Question

On a coordinate plane, an absolute value graph has a vertex at (0, 0). complete the statements for the graph of f(x) = |x|. the domain of the function is . the range of the function is . the graph is over the interval (0, [infinity]). the graph is over the interval (–[infinity], 0).

Answer 1

The graph of f(x) = |x| has a domain of all real numbers, a range of non-negative real numbers, increases over the interval (0, infinity), and appears to be increasing over the interval (–infinity, 0) due to reflection.

Step-by-step explanation:

For the graph of f(x) = |x|, with its vertex at (0,0), we can complete the following statements:

• The domain of the function is –[infinity, infinity], which means x can be any real number.
• The range of the function is [0, infinity], because the absolute value of x cannot be negative.
• The graph is increasing over the interval (0, infinity) as x gets larger, the value of |x| also increases.
• The graph is decreasing over the interval (–infinity, 0), but because |x| takes the absolute value, the graph is reflected upwards and still appears to be increasing.

Therefore, the graph forms a V-shape centered at the origin. Over the interval (0, infinity), the graph mirrors the positive side of the x-axis ascending. Conversely, for the interval (–infinity, 0), the graph mirrors the negative side of the x-axis but is reflected upwards due to taking the absolute value.

Answer 2

The graph of f(x) = |x| has a domain of all real numbers and a range of all non-negative real numbers. The graph increases over the interval (0, infinity) and decreases over the interval (-infinity, 0).

Step-by-step explanation:

On a coordinate plane, the graph of f(x) = |x| with a vertex at (0, 0) will create a V-shaped graph that opens upwards. The domain of this function is all real numbers, because |x| is defined for any real number x.

The range of the function is all non-negative real numbers (y ≥ 0), since the absolute value cannot be negative.

The graph is increasing over the interval (0, [infinity]), because as x increases, so does |x|. Conversely, the graph is decreasing over the interval (–[infinity], 0) since as x decreases, |x| increases.

However, the graph appears as a reflection across the y-axis because |x| yields the same value for both positive and negative x of the same magnitude.