How to Graph Absolute Value Functions Step by Step

TL;DR

To graph absolute value functions, start by finding the vertex by setting the inside expression to zero. Choose points around the vertex to calculate corresponding y-values, plot them, and draw the V-shape. The axis of symmetry is the vertical line through the vertex, while the domain is all real numbers, and the range depends on the lowest y-value and approaches infinity.

Transcript

in this video we're going to focus on graphing absolute value functions and we're going to talk about how to find the axis of symmetry vertex the transformations domain and range and things like that so let's say if you have this function y is equal to the absolute value of x plus 2. how would you graph it using a table first what you want to do is... Read More

Key Insights

• 🧡 Graphing absolute value functions involves finding the vertex and axis of symmetry, as well as determining the domain and range of the function.
• 😑 The vertex is found by setting the inside expression equal to zero and solving for x.
• 🫥 The axis of symmetry is the vertical line that passes through the vertex and represents the line of symmetry.
• 💛 The domain of an absolute value function is all real numbers, while the range depends on the lowest and highest y-values of the graph.
• 📈 Transformations, such as shifting and reflecting the graph, can be determined by the values in the equation.
• 😥 It is important to plot points around the vertex to ensure a correct graph.

Questions & Answers

Q: How can you find the x-coordinate of the vertex of an absolute value function?

To find the x-coordinate of the vertex, set the inside expression equal to zero and solve for x. This will give you the x-coordinate of the vertex.

Q: What does the axis of symmetry represent in a graph of an absolute value function?

The axis of symmetry is a vertical line that passes through the vertex of the absolute value function. It represents the line of symmetry in the graph.

Q: How do you determine the domain of an absolute value function?

The domain of an absolute value function is all real numbers, as long as there are no restrictions such as fractions, logarithms, or square roots.

Q: How can transformations affect the graph of an absolute value function?

Transformations, such as shifting the graph horizontally or vertically, can be determined by the values in the equation. For example, adding or subtracting a value inside the absolute value symbol will shift the graph horizontally, while adding or subtracting a value outside the absolute value symbol will shift the graph vertically.

Summary & Key Takeaways

• Graphing absolute value functions involves finding the vertex, which can be determined by setting the inside expression equal to zero and solving for x.

• To graph the function, choose points around the vertex and calculate their corresponding y-values.

• The axis of symmetry is the vertical line that passes through the vertex, and the domain of an absolute value function is all real numbers. The range depends on the lowest and highest y-values of the graph.