To answer your questions, I'll walk you through how to interpret a graph to find the domain, range, x-intercepts, y-intercept, and specific function values like \( f(-2) \) and \( f(2) \). Since I cannot see the graph you're referring to, I'll explain how you would typically provide the answers based on a graph.
a. The Function's Domain
The domain of a function consists of all the possible input values (x-values) for which the function is defined.
- How to find it: Look at the extent of the graph from left to right. If the graph continues infinitely in both directions (or has no restrictions), then the domain is \((-∞, ∞)\). If there are gaps or it stops at certain points, note those intervals.
b. The Function's Range
The range includes all the possible output values (y-values) the function can produce.
- How to find it: Look at the graph from the bottom to the top. Identify the lowest and highest points the graph reaches. If it covers all values from a minimum to maximum, indicate that range in interval notation.
c. The x-intercepts
The x-intercepts are the points where the graph intersects the x-axis (i.e., where \(f(x) = 0\)).
- How to find it: Look for points on the graph where it touches or crosses the x-axis. The x-coordinates of those points are the x-intercepts.
d. The y-intercept
The y-intercept is the point where the graph intersects the y-axis (i.e., when \(x = 0\)).
- How to find it: Identify where the graph crosses the y-axis. The y-coordinate at that point is the y-intercept.
e. Missing function values
For \(f(-2)\) and \(f(2)\), you would evaluate the graph at these x-values.
- How to find it: Locate \(x = -2\) and \(x = 2\) on the x-axis and determine the corresponding y-values of the graph.
Example Summary
- a. Domain: \(\text{Interval notation based on the graph}\)
- b. Range: \(\text{Interval notation based on the graph}\)
- c. X-intercepts: \(\text{List the points, if any}\)
- d. Y-intercept: \(\text{Point, if any}\)
- e. \(f(-2) = \text{value from the graph}\), \(f(2) = \text{value from the graph}\)
If you have the graph's key features, you can fill in the blanks based on the steps outlined above.
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