Question
\( 1 \leftarrow \quad \) Graph the linear function. Give its domain and range.
Ask by Tran Edwards. in the United States
Feb 16,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
The graph of the function y = 1 is a horizontal line at y = 1. The domain is all real numbers, and the range is just the single value 1.
Solution
We are given the function
y = 1
which is a horizontal line passing through the point (0, 1).
• Graph Description:
– On the coordinate plane, plot the point (0, 1) on the y‐axis.
– Draw a horizontal line through (0, 1) that extends left and right indefinitely.
– Every point on the line has y-coordinate equal to 1.
• Domain:
Since x can be any real number, the domain is all real numbers.
In interval notation: (–∞, ∞).
• Range:
Since y is always 1 (no matter what x is), the range is just the single value {1}.
Thus, the graph of the linear function y = 1 is a horizontal line at y = 1, with domain (–∞, ∞) and range {1}.
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Simplify this solution Bonus Knowledge
To graph the linear function \( y = 1 \), you simply draw a horizontal line that crosses the y-axis at 1. This line extends infinitely to the left and right, representing that for every value of x, the output (y) will always be 1. The domain of this function is all real numbers: \( (-\infty, \infty) \). The range, however, is quite specific since the output never changes; it is just the single value \( 1 \): \( \{ 1 \} \). So, you get a straight line and clear constraints!
