Practice Shifting Functions in Math
Use these practice problems to test your method after reviewing the concept explanation and worked examples.
Quick Recap
Shifting a function translates its graph horizontally or vertically without changing its shape: f(x - h) + k shifts right by h and up by k.
Shifting is like sliding the entire graph on the coordinate plane — the function's shape is completely unchanged, only its position moves.
Example 1
easyStarting from f(x)=x^2, describe and sketch the transformations for g(x)=(x-3)^2+2.
Example 2
mediumThe graph of f(x)=e^x is shifted left 2 units and down 5 units to give g(x). Write g(x), find g(0), and determine if the horizontal asymptote changes.
Example 3
easyThe point (4, 7) is on the graph of y=f(x). Find the corresponding point on each shifted graph: (a) y=f(x-1)+3, (b) y=f(x+5)-2.
Example 4
mediumWrite the equation of the function whose graph is y=\sqrt{x} shifted right 9 and reflected over the x-axis. State the domain.