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) = x2 + 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.