Worksheet: Domain and Range of a Piecewise Function

In this worksheet, we will practice finding the domain and range of a piecewise-defined function.

Q1:

Find the range of the function 𝑓(𝑥)=𝑥+5,𝑥[5,1],𝑥+3,𝑥(1,3].

  • A(,4]
  • B[5,3]
  • C{0,4}
  • D[0,4]

Q2:

Determine the domain of the function 𝑓(𝑥)=𝑥,𝑥[0,1),1,𝑥[1,8],9𝑥,𝑥(8,9].

  • A{0,9}
  • B[0,9]
  • C[0,1]
  • D{0,1}
  • E{0,9}

Q3:

Determine the domain and the range of the function 𝑓(𝑥)=6,𝑥<0,4,𝑥>0.

  • AThe domain is {6,4}, and the range is {4,6}.
  • BThe domain is {4,6}, and the range is {0}.
  • CThe domain is {0}, and the range is {4,6}.
  • DThe domain is {4,6}, and the range is .
  • EThe domain is , and the range is {4,6}.

Q4:

Find the domain of the real function 𝑓(𝑥)=6𝑥15<𝑥<206𝑥20𝑥<50.ifif

  • A[15,50)
  • B[15,50]
  • C(15,50]
  • D(15,50)

Q5:

Determine the intervals of increase and decrease of the function 𝑓(𝑥)=7𝑥8𝑥<0,7𝑥8𝑥0.ifif

  • A𝑓(𝑥) is increasing on the interval (0,) and decreasing on the interval (,0).
  • B𝑓(𝑥) is increasing on the interval (8,) and decreasing on the interval (,8).
  • C𝑓(𝑥) is increasing everywhere.
  • D𝑓(𝑥) is increasing on the interval (,0) and decreasing on the interval (0,).
  • E𝑓(𝑥) is decreasing everywhere.

Q6:

Find the domain and the range of the function 𝑓(𝑥)=𝑥+1,𝑥0,14,𝑥>0.

  • Adomain =, range =(4,)
  • Bdomain =, range =(0,)
  • Cdomain =, range =
  • Ddomain =, range =
  • Edomain =(1,), range =

Q7:

Determine the range of the function 𝑓(𝑥)=𝑥+2,𝑥[2,3],5𝑥+20,𝑥(3,4].

  • A
  • B{0,5}
  • C[0,5]
  • D{2,4}
  • E[2,4]

Q8:

Find the range of the function 𝑓(𝑥)=𝑥,𝑥[0,1),1,𝑥[1,7],8𝑥,𝑥(7,8].

  • A{0,8}
  • B[0,1]
  • C{0,8}
  • D[0,8]
  • E{0,1}

Q9:

Find the domain of the function 𝑓(𝑥)=𝑥,𝑥[0,1),1,𝑥[1,7],8𝑥,𝑥(7,8].

  • A[0,8]
  • B{0,1}
  • C[0,1]
  • D{0,8}
  • E{0,8}

Q10:

Find the domain of the real function 𝑓(𝑥)=𝑥19,𝑥6,19,6<𝑥<23.

  • A(23,)
  • B[23,)
  • C(,23)
  • D[6,23)
  • E(,23]

Q11:

Determine the domain of the function 𝑓(𝑥)=𝑥,8𝑥<1,2𝑥,1𝑥2.

  • A{8,1}
  • B[8,1]
  • C{8,2}
  • D[8,2]
  • E{8,1}

Q12:

Determine the domain of the function 𝑓(𝑥)=𝑥,𝑥[0,1),1,𝑥[1,2],5𝑥,𝑥(2,5].

  • A{1,0}
  • B{0,5}
  • C{0,5}
  • D[0,5]
  • E[1,0]

Q13:

Find the domain of the real function 𝑓(𝑥)=9𝑥𝑥[8,12],108𝑥(12,18),𝑥+90𝑥[18,23).ififif

  • A(8,23)
  • B[8,23]
  • C(8,23]
  • D[8,23)

Q14:

Find the domain of the function 𝑓(𝑥)=𝑥,𝑥[0,2),2,𝑥[2,6],8𝑥,𝑥(6,8].

  • A{0,2}
  • B{0,8}
  • C[0,8]
  • D[0,2]

Q15:

Determine the domain of the function 𝑓(𝑥)=𝑥+4,𝑥[4,8],7𝑥63,𝑥(8,9].

  • A{0,12}
  • B[4,9]
  • C
  • D{4,9}
  • E[0,12]

Q16:

Determine the domain of the function 𝑓(𝑥)=𝑥+1,𝑥[1,7],8𝑥+64,𝑥(7,8].

  • A
  • B[1,8]
  • C[0,8]
  • D{0,8}
  • E{1,8}

Q17:

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

  • A[2,3]
  • B{2,6}
  • C{2,3}
  • D[0,4]
  • E{2,3}

Q18:

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

  • A[1,)
  • B
  • C{1}
  • D[1,7]
  • E{4}

Q19:

Find the range of the following function.

  • A[0,4]
  • B[7,7]
  • C{0,4}
  • D[7,7]
  • E[0,4]

Q20:

Determine the range of the function 𝑓(𝑥)=𝑥1𝑥[1,6],5𝑥+35𝑥(6,7].ifif

  • A{6,1}
  • B{0,5}
  • C
  • D[6,1]
  • E[0,5]

Q21:

Determine the range of the function 𝑓(𝑥)=𝑥7𝑥<3,6𝑥3𝑥6.ifif

  • A{0,3}
  • B{7,6}
  • C{7,3}
  • D[7,3]

Q22:

Find the range of the function 𝑓(𝑥)=1,11𝑥11,𝑥4,5𝑥19.

  • A[1,15]{1}
  • B(1,15]{1}
  • C[1,15]{1}
  • D(1,15]

Q23:

Find the range of the function 𝑓(𝑥)=|𝑥+9|8𝑥<9,(𝑥+9)8𝑥9.ifif

  • A(,8]
  • B{9}
  • C{8}
  • D[8,)

Q24:

Find the range of the function 𝑓(𝑥)=8𝑥𝑥[0,1),8𝑥[1,7],15𝑥𝑥(7,15].ififif

  • A{0,8}
  • B{0,9}
  • C[0,9]
  • D{0,9}
  • E[0,8]

Q25:

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

  • A(0,){3}
  • B(,4)
  • C(,3]{0}
  • D(6,)

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