Name:_________
Chapter 6 Review – Part One
Prior to taking the exam, you should be able to:
-
Explain the relationship between roots and exponents.
Sketch the graph of a square root function.
State the starting point, domain, & range of the square root function.
Solve equations of the form 𝑎𝑥 2 + 𝑐 = 𝑑, where 𝑎, 𝑐, 𝑎𝑛𝑑 𝑑 are real numbers, including
complex solutions.
Rewrite radicals as rational exponents
Simplify radicals.
Apply exponent rules to radicals.
Combine functions using arithmetic operations (addition, subtraction, multiplication, and
division) and fully simplify these expressions
Evaluate combined operations using equations, tables, or graphs.
Compose two functions
Evaluate a composition of functions
Algebraically solve for a functions inverse.
Identify whether two functions are inverses using composition
Sketch a graph of an inverse given the graph of a function.
Determine if a function is invertible, using a graph or a table.
Name:_________
Chapter 6 Review – Part 2
1. Without a calculator, estimate √90
2. The volume of a cube is 173 cubic inches. Find the side length of the cube.
3. Graph 𝑓(𝑥) = √𝑥 + 3 + 1. Ensure that you label the starting point. State the domain and
range of this function.
4. Solve for 𝑥
1
a. 2 𝑥 2 + 7 = 9
b.
2
3
𝑥2 + 6 = 0
c. 5𝑥 2 + 3 = 19
5. Rewrite each expression using exponents instead of radicals.
a. √24
3
b. √𝑎2 𝑏
3
2
c. ( √6)
6. Simplify the radicals
a. √𝑥 2 𝑦 4
3
b. √27𝑎
c. √9𝑎3 𝑏 7
7. Given the graph of 𝑓(𝑥) and table of ℎ(𝑥), let 𝑔(𝑥) = 𝑥 3 + 6. Evaluate the following.
a.
𝑓(3)
ℎ(0)
b. 𝑔(7) ∗ ℎ(6)
c. ℎ(4) − 𝑔(4)
𝑥
0
1
4
6
ℎ(𝑥)
6
3
-9
-10
Name:_________
8. The length of the sides of an equilateral triangle is described by the function 𝑠(𝑥) = 6𝑥 −
3
a. Write a function, 𝑃(𝑥), to describe the perimeter of the triangle.
b. Given that the height of the triangle is modeled by ℎ(𝑥) = 23𝑥 2 + 18𝑥, write a
function, 𝐴(𝑥), describing the area of the triangle.
1
2
9. Given the table for ℎ(𝑥), 𝑓(𝑥) = 3𝑥 2 + 2, 𝑔(𝑥) = √3 𝑥 − 3, Evaluate:
𝑥
3
6
12
a. 𝑓(ℎ(3))
b. 𝑓(𝑓(2))
c. 𝑓(𝑔(𝑥))
10. Find the inverse of 𝑓(𝑥) = 3(𝑥 − 1)3 + 6.
11. Given the following table, determine whether the functions are inverses:
𝑥
𝑓(𝑥)
𝑔(𝑥)
-3
6
9
3
3
3
3
6
9
-3
12. Determine if 𝑓(𝑥) = √𝑥 + 6 and 𝑔(𝑥) = 𝑥 3 − 6 are inverses.
9
-3
6
ℎ(𝑥)
5
5
9
Name:_________
13. Given the graph below, sketch the graph of its inverse on the same graph.
14. Given the table, determine if this function is invertible.
-2
-1
0
𝑥
2
7
-3
𝑓(𝑥)
1
0
2
7