Question

What are the domain and range of this function?

Answer 1

Answer: Choice D

• Domain: all real numbers
• Range: $y \ge 1$

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Explanation:

The domain is the set of allowed x inputs. We can plug in any x value we want as the graph stretches on forever to the left and to the right. There aren't any division by zero errors or any issues like that to worry about, so that's why we don't kick out any x values from the domain.

The domain being all real numbers translates to the interval notation $(-\infty, \infty)$ which is basically saying $-\infty < x < \infty$

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The range is the set of y outputs possible. The graph shows that y = 1 is the smallest y output, so y = 1 or y can be greater than this.

In short, $y \ge 1$ is the range which converts to the interval notation $[1, \infty)$ which is the same as saying $1 \le y < \infty$

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Extra info:

The equation of this absolute value function is y = |x|+1