Reflections in the y-axis

If f(x) is a function, the function g(x) = f(-x) is the reflection of f in the y-axis. In all of the problems below, g(x) = f(-x).

1. If f(x) = x – 1, what is the formula for g(x)? Sketch the graphs of f and g on the same set of axes.

2. If f(x) = |x – 1|, what is the formula for g(x)? Sketch the graphs of f and g on the same set of axes.

3. If f(x) = x^{2} + 1, what is the formula for g(x)? Sketch the graphs of f and g on the same set of axes.

4. If f(x) = -(x – 1)^{2}, what is the formula for g(x)? Sketch the graphs of f and g on the same set of axes.

5. If f(x) = |x + 2|, what is the formula for g(x)? Sketch the graphs of f and g on the same set of axes.