Lesson Worksheet: Cubic Functions and Their Graphs Mathematics • 10th Grade

In this worksheet, we will practice graphing cubic functions, writing their rules from their graphs, and identifying their features.

Q1:

Which equation matches the graph?

  • A𝑦=(π‘₯βˆ’2)βˆ’1
  • B𝑦=(π‘₯βˆ’2)+1
  • C𝑦=(π‘₯+2)βˆ’1
  • D𝑦=(π‘₯+2)+1

Q2:

Consider the graph of the function 𝑦=(π‘₯+2)βˆ’2.

Write down the coordinates of the point of symmetry of the graph, if it exists.

  • A(βˆ’1,βˆ’1)
  • B(βˆ’2,βˆ’2)
  • C(βˆ’2,2)
  • D(0,0)
  • EIt does not exist.

Q3:

Which of the following is the graph of 𝑓(π‘₯)=βˆ’(π‘₯βˆ’2)?

  • A
  • B
  • C
  • D
  • E

Q4:

Which equation matches the red graph?

  • A𝑦=π‘₯
  • B𝑦=0.5π‘₯
  • C𝑦=0.25π‘₯
  • D𝑦=2π‘₯
  • E𝑦=4π‘₯

Q5:

Which equation matches the green graph?

  • A𝑦=(π‘₯+2)
  • B𝑦=π‘₯
  • C𝑦=(π‘₯βˆ’4)
  • D𝑦=(π‘₯+4)
  • E𝑦=(π‘₯βˆ’2)

Q6:

Which of the following graphs represents 𝑓(π‘₯)=2βˆ’(π‘₯βˆ’5)?

  • A(d)
  • B(a)
  • C(c)
  • D(b)

Q7:

Which equation matches the graph?

  • A𝑦=12(π‘₯βˆ’1)+4
  • B𝑦=13(π‘₯βˆ’1)+4
  • C𝑦=3(π‘₯βˆ’1)+4
  • D𝑦=2(π‘₯βˆ’1)+4
  • E𝑦=(π‘₯βˆ’1)+4

Q8:

If 𝑓(π‘₯)=π‘₯ is changed to 𝑓(π‘₯)=(π‘₯βˆ’1)+5, how is the graph transformed?

  • AHorizontally shifted left by 5 and vertically shifted up by 1
  • BHorizontally shifted left by 5 and vertically shifted down by 1
  • CHorizontally shifted right by 1 and vertically shifted down by 5
  • DHorizontally shifted left by 1 and vertically shifted up by 5
  • EHorizontally shifted right by 1 and vertically shifted up by 5

Q9:

If 𝑓(π‘₯)=π‘₯ is changed to 𝑦=0.1(π‘₯βˆ’10), how is the graph transformed?

  • AStretched by a factor of 10 in the 𝑦-direction and shifted right by 0.1
  • BStretched by a factor of 0.1 in the 𝑦-direction and shifted right by 10
  • CStretched by a factor of 0.1 in the 𝑦-direction and shifted left by 10
  • DStretched by a factor of 0.1 in the 𝑦-direction and shifted right by 10
  • EStretched by a factor of 10 in the 𝑦-direction and shifted left by 0.1

Q10:

Find the function shown in the figure.

  • A𝑓(π‘₯)=βˆ’(π‘₯βˆ’4)+4
  • B𝑓(π‘₯)=(π‘₯βˆ’4)+4
  • C𝑓(π‘₯)=βˆ’(π‘₯+4)βˆ’4
  • D𝑓(π‘₯)=(π‘₯+4)βˆ’4

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