Transforming Functions

Unlock function transformations! Practice shifts, reflections, and more with interactive worksheets.

How does the graph of f(x) compare to the graph of f(x)-k? (Assume k is a positive integer) shifts it up shifts it right shifts it down shifts it left How does the graph of f(x) compare to the graph of f(x-k)? (assume k is a positive number) shifts it up shifts it right shifts it down shifts it left How does the graph of kf(x) compare to the graph of kf(x) when 0 <k < 1? reflects it over the x-axis makes it narrower shifts it to the right makes it wider How does the graph of f(x) compare to the graph of f(x+k)? (Assume k is a positive number) shifts it up shifts it right shifts it down shifts it left How does the graph of -f(x) compare to the graph of f(x)? shifts it down reflected over the y-axis reflected over the x-axis makes it wider How does the graph of f(x) compare to the graph of f(x)+k? (Assume k is a positive integer) shifts it up shifts it right shifts it down shifts it left How does the graph of kf(x) compare to the graph of kf(x) when k > 1? reflects it over the y-axis makes it narrower shifts it up makes it wider Matching Match the change in the function on the left to the transformation on the right -f(x) --> negative sign in front reflects over x-axis kf(x) --> a number in front bigger than 1. narrower kf(x) --> number in front between 0 and 1 wider f(x + k) --> adding to x inside the parenthesis / absolute value shift left f(x - k) --> subtracting from x inside the parenthesis / absolute value shift right f(x) + k --> adding a number outside the parenthesis / absolute value shift up f(x) - k --> subtracting a number outside the parenthesis / absolute value shift down In the following picture, the red graph represents a transformation of the parent function, f(x)=x3, in black. Choose the equation that most likely represents the red graph. f(x) = x3 + 3 f(x) = x3 -3 f(x) = (x + 3)3 f(x) = (x -3)3 In the following picture, the red graph represents a transformation of the parent function, f(x)=x2, in black. Choose the equation that most likely represents the red graph. f(x) = 2x2 f(x) = -2x2 f(x) = x2+ 2 f(x) = x2- 2 In the following picture, the red graph represents a transformation of the parent function, f(x)=|x|, in black. Choose the equation that most likely represents the red graph. f(x) = |x| + 2 f(x) = |x| - 2 f(x) =|x+ 2| f(x) =|x -2| Sort the functions into the correct transformation category: Reflected across the x-axis f(x) = -x2 f(x) = -x3 f(x) = -x Wider f(x) = .5x2 f(x) = .25|x| f(x) = (2 Narrower f(x) = 4x2 f(x) = 1.5x f(x) = 2x3 Horizontal Shift (Left or Right) f(x) = (x + 2)2 f(x) = (x - 6)3 f(x) = |x+ 1| Vertical Shift (Up or Down) f(x) = x3 - 6 f(x) = x + 1