Which of the following is NOT a space curve? Tick all that apply A \( x=f(t), y=g(t), z=h(t) \) B \( x=2, y=3, z=4 \) C \( x=t, y=t, z=t \) D \( x=1+t, y=t^{3}, z=t^{2}-1 \)

1. A space curve is typically defined as a one-dimensional curve embedded in three-dimensional space. It is expressed with equations of the form \[ x = f(t),\quad y = g(t),\quad z = h(t) \] where \(t\) is a parameter. 2. **Option A:** \[ x = f(t),\quad y = g(t),\quad z = h(t) \] This is the standard form of a space curve. 3. **Option B:** \[ x = 2,\quad y = 3,\quad z = 4 \] Since there is no parameter and the coordinates are constant, this represents a single point in space rather than a curve. 4. **Option C:** \[ x = t,\quad y = t,\quad z = t \] This describes a line in space along the direction \((1,1,1)\), which is a space curve. 5. **Option D:** \[ x = 1+t,\quad y = t^{3},\quad z = t^{2}-1 \] This is a parametric representation of a curve in space. Thus, the option that is NOT a space curve is: B