Reporting Category 5: Square Root Functions
Algebra 2: RC 5
2A.9A (S)
1.The graph of the square root function f is shown on the grid below.
If the graph of f is translated 5 units to the left and 4 units up to create a new graph, write the function to represent the new graph.
Describe the domain and range of the new function.
2.The graph of f(x)= -3 is transformed to produce the graph of g(x)=+3. Describe the change in f(x).
F.Reflection in the x-axis
G.Vertical compression
H.Translated left 2 units and up 3 units
J.Translated right 2 units and up 6 units
Describe the domain and range of f(x) and g(x).
3.Which of the following sentences is true about the graphs of f(x)=2-1 and g(x)=-2 +1?
A.g(x) is f(x) reflected in the x-axis and translated 5 units left.
B.g(x) is f(x) vertically stretched and translated 5 units right.
C.g(x) is f(x) vertically compressed and translated 10 units left.
D.g(x) is f(x) reflected in the x-axis and translated 10 units right.
Describe the domain and range of f(x) and g(x).
Algebra 2: RC 5
2A.9A (S)
4.In the function f(x)=a, where a>0, what happens to the graph of f(x) as the value of a increases?
F.The graph is vertically compressed.
G.The graph is vertically stretched.
H.The graph is vertically translated up.
J.The graph is horizontally translated to the right.
Describe the domain and range of f(x).
5.The graph of the square root function f is shown on the grid below.
If the graph of f is translated 3 units to the right and 5 units down to create a new graph, write the function to represent the new graph.
Describe the domain and range of the new function.
Algebra 2: RC 5
2A.9B (S)
1.Write an equation to describe the square root function below. The table of values shows points on the curve.
x / -6 / -5 / -4 / -1f(x) / error / -3 / -4 / -5
2.There are several sizes of ice cream cones available at Johnson’s Real Ice Cream Shoppe, but all of them are 5 inches long.
a.Write a square root function that expresses the radius r of the cones as a function of volume V.
b.Describe the domain and range of the function.
c.Determine the radius of a cone with volume of 22 cubic inches.
d.Graph the square root function and use the graph to verify answer to part c.
Algebra 2: RC 5
2A.9B (S)
3.The function d= represents the greatest distance d in miles that a person h feet high can see on a clear day. Suppose William is standing on the 102nd floor observation deck of the Empire State Building, 1250 feet high, on a clear day.
a.What is the greatest distance that William can see?
b.Graph the function and verify the answer to part a.
c.What are the domain and range of the function?
Algebra 2: RC 5
2A.9C (S)
1.Graph y<.
Describe the range of the graph.
2.Graph y= +2. State the domain and range of the function.
Algebra 2: RC 5
2A.9D (S)
1.What value of p is a solution to the equation below?
8 -1=3
Record your answer and fill in the bubbles.
2.Solve = - .
3.Solve 3+ =10.
4.Solve = .
5.Solve = - .
Algebra 2: RC 5
2A.9E (S)
1.Solve 3+ ≤ 10.
2.Solve ≥ 8.
3.Solve - .
4.Solve – ≤ 4.
5.Solve - 2 .
Algebra 2: RC 5
2A.9F (R)
1.The formula P=2 can be used to approximate the period of a pendulum, where L is pendulum’s length in feet and P is the pendulum’s period in seconds. If a pendulum’s period is 1.6 seconds, which is the closest to the length of the pendulum?
A.1.4 ft.C.2.1 ft.
B.4.2 ft.D.3.2 ft.
2.At a building construction site, carts loaded with concrete must cross a 25 foot gap between two towers that are 20 stories high. The construction manager needs to select a beam strong enough to support a worker pushing a fully loaded cart. The beam must be at least 2 feet wide to accommodate the wheels of the cart. A beam 6 inches thick will be able to safely support the load of the cart (865 lbs.) and the worker (250 lbs. maximum)? The construction manager uses the formula =d. This formula expresses the relationship of the safe load s of a beam to its width w in feet and depth d in inches. k is a constant and L is the distance between the supports.
Find the value of k.
3.The organizers of a rock concert are preparing for the arrival of 50,000 fans in the open field where the concert will take place. It is reasonable to allow each person 5 square feet of space, so the organizers need to rope off a circular area of 250,000 square feet. Find the radius of this region.
4.Solve T=2 for g.
Algebra 2: RC 5
2A.9F (R)
5.The surface area of a cone can be found using S=, where r is the radius of the base and h is the height of the cone. Find h is S=225 cm² and r=5 cm.
Algebra 2: RC 5
2A.9G (S)
1.Find the inverse of f(x)= +9. Graph f(x) and f-1(x) on the same set of axes.
2.Find the inverse of g(x)= -2. Graph g(x) and g-1(x) on the same set of axes.
3.Determine if f(x) and g(x) are inverses of each other.
f(x)=x²+4
g(x)=
4.Determine if h(x) and j(x) are inverses of each other.
h(x)=2 +6
j(x)= - (x²-12x+24)
5.Is f(x) the inverse of g(x)?
f(x)=
g(x)=
6.Which of the following conclusions is true about x²= ?
F.The statement is always true.
G.The statement is always true when x<0.
H.The statement is only true when x=0.
J.The statement is never true.
Algebra 2STAAR Page 1