Questions: a) Graph f(x)=3x, b) Find f(-3) and f(4) c) State the domain of the function.

Solution Steps

The given function is \( f(x) = |3x| \). This is an absolute value function, which means it will always produce non-negative outputs regardless of the input.

The graph of \( f(x) = |3x| \) will be a V-shaped graph that opens upwards. The vertex of the graph will be at the origin (0,0), and the graph will be symmetric about the y-axis.

Among the given options, the correct graph is the one that shows a V-shaped graph opening upwards with the vertex at the origin. This corresponds to option A.

To find \( f(-3) \) and \( f(4) \):

• \( f(-3) = |3(-3)| = | -9 | = 9 \)
• \( f(4) = |3(4)| = | 12 | = 12 \)

The domain of \( f(x) = |3x| \) is all real numbers, since the absolute value function is defined for all real numbers.

Final Answer