Question

describe the symmetry of these functions.

Explanation:

Step1: Check left - right symmetry

For the left - hand function, if we fold the graph along the y - axis, the two halves match. A function \(y = f(x)\) has line symmetry about the y - axis if \(f(-x)=f(x)\). This function has line symmetry about the y - axis and no rotational symmetry (a rotation of \(180^{\circ}\) or any other non - zero angle will not map the function onto itself).

Step2: Analyze the right - hand function

For the right - hand function, there is no line of symmetry (no vertical or horizontal line can be drawn such that the two halves of the graph match). Also, there is no rotational symmetry (a \(180^{\circ}\) or other non - zero angle rotation will not map the function onto itself).

Answer:

The left - hand function has line symmetry only; the right - hand function has no symmetry.