Function Graphs Worksheet
Explore and analyze various function graphs including linear, quadratic, cubic, and trigonometric functions. This worksheet covers identifying key features, transformations, and interpreting graphical representations of functions.
Includes
Standards
Topics
Function Graphs Exploration
Name:
Date:
Score:
Read each question carefully and provide your answers in the space provided. Show all your work for full credit.
1. Consider the function f(x) = x³ - 4x. Sketch its graph and identify all x-intercepts, y-intercepts, and intervals where the function is increasing or decreasing.
X-intercepts:
Y-intercepts:
Increasing intervals:
Decreasing intervals:
2. The graph of y = |x| is transformed to obtain the graph of y = -2|x + 3| + 1. Which of the following describes the transformations applied?
Reflected across the x-axis, stretched vertically by a factor of 2, shifted left by 3 units, and shifted up by 1 unit.
Reflected across the y-axis, stretched vertically by a factor of 2, shifted right by 3 units, and shifted up by 1 unit.
Reflected across the x-axis, compressed vertically by a factor of 2, shifted left by 3 units, and shifted up by 1 unit.
Reflected across the x-axis, stretched horizontally by a factor of 2, shifted left by 3 units, and shifted up by 1 unit.
3. For the function y = 3sin(2x - π) + 4, the amplitude is , the period is , the phase shift is , and the vertical shift is .
4. Graph the piecewise function f(x) = { x + 2 if x < 0, x² if x ≥ 0 } on the coordinate plane below.
Explain any discontinuities in the graph.
Related Worksheets
Grade 12 Math: Function Mapping Worksheet
This worksheet focuses on understanding and applying function mapping concepts, including domain, codomain, range, and types of mappings (one-to-one, onto, bijective).
Domain, Range, and End Behavior of Functions
Explore and analyze the domain, range, and end behavior of various functions at a Grade 12 level, including polynomial, rational, and radical functions.
Grade 12 Function Relations Worksheet
A Grade 12 Math worksheet focusing on understanding and analyzing function relations, including domain, range, inverse functions, and composition of functions.
Parent Functions and Transformations
Explore parent functions and their transformations including translations, reflections, stretches, and compressions at a Grade 12 level.
Grade 12 Function Composition Worksheet
This worksheet covers key concepts and applications of function composition for Grade 12 students, including evaluating composite functions and finding domains.
Transformation of Graphs Worksheet
Grade 12 Math worksheet on graph transformations including translations, reflections, stretches, and compressions.
Exponential Function Manipulation
A Grade 12 math worksheet focusing on manipulating and understanding exponential functions, including graphing, transformations, and solving equations.
Grade 12 Function Transformation Worksheet
A Grade 12 Math worksheet on function transformations, covering translations, reflections, stretches, and compressions.