Five-Minute Check (over Lesson 6–2)
CCSS
Then/Now
New Vocabulary
Key Concept: Parent Function of Square Root Functions
Example 1: Identify Domain and Range
Key Concept: Transformations of Square Root Functions
Example 2: Graph Square Root Functions
Example 3: Real-World Example: Use Graphs to Analyze
Square Root Functions
Example 4: Graph a Square Root Inequality
Over Lesson 6–2
Find the inverse of {(4, 3), (8, 0), (–5, 6)}.
A. {(–4, –3), (8, 0), (5, –6)}
B. {(1, 5, 2), (0, 4), (–3, 2.5)}
C.
D. {(3, 4), (0, 8), (6, –5)}
Over Lesson 6–2
1
Find the inverse of f(x) = __
x + 3.
4
A. f–1(x) = 4x – 12
B. f–1(x) = 4x + 3
1
__
C. f (x) = 4x +
3
–1
D. f–1(x) = x + 3
3
__
9
Over Lesson 6–2
Find the inverse of f(x) = 2x – 1.
A.
B.
C.
D.
Over Lesson 6–2
Determine whether the pair of functions are inverse
functions. Write yes or no.
f(x) = x + 7
g(x) = x – 7
A. yes
B. no
Over Lesson 6–2
Determine whether the pair of functions are inverse
functions. Write yes or no.
f(x) = 3x + 4
1x–4
g(x) = __
3
A. yes
B. no
Over Lesson 6–2
Which of the following functions has an inverse
that is also a function?
A. f(x) = x2 + 3x – 2
B. g(x) = x3 – 8
C. h(x) = x5 + x2 – 4x
D. k(x) = 2x2
Content Standards
F.IF.7.b Graph square root, cube root, and piecewisedefined functions, including step functions and absolute
value functions.
F.BF.3 Identify the effect on the graph of replacing f(x) by
f(x) + k, k f(x), f (kx), and f(x + k) for specific values of k
(both positive and negative); find the value of k given the
graphs. Experiment with cases and illustrate an
explanation of the effects on the graph using technology.
Mathematical Practices
3 Construct viable arguments and critique the
reasoning of others.
You simplified expressions with square roots.
• Graph and analyze square root functions.
• Graph square root inequalities.
• square root function
• radical function
• square root inequality
Identify Domain and Range
The domain only includes values for which the radicand
is nonnegative.
x–2 ≥0
Write an inequality.
x ≥2
Add 2 to each side.
Thus, the domain is {x | x ≥ 2}.
Find f(2) to determine the lower limit of the range.
So, the range is {f(x) | f(x) ≥ 0}.
Answer: D: {x | x ≥ 2}; R: {f(x) | f(x) ≥ 0}
A. D: {x | x ≥ –4}; R: {f(x) | f(x) ≤ 0}
B. D: {x | x ≥ 4}; R: {f(x) | f(x) ≥ 0}
C. D: {x | x ≥ –4}; R: {f(x) | f(x) ≥ 0}
D. D: {x | all real numbers};
R: {f(x) | f(x) ≥ 0}
Graph Square Root Functions
Graph Square Root Functions
Notice the end behavior; as
x increases, y increases.
Answer: The domain is {x | x ≥ 4} and the
range is {y | y ≥ 2}.
Graph Square Root Functions
Graph Square Root Functions
Notice the end behavior; as
x increases, y decreases.
Answer: The domain is {x | x ≥ –5} and
the range is {y | y ≤ –6}.
A.
B.
C.
D.
A. D: {x | x ≥ –1}; R: {y | y ≤ –4}
B. D: {x | x ≥ 1}; R: {y | y ≥ –4}
C. D: {x | x ≥ –1}; R: {y | y ≤ 4}
D. D: {x | x ≥ 1}; R: {y | y ≤ 4}
Use Graphs to Analyze Square
Root Functions
A. PHYSICS When an object is spinning in a
circular path of radius 2 meters with velocity v, in
meters per second, the centripetal acceleration a, in
meters per second squared, is directed toward the
center of the circle. The velocity v and acceleration
a of the object are related by the function
.
Graph the function in the domain {a|a ≥ 0}.
Use Graphs to Analyze Square
Root Functions
The function is
{a | a ≥ 0} and graph.
. Make a table of values for
Answer:
Use Graphs to Analyze Square
Root Functions
B. What would be the centripetal acceleration of an
object spinning along the circular path with a
velocity of 4 meters per second?
It appears from the graph that the acceleration would
be 8 meters per second squared. Check this estimate.
Original equation
Replace v with 4.
Square each side.
Divide each side by 2.
Answer: The centripetal acceleration would be 8 meters
per second squared.
A. GEOMETRY The volume V and surface area A of a soap
bubble are related by the function
graph of this function?
A.
B.
C.
D.
Which is the
B. GEOMETRY The volume V and surface area A of a
soap bubble are related by the function
What would the surface area be if the volume was
3 cubic units?
A. 10.1 units2
B. 31.6 units2
C. 100 units2
D. 1000 units2
Graph a Square Root Inequality
Graph
.
Graph the boundary
. Since the boundary
should not be included, the graph should be dashed.
Graph a Square Root Inequality
The domain is
. Because y is greater than, the
shaded region should be above the boundary and
within the domain.
Select a point to see if it is in the shaded region.
Test (0, 0).
Answer:
?
Shade the region that
does not include (0, 0).
Which is the graph of
?
A.
B.
C.
D.