Graph this function:y=5|x|Click to plot the vertex first.

The given function is \( y = 5|x| \), which represents a V-shaped graph due to the absolute value. The vertex of this function is at the origin, \( (0, 0) \), since no horizontal or vertical shifts have been applied.

### Steps to Graph:
1. **Plot the Vertex:**
   The vertex of \( y = 5|x| \) is at \( (0, 0) \). This is the starting point of the graph.

2. **Plot Additional Points:**
   The absolute value function produces two linear parts, one for \( x \geq 0 \) and one for \( x < 0 \). The slope for the positive part is 5, and the slope for the negative part is also 5.

3. **Direction of the Graph:**
   For \( x > 0 \), the graph follows \( y = 5x \).  
   For \( x < 0 \), the graph follows \( y = 5(-x) \), which is equivalent to \( y = -5x \).

4. **Shape of the Graph:**
   The result is a V-shaped graph with steep lines due to the coefficient 5.

### Vertex:
You can click to plot the vertex at \( (0, 0) \).

Would you like further details or to explore specific points on the graph?

### Related Questions:
1. What would the graph look like if the function was \( y = 5|x| + 3 \)?
2. How would changing the coefficient from 5 to 2 affect the graph?
3. How do you graph an absolute value function when it's shifted horizontally?
4. What is the difference in graphing \( y = 5|x - 2| \) versus \( y = 5|x + 2| \)?
5. How does the slope of an absolute value graph affect its steepness?

### Tip:
When graphing absolute value functions, the coefficient outside the absolute value affects the steepness of the lines, while constants inside the absolute value affect horizontal shifts.

Graph this function: y=5|x| Click to plot the vertex first.

Learn how to graph the absolute value function y = 5|x|. This example focuses on plotting the vertex at the origin and understanding the V-shape formed by the function. Suitable for students in Grades 8-10, it covers the basic concepts of absolute value graphs and their slopes.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation