5.3-5.4 Quiz Review

Describing Transformed Radical Functions

100

Describe the transformation of f(x)= ³√(x) -2 

down 2

200

Describe the transformation of f(x)=√ (x-3) +4

right 3, up 4

300

Describe the transformation of f(x)= -³√ (2x)

horizontal/vertical reflection, horizontal shrink by 1/2

400

Describe the transformation of f(x)= 3 ³√ (x-2) -1

Vertical stretch by 3, right 2, down 1

500

Describe the transformation of f(x)= -√ (2x-8) -2

Reflect x-axis, horizontal shrink by 1/2, right 4, down 2

Writing a Transformed Radical Function

100

Let the graph of g be a horizontal shrink of 1/6 followed by a translation 3 units to the left of the graph of f(x)=√ x

√(6x-18)

200

Let the graph of g be a horizontal stretch by a factor of 3 followed by a translation 6 units to the right of the graph of ³√ x

³√(1/3x-2)

300

Let the graph of g be a reflection in the y-axis followed by a translation 2 up and 1 unit to the right of the graph of f(x)= 2 ³√ (x-1)

2 ³√ (-x) +2

400

Let the graph g be a translation 2 units up and 4 units left, followed by a reflection in the y-axis of the graph of f(x)=√(-x)- 1/3

√(x-4) +5/3

500

Let g be a vertical stretch by a factor of 2 followed by a reflection in the y-axis and a shift 1 unit up of the graph of f(x)=3 ³√ (x+1)

6 ³√ (-x+1) +1

Solving Equations with a Rational Exponent

100

(x)^1/2=5

x=25

200

(2x)^3/4+2=10

x=8

300

(8x)^4/3+44=300

x=-8,8

400

(x-7)⁴=16

x=5,9

500

(x+30)^1/2=x

x=-5,6 BUT -5 is an extraneous solution

Solving Radical Equations

100

2√(x+1)=4

x=3

200

√(2x+5)=√(x+7)

x=2

300

5 ³√(2x-5) - 10= 15

x=65

400

x+1=√(7x+15)

x=-2,7 BUT x=-2 is an extraneous solution.

500

√(x+2) +1=√(3-x)

x=-1,2 BUT x=2 is an extraneous solution

Solving Radical Inequalities

100

4√(x-2)>20

x>27

200

7 ³√(x-3) ≥ 21

x≥30

300

3 √(x) -4 ≤ 8

0≤ x ≤ 16

400

3 √(x-1) ≤ 12

1≤ x≤ 17

500

4 ³√(x+1) < 8

x<7