The function you provided is $f(x) = 5|x|$. This is an absolute value function, scaled by a factor of 5.

How to Graph $f(x) = 5|x|$:

1. Basic Shape: The graph of $f(x) = |x|$ is a "V" shape with its vertex at the origin $(0, 0)$.
2. Scaling Factor (5): The coefficient of 5 causes the graph to stretch vertically by a factor of 5. This makes the arms of the "V" steeper compared to the graph of $|x|$.
3. Behavior of the Function:
   • For $x \geq 0$, $f(x) = 5x$, so the graph is a straight line with slope 5.
   • For $x < 0$, $f(x) = -5x$, so the graph is a straight line with slope -5.

Key Points to Plot:

• Vertex: $(0, 0)$
• Point when $x = 1$: $f(1) = 5$
• Point when $x = -1$: $f(-1) = 5$
• Point when $x = 2$: $f(2) = 10$
• Point when $x = -2$: $f(-2) = 10$

You can plot these points and then draw straight lines through them to form the "V" shape.

Would you like further details on how to graph this or ask any related questions?

Here are 5 related questions you might find interesting:

1. What is the domain and range of $f(x) = 5|x|$?
2. How does changing the coefficient affect the steepness of the graph?
3. What happens if you add a constant, like $f(x) = 5|x| + 3$?
4. How do you reflect the graph of $f(x) = 5|x|$ across the x-axis?
5. How does the absolute value function affect the graph's symmetry?

Tip: The absolute value function always produces a graph that is symmetric about the y-axis!