Math 2: Algebra 2, Geometry and Statistics Ms. Sheppard-Brick Chapter 4 Test Review

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1 Chapter 4 Test Review Students will be able to (SWBAT): Write an explicit and a recursive function rule for a linear table of values. Write an explicit function rule for a quadratic table of values. Determine whether a function is linear, quadratic, cubic, or exponential based on a table of values. Determine whether a relation is a function based on a description, a table, or a graph. Find domain and range of a function from a graph. Based on an equation, determine domain restrictions for rational and radical functions. Find the inverse of a linear function from its equation or table. Given the graph of a linear function, graph its inverse. Evaluate compositions of functions, and find a rule for a composition. 1. Consider the functions f(x)=3x+7 g(x)= x +1 2 Find each value or expression. a. f(2) b. g(3) c. f(g(5)) d. g(f(2)) e. f (2) g(3) f. f(2) + g(3) g. f g a h. g f a

2 2. Given the functions R(x) = x 2 Q(x)= x 2 + 4x +1 a. Find a formula for R(Q(x)) b. Find a formula for Q(R(x)) 3. State the domain and range of each function. Use set notation. a. b(x) = 2x 2 6 b. c(x) = 2x 6 c. d(x) = x d. e(x) = 1+ x 1+ x

3 a. 4. State the domain and range of each function. The functions do NOT extend beyond the graphs shown. b. c. d

4 5. a. Complete the difference column for this table. b. Find a recursive function definition and an explicit (closed form) function definition that agree with the table below. Input, n Output, p(n) 0-8 Δ Recursive definition: p(n) = " # $ Explicit definition: p(n) = 6. Find the domain and range of each function. The function does not extend beyond the table as given. a. b. x f(x) x g(x)

5 7. For each function: a. Sketch a graph of the function below by making a table of values or using your graphing calculator. b. On the same graph, graph the inverse function or relation. Label both graphs to distinguish them. c. Is the inverse a function or merely a relation? d. Find the inverse function or relation. f(x)= x g(x)= 8x 4 h(x)= 0.5x 2 j(x)= 3x i. f(x)= x ii. g(x)= 8x 4 Graph f(x) and its inverse. Graph g(x) and its inverse. Is the inverse a function? Write the inverse using the correct notation (in this case f 1 (x)). Is the inverse a function? Write the inverse using the correct notation. Is the function one-to-one? Is the function one-to-one?

6 iii. h(x)= 0.5x 2 iv. j(x)= 3x Graph h(x) and its inverse. Graph j(x) and its inverse. Is the inverse a function? Write the inverse using the correct notation. Is the inverse a function? Write the inverse using the correct notation. Is the function one-to-one? Is the function one to one?

7 8. Find the inverse of the relation given by each table. Determine whether the function is oneto-one. Justify your answer. a. x h(x) b. x k(x) Find the inverse relation. Find the inverse relation. x h!! (x) x k!! (x) Is h(x) one-to-one? Justify your answer. Is k(x) one-to-one? Justify your answer.

8 9. a. Which of the following recursive functions best fits the table below? # 2 if n = 0 i. a(n) = $ % a(n 1) 3 if n > 0 Input, n $ 2 if n = 0 ii. a(n) = % & 2 a(n 1) 5 if n > 0 # 2 if n = 0 iii. a(n) = $ % a(n 1) + 2n 5 if n > 0 # 2 if n = 0 iv. a(n) = $ % a(n 1) 2n 2 if n > 0 Output, a(n) b. Fill in the value for a(5) in the table using the definition you chose. 5

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