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.
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Function Graphs Exploration
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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.