draw the graph of y=f(x) for: a. f(x)=|x|+3x and b. f(x)= 2|x|-4

Here are the graphs of the two functions:

1. \( f(x) = |x| + 3x \): This function shows a V-shape with the left side sloping down and the right side sloping up more steeply due to the \(3x\) term.
2. \( f(x) = 2|x| - 4 \): This function also creates a V-shape but is shifted down by 4 units, with both branches of the graph rising, though less steeply than the first graph.

Would you like more details or have any questions?

Here are some follow-up questions related to this topic:
1. How do absolute value functions generally affect the graph of a function?
2. What is the significance of the term \(3x\) in the first function?
3. How does the transformation \( -4 \) affect the graph in the second function?
4. What would happen if the constant terms were removed from both functions?
5. Can you analyze how symmetry plays a role in both graphs?

**Tip:** Always check for points of intersection with the x-axis (roots) to better understand graph behavior.

Draw the graph of y=f(x) for: a. f(x)=|x|+3x and b. f(x)= 2|x|-4

Learn how to graph the absolute value functions f(x) = |x| + 3x and f(x) = 2|x| - 4. Explore key concepts such as graph transformations, absolute value behavior, and function intersections. Suitable for students in Grades 9-11.

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