Lesson Worksheet: Graphs of Piecewise Functions Mathematics • 10th Grade

In this worksheet, we will practice graphing and analyzing a piecewise-defined function and studying its different characteristics.


What kind of function is depicted in the graph?

  • Aan even function
  • Ba logarithmic function
  • Ca piecewise function
  • Da polynomial function


Give the piecewise definition of the function β„Ž whose graph is shown.

  • Aβ„Ž(π‘₯)=π‘₯2π‘₯≀2,3+π‘₯2≀π‘₯ifif
  • Bβ„Ž(π‘₯)=π‘₯2π‘₯≀2,3βˆ’π‘₯2≀π‘₯ifif
  • Cβ„Ž(π‘₯)=3+π‘₯π‘₯≀2,π‘₯22≀π‘₯ifif
  • Dβ„Ž(π‘₯)=3βˆ’π‘₯π‘₯<2,π‘₯22≀π‘₯ifif
  • Eβ„Ž(π‘₯)=3βˆ’2π‘₯π‘₯≀2,π‘₯22≀π‘₯ifif


Give the piecewise definition of the function 𝑓 whose graph is shown.

  • A𝑓(π‘₯)=⎧βŽͺ⎨βŽͺ⎩π‘₯2+2π‘₯<2,2π‘₯=2,3+π‘₯2<π‘₯ififif
  • B𝑓(π‘₯)=⎧βŽͺ⎨βŽͺ⎩3βˆ’π‘₯π‘₯<2,2π‘₯=2,π‘₯2+22<π‘₯ififif
  • C𝑓(π‘₯)=⎧βŽͺ⎨βŽͺ⎩π‘₯2+2π‘₯<2,2π‘₯=2,3βˆ’π‘₯2<π‘₯ififif
  • D𝑓(π‘₯)=⎧βŽͺ⎨βŽͺ⎩3βˆ’2π‘₯π‘₯<2,2π‘₯=2,π‘₯2+22<π‘₯ififif
  • E𝑓(π‘₯)=⎧βŽͺ⎨βŽͺ⎩3+π‘₯π‘₯<2,2π‘₯=2,π‘₯2+22<π‘₯ififif


Determine the range of the function represented by the given graph.

  • A{βˆ’7}
  • Bℝ
  • C{βˆ’7,7}
  • D{7}
  • Eβ„βˆ’{βˆ’7}


Determine the domain of the function represented by the given graph.

  • Aβ„βˆ’{βˆ’4}
  • Bℝ
  • C]βˆ’2,∞[
  • D{βˆ’2,1}


Find the range of the function.

  • A[βˆ’2,∞[
  • Bℝ
  • C]βˆ’βˆž,βˆ’2]
  • D[βˆ’1,∞[
  • E]βˆ’βˆž,βˆ’1]


Determine the range of the function represented by the following graph.

  • A]βˆ’3,∞[
  • Bβ„βˆ’{βˆ’3,2}
  • Cβ„βˆ’[βˆ’3,2]
  • D]βˆ’1,∞[
  • Eβ„βˆ’{βˆ’1}


Give the piecewise definition of the function 𝑔 whose graph is shown.

  • A𝑔(π‘₯)=1π‘₯<βˆ’1,(π‘₯βˆ’2)(π‘₯βˆ’3)1≀π‘₯≀4,π‘₯βˆ’24<π‘₯ififif
  • B𝑔(π‘₯)=1π‘₯≀1,(π‘₯+2)(π‘₯βˆ’3)1<π‘₯<4,π‘₯βˆ’24≀π‘₯ififif
  • C𝑔(π‘₯)=1π‘₯<βˆ’1,(π‘₯+2)(π‘₯βˆ’3)1≀π‘₯≀4,π‘₯βˆ’24<π‘₯ififif
  • D𝑔(π‘₯)=1π‘₯≀1,(π‘₯βˆ’2)(π‘₯βˆ’3)1<π‘₯<4,π‘₯βˆ’24≀π‘₯ififif
  • E𝑔(π‘₯)=1π‘₯<1,(π‘₯+2)(π‘₯βˆ’3)1≀π‘₯≀4,π‘₯βˆ’24<π‘₯ififif


Which of the following is the piecewise definition of the function 𝑓(π‘₯) whose graph is shown?

  • A𝑓(π‘₯)=π‘₯+3,βˆ’8<π‘₯β‰€βˆ’3,π‘₯βˆ’9,βˆ’3<π‘₯<2,βˆ’5,2≀π‘₯<6
  • B𝑓(π‘₯)=π‘₯+3,βˆ’8<π‘₯β‰€βˆ’3,π‘₯βˆ’9,βˆ’3<π‘₯<2,βˆ’5π‘₯,2≀π‘₯<6
  • C𝑓(π‘₯)=π‘₯+3,βˆ’8<π‘₯β‰€βˆ’3,π‘₯βˆ’3,βˆ’3<π‘₯<2,βˆ’5π‘₯,2<π‘₯<6
  • D𝑓(π‘₯)=π‘₯+3,βˆ’8<π‘₯β‰€βˆ’3,π‘₯βˆ’3,βˆ’3<π‘₯<2,βˆ’5,2≀π‘₯<6
  • E𝑓(π‘₯)=π‘₯+2,βˆ’8<π‘₯β‰€βˆ’3,π‘₯βˆ’9,βˆ’3<π‘₯<2,βˆ’5,2≀π‘₯<6


State which of the following graphs represents the function 𝑓(π‘₯)=π‘₯,π‘₯<2,βˆ’2π‘₯+10,π‘₯β‰₯2.

  • A
  • B
  • C
  • D
  • E

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