 and x=2x = 2.
    • y-intercept: The graph crosses the y-axis at y=0y = 0.
  5. Graph 5:

    • x-intercept(s): No x-intercept.
    • y-intercept: No y-intercept.
  6. Graph 6:

    • x-intercept(s): The graph crosses the x-axis at x=3x = 3.
    • y-intercept: The graph crosses the y-axis at y=1y = 1.

Would you like a more detailed breakdown for any of these? Here are some relative questions to expand your understanding:

  1. What are the properties of functions that don't have x-intercepts or y-intercepts?
  2. How can we determine the number of x-intercepts of a quadratic function by looking at its equation?
  3. What are the differences between linear and nonlinear functions in terms of intercepts?
  4. Can a graph have more than one y-intercept? Why or why not?
  5. How do you find intercepts algebraically if the function's equation is given?

Tip: A function's x-intercept(s) can be found by setting f(x)=0f(x) = 0, while the y-intercept is found by setting x=0x = 0.

Ask a new question for Free

By Image

Drop file here or Click Here to upload

Math Problem Analysis

Mathematical Concepts

Functions
Intercepts
Graph Analysis

Formulas

y = f(x)

Theorems

-

Suitable Grade Level

Grades 8-10