6.1-6.5 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 vertical shrink of 1/6 followed by a translation 3 units to the left of the graph of f(x)=√ x

1/6√(x+3)

200

Let the graph of g be a vertical stretch by a factor of 3 followed by a translation 6 units to the up of the graph of  y = x²

g(x) = 3x²+6

300

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

g(x) = |x - 1|+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) -3

g(x) = √(x-4) -1

500

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

g(x) = -6 √ (x+1) +1

Solving Equations with Exponents

100

Find EXACT solution(s) 

x²=5

x=sqrt 5 and - sqrt 5

200

Find decimal approximations to 2 decimals

x⁴+2=10

x=-1.68, 1.68

300

(8x)³+44=260

x=-3/4, 3/4

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

Application

100

If a ball takes 3 seconds to hit the ground, determine the height in meters the ball fell given:     h = 5t².

45 meters

200

If a driver hits the brakes and it takes the car 200 feet to stop, estimate the speed she was driving using          s = √(15d).  Find speed in MPH rounded to 2 decimals.

54.77 MPH

300

If the radius of a dinner plate is 6 in, how much space do you have to put your food (assume you fill it completely).  A = 3.14r².  Round to 2 decimals.

113.04 in²

400

If the area of a salad plate is 314 cm², what is the diameter? r = √(A/3.14).  Round to 2 decimals.

20 cm  (radius is 10 cm :)

500

If a ball is dropped 25 meters, how many seconds before it hits the ground?  Use the formula:                   t =  √(h/5) and round to hundredths. 

2.24 seconds (mathematically there are two solutions but only the positive answer makes sense)