Cogito
Algebra 2 · Chapter 5 · Lesson 3
Graphing Radical Functions
Half a parabola, lying on its side.
12 problems · about 21 minutes · F-IF.C.7, F-BF.B.3
What this lesson teaches
The student graphs square root and cube root functions and states their domain and range.
- y = √x starts at the origin and rises ever more slowly.
- Set the inside to zero to find where a radical graph begins.
- Cube roots accept every real number; square roots do not.
Warm Up
Straightforward practice. Get the method working first.
5 problemsy = √(x − 8). What is the smallest allowed value of x?
Answer 8
Why 8.
Why does a cube root accept negative inputs?
Answer Cubing keeps the sign, so the cube root can return one.
Why Cubing preserves the sign, unlike squaring.
y = √(x − 2). Smallest allowed x?
Answer 2
Why x − 2 ≥ 0.
y = √(x + 7). Smallest allowed x?
Answer -7
Why x + 7 ≥ 0.
y = √x + 3. What is y when x = 16?
Answer 7
Why 4 + 3.
Build It Up
The same ideas with more to keep track of.
3 problemsy = √(x − 1) + 5. What is the smallest value of y?
Answer 5
Why The root is at least 0.
What is the cube root of −27?
Answer -3
Why (−3)³ = −27.
y = 2√x. What is y when x = 25?
Answer 10
Why 2 × 5.
Stretch Yourself
Mixed problems. Work out what kind of question it is before you start.
4 problemsSort each function by whether negatives are allowed as inputs.
Answer Negatives allowed: Cube root of x, x cubed · Negatives not allowed: Square root of x, Square root of x minus 3
Why Only even roots reject negative inputs.
y = √(2x − 6). Smallest allowed x?
Answer 3
Why 2x − 6 ≥ 0.
The Domain: For y = √(x − 5), what is the smallest allowed value of x?
Answer 5
Why 5.
The Pendulum: A pendulum period is T = 2√L seconds, with L in metres. What is T when L = 9?
Answer 6 seconds
Why 6 seconds.