SME
Grade 11 Math · Problem type
Graph a cube root function
Use this for “Graph y = 2∛(x + 1) − 3: its center, and y at x = 7” or “Find x where y = 5.”
Chart
Center (−1, −3)
Zero: x = 2.375
f(7) = 1
The parent y = ∛x is dashed
This is an example. Type your own values to start a new problem.
y
=
a
3
−
(
)
+
(
k
)
Formulas
y
=
a
×
∛(
x
−
h
)
+
k
1 = 2 × ∛(7 − (−1)) + (−3)
Assumptions
•
y = a∛(x − h) + k is the parent ∛x moved right h and up k: its center is (h, k).
•
A cube root of a negative number is negative, so the domain and range are all real numbers.
•
a > 0 rises left to right; a < 0 falls.
Step-by-step
WE KNOW
x = 7, a = 2, h = −1, k = −3
FIND
output (y)
Step 1 · Find output (y)
Use y = a × ∛(x − h) + k
Take
the
cube
root
of
x
−
h
(negative
when
x
is
left
of
h
),
multiply
by
a
,
then
add
k
.
y
=
2
×
∛(7
−
(−1))
−
3
y
=
2
×
∛8
−
3
y
=
2
×
2
−
3
y
=
4
−
3
y
=
1
Check
Put the numbers back in. Both sides should match.
1 = 2 × ∛(7 − (−1)) − 3 ✓
Topic check
See what you know: 5 questions on this topic
New questions each time. Pass to mark it complete.
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Related lessons
Radical functions and equations
Main lesson
Extraneous solutions
Use this for “Solve √(x + 7) = x + 1” and reject the extraneous solution.
Graph a square root function
Use this for “Graph y = 2√(x + 3) + 1: where it starts, which way it goes, and y at x = 6.”
Rational exponents
Use this for “Evaluate 82/3”, “Graph y = 2x−1/2” or “Solve x3/2 = 27.”