Transformations of functions are an important concept in mathematics that involve changing the shape, size, and position of a function graph. Understanding how functions can be transformed is crucial in solving various mathematical problems. This worksheet is designed to help students practice and master the skills of transforming functions.
By working through this worksheet, students will be able to apply different transformations such as translations, reflections, and dilations to various types of functions. They will learn how these transformations affect the graph of a function and how they can be used to manipulate the behavior of a function. This hands-on practice will enhance their understanding of functions and their properties.
Worksheet on Transformations of Functions
1. Given the function f(x) = x^2, apply a vertical stretch of 2 to obtain the function g(x) = 2x^2. Graph both functions on the same set of axes and describe how the transformation changed the shape of the graph.
2. Transform the function h(x) = |x| by reflecting it across the y-axis to obtain the function k(x) = |-x|. Compare the graphs of h(x) and k(x) and explain the differences in their behavior.
3. Apply a horizontal translation of 3 units to the function p(x) = sin(x) to obtain the function q(x) = sin(x – 3). Graph both functions and analyze how the translation affected the position of the graph.
4. Dilate the function r(x) = sqrt(x) by a factor of 1/2 to obtain the function s(x) = sqrt(1/2x). Compare the graphs of r(x) and s(x) and determine how the dilation changed the size of the graph.
5. Given the function t(x) = 3/x, apply a vertical compression of 1/4 to obtain the function u(x) = 3/(4x). Graph both functions and discuss how the compression altered the behavior of the function.
By completing this worksheet, students will gain a deeper insight into the transformations of functions and how they can be used to manipulate graphs. Practicing these skills will improve their problem-solving abilities and enable them to tackle more complex mathematical concepts with confidence.