Question

Which phrases describe the graph of f(x) = |x| ? Check all that apply.

V-shaped
U-shaped
opens up
opens down
symmetric with respect to the x-axis
symmetric with respect to the y-axis

Answer 1

Correct choices:
- V-shaped — yes (two straight rays meeting at a vertex).
- opens up — yes (minimum at (0,0) and the graph extends upward).
- symmetric with respect to the y-axis — yes (|x| = |−x|, so it's even).

Not correct:
- U-shaped — no (U-shape implies a smooth parabola, not the sharp V).
- opens down — no (the graph does not extend downward).
- symmetric with respect to the x-axis — no (there are no negative y-values).