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Cogito

Algebra 2 · Chapter 5 · Lesson 3

Practice Worksheet

Graphing Radical Functions

Half a parabola, lying on its side.

12 problems · about 21 minutes · F-IF.C.7, F-BF.B.3

NameDate

Figure — use these to answer the problems

Change the coefficient and follow the starting point, then read where the curve is allowed to exist.
-8-8-6-6-4-4-2-222446688
y = 1√x + 0
  • Point(4, 2)
a, vertical stretch1
Point on the curve4
Figure 1

Warm Up

Straightforward practice. Get the method working first.

5 problems

  1. y = √(x − 8). What is the smallest allowed value of x?

    Answer

  2. Why does a cube root accept negative inputs?

    • Cubing keeps the sign, so the cube root can return one.
    • Cube roots are larger.

  3. y = √(x − 2). Smallest allowed x?

    Answer

  4. y = √(x + 7). Smallest allowed x?

    Answer

  5. y = √x + 3. What is y when x = 16?

    Answer

Build It Up

The same ideas with more to keep track of.

3 problems

  1. y = √(x − 1) + 5. What is the smallest value of y?

    Answer

  2. What is the cube root of −27?

    Answer

  3. y = 2√x. What is y when x = 25?

    Answer

Stretch Yourself

Mixed problems. Work out what kind of question it is before you start.

4 problems

  1. Sort each function by whether negatives are allowed as inputs.

    Write each item under the heading it belongs to: Cube root of x · Square root of x · x cubed · Square root of x minus 3

    Negatives allowed

    Negatives not allowed

  2. y = √(2x − 6). Smallest allowed x?

    Answer

  3. The Domain

    For y = √(x − 5), what is the smallest allowed value of x?

    Answer

  4. The Pendulum

    A pendulum period is T = 2√L seconds, with L in metres. What is T when L = 9?

    Answerseconds