88.1k views
2 votes
Part A: Given the function g(x) = |x − 5|, describe the graph of the function, including the vertex, domain, and range. (5 points)

User Kdeez
by
8.8k points

1 Answer

3 votes

Final answer:

The graph of g(x) = |x - 5| is a V-shaped graph with its vertex at (5, 0), the domain is all real numbers, and the range is all non-negative real numbers.

Step-by-step explanation:

The graph of the function g(x) = |x - 5| is a V-shaped graph. This is because the absolute value function takes all negative inputs and makes them positive, which causes the graph to reflect across the x-axis when x is less than 5. The vertex of this graph appears when the expression inside the absolute value is zero; hence for g(x), the vertex is at (5, 0).

The domain of g(x) is all real numbers because there are no restrictions on the values that x can take, so the domain is (-∞, +∞). The range is all non-negative real numbers since the absolute value is always zero or positive, and so the range is [0, +∞). When sketching the graph, it is crucial to scale the x and y axes and label the graph with g(x) and x correctly.

User Aphoe
by
7.6k points

No related questions found

Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories