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Worksheet: Graphing Cubic Functions

Q1:

Find the equation for the graph.

  • A 𝑓 ( π‘₯ ) = π‘₯ 2
  • B 𝑓 ( π‘₯ ) = √ π‘₯
  • C 𝑓 ( π‘₯ ) = 1 π‘₯
  • D 𝑓 ( π‘₯ ) = π‘₯ 3

Q2:

Find the function shown in the figure.

  • A 𝑓 ( π‘₯ ) = ( π‘₯ βˆ’ 4 ) + 4 3
  • B 𝑓 ( π‘₯ ) = ( π‘₯ + 4 ) βˆ’ 4 3
  • C 𝑓 ( π‘₯ ) = βˆ’ ( π‘₯ βˆ’ 4 ) + 4 3
  • D 𝑓 ( π‘₯ ) = βˆ’ ( π‘₯ + 4 ) βˆ’ 4 3

Q3:

Which of the following graphs represents 𝑓 ( π‘₯ ) = 2 βˆ’ ( π‘₯ βˆ’ 5 ) 3 ?

  • A(c)
  • B(a)
  • C(d)
  • D(b)

Q4:

Consider the graph of the function 𝑦 = ( π‘₯ + 2 ) βˆ’ 2 3 .

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

  • A ( 2 , βˆ’ 2 )
  • B ( 0 , 0 )
  • C ( βˆ’ 2 , 2 )
  • D ( βˆ’ 2 , βˆ’ 2 )
  • E ( βˆ’ 1 , βˆ’ 1 )

Q5:

The given figure shows the graph of 𝑓 ( π‘₯ ) = π‘₯ βˆ’ 4 π‘₯ + 1 3 2 .

Use the graph to determine the number of solutions to the equation π‘₯ = 4 π‘₯ βˆ’ 1 3 2 .

Use the graph to determine the intervals in which the solutions to π‘₯ = 4 π‘₯ βˆ’ 1 3 2 lie.

  • A βˆ’ 1 < π‘₯ < 0 , 0 < π‘₯ < 1 , and 3 < π‘₯ < 4
  • B βˆ’ 0 . 5 < π‘₯ < 0 , 0 < π‘₯ < 2 , and 3 < π‘₯ < 4
  • C βˆ’ 1 < π‘₯ < 0 , 0 < π‘₯ < 1 , and 4 < π‘₯ < 5
  • D βˆ’ 1 < π‘₯ < βˆ’ 0 . 5 , βˆ’ 0 . 5 < π‘₯ < 0 , and 3 < π‘₯ < 4
  • E βˆ’ 0 . 5 < π‘₯ < 0 , 0 < π‘₯ < 0 . 5 , and 4 < π‘₯ < 5

Q6:

Which of the following is the graph of 𝑓 ( π‘₯ ) = βˆ’ ( π‘₯ βˆ’ 2 ) 3 ?

  • A
  • B
  • C
  • D
  • E

Q7:

David starts with 𝑓 ( π‘₯ ) = π‘₯ βˆ’ 3 2 and has a graph ( ) a that satisfies 𝑓 ( 1 ) = 0 . He sees that the function 𝑔 ( π‘₯ ) = ( π‘₯ βˆ’ π‘˜ ) βˆ’ ( 1 βˆ’ π‘˜ ) 3 3 will have a graph that also has π‘₯ -intercept 1.

What is the value of π‘˜ that gives the graph in ( ) b ?