Worksheet: Graphs of Piecewise Functions

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

Q1:

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

  • A{4}
  • B
  • C(2,)
  • D{2,1}

Q2:

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

  • A[7,7]
  • B{7,7}
  • C{0}
  • D

Q3:

Find the range of the function.

  • A[2,)
  • B
  • C(,2]
  • D[1,)
  • E(,1]

Q4:

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

  • A(3,)
  • B{3,2}
  • C[3,2]
  • D(1,)
  • E{1}

Q5:

Find the domain of the real function 𝑓(𝑥)=1,𝑥<7,24,𝑥7.

  • A(,7)
  • B
  • C{7}
  • D(7,)

Q6:

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

  • A𝑓(𝑥)=13<𝑥<2,32𝑥3,13<𝑥4ififif
  • B𝑓(𝑥)=13𝑥3,31<𝑥<3,13<𝑥4ififif
  • C𝑓(𝑥)=13<𝑥<2,31𝑥3,13<𝑥4ififif
  • D𝑓(𝑥)=13𝑥2,32<𝑥<3,13<𝑥4ififif
  • E𝑓(𝑥)=13<𝑥<3,32𝑥3,13<𝑥4ififif

Q7:

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

  • A(𝑥)=𝑥2𝑥2,3+𝑥2𝑥ifif
  • B(𝑥)=𝑥2𝑥2,3𝑥2𝑥ifif
  • C(𝑥)=3+𝑥𝑥2,𝑥22𝑥ifif
  • D(𝑥)=3𝑥𝑥<2,𝑥22𝑥ifif
  • E(𝑥)=32𝑥𝑥2,𝑥22𝑥ifif

Q8:

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

  • A𝑝(𝑥)=𝑥2+2𝑥<2,3+𝑥2<𝑥ifif
  • B𝑝(𝑥)=32𝑥𝑥<2,𝑥2+22<𝑥ifif
  • C𝑝(𝑥)=3𝑥𝑥<2,𝑥2+22<𝑥ifif
  • D𝑝(𝑥)=𝑥2+2𝑥<2,3𝑥2<𝑥ifif
  • E𝑝(𝑥)=3+𝑥𝑥<2,𝑥2+22<𝑥ifif

Q9:

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

  • A𝑓(𝑥)=𝑥2𝑥<2,2𝑥=2,3+𝑥2<𝑥ififif
  • B𝑓(𝑥)=3𝑥𝑥<2,2𝑥=2,𝑥22<𝑥ififif
  • C𝑓(𝑥)=𝑥2𝑥<2,2𝑥=2,3𝑥2<𝑥ififif
  • D𝑓(𝑥)=32𝑥𝑥<2,2𝑥=2,𝑥22<𝑥ififif
  • E𝑓(𝑥)=3+𝑥𝑥<2,2𝑥=2,𝑥22<𝑥ififif

Q10:

The graph of the function 𝑓 is formed of a ray with slope 3 from the point (1,2), a line segment between the points (1,2) and (2,1), and a ray with slope 7 from the point (2,1). Write the function in the form 𝑓(𝑥)=𝑎+𝑏𝑥+𝑐|𝑥+1|+𝑑|𝑥2|, where 𝑎, 𝑏, 𝑐, and 𝑑 are numbers that you should find.

  • A𝑓(𝑥)=92𝑥2|𝑥+1|+3|𝑥2|
  • B𝑓(𝑥)=9+2𝑥+|𝑥+1|+3|𝑥2|
  • C𝑓(𝑥)=9+2𝑥+2|𝑥+1|+3|𝑥2|
  • D𝑓(𝑥)=9+𝑥+|𝑥+1|+3|𝑥2|
  • E𝑓(𝑥)=9+𝑥+2|𝑥+1|+3|𝑥2|

Q11:

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

  • A𝑔(𝑥)=1𝑥<1,(𝑥2)(𝑥3)1𝑥4,𝑥24<𝑥ififif
  • B𝑔(𝑥)=1𝑥1,(𝑥+2)(𝑥3)1<𝑥<4,𝑥24𝑥ififif
  • C𝑔(𝑥)=1𝑥<1,(𝑥+2)(𝑥3)1𝑥4,𝑥24<𝑥ififif
  • D𝑔(𝑥)=1𝑥1,(𝑥2)(𝑥3)1<𝑥<4,𝑥24𝑥ififif
  • E𝑔(𝑥)=1𝑥<1,(𝑥+2)(𝑥3)1𝑥4,𝑥24<𝑥ififif

Q12:

Write an equation for each part of the domains 𝑥1 and 𝑥>1 of the piecewise-defined function shown in the graph.

  • A𝑥1𝑓(𝑥)=𝑥+4𝑥+2𝑥>1𝑓(𝑥)=𝑥+8𝑥::
  • B𝑥1𝑓(𝑥)=𝑥+8𝑥𝑥>1𝑓(𝑥)=𝑥+4𝑥+2::
  • C𝑥1𝑓(𝑥)=𝑥+4𝑥+2𝑥>1𝑓(𝑥)=𝑥8𝑥::
  • D𝑥1𝑓(𝑥)=95𝑥+365𝑥+2𝑥>1𝑓(𝑥)=𝑥+8𝑥::
  • E𝑥1𝑓(𝑥)=𝑥+4𝑥+2𝑥>1𝑓(𝑥)=𝑥+8𝑥::

Q13:

Write an equation for each part of the domains 8𝑥2, 2<𝑥<2, 2𝑥<8, and 8𝑥10 of the piecewise-defined function shown in the graph.

  • A8𝑥2𝑓(𝑥)=42<𝑥<2𝑓(𝑥)=2𝑥82𝑥<8𝑓(𝑥)=𝑥6𝑥48𝑥10𝑓(𝑥)=12
  • B8𝑥2𝑓(𝑥)=42<𝑥<2𝑓(𝑥)=2𝑥82𝑥<8𝑓(𝑥)=𝑥+6𝑥+208𝑥10𝑓(𝑥)=12
  • C8𝑥2𝑓(𝑥)=42<𝑥<2𝑓(𝑥)=2𝑥82𝑥<8𝑓(𝑥)=𝑥+6𝑥+208𝑥10𝑓(𝑥)=12
  • D8𝑥2𝑓(𝑥)=42<𝑥<2𝑓(𝑥)=2𝑥82𝑥<8𝑓(𝑥)=𝑥6𝑥48𝑥10𝑓(𝑥)=12

Q14:

Which of the following is the function whose graph is shown?

  • A𝑓(𝑥)=3𝑥7,𝑥1𝑥1,1<𝑥17𝑥13,1<𝑥
  • B𝑓(𝑥)=3𝑥7,𝑥1𝑥+1,1<𝑥27𝑥13,2<𝑥
  • C𝑓(𝑥)=3𝑥7,𝑥1𝑥1,1<𝑥27𝑥13,2<𝑥
  • D𝑓(𝑥)=7𝑥3,𝑥1𝑥1,1<𝑥27𝑥13,2<𝑥
  • E𝑓(𝑥)=7𝑥3,𝑥1𝑥+1,1<𝑥7𝑥13,1<𝑥

Q15:

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

  • A{2}
  • B
  • C(3,)
  • D{3,2}

Q16:

What kind of function is depicted in the graph?

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

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