(a)
To fill: The blanks provided for the statement “In the given graph of a function, as
(b)
To fill: The blanks provided for the statement “In the given graph of a function, as
(c)
To fill: The blanks provided for the statement “In the given graph of a function, as
(d)
To fill: The blanks provided for the statement “In the given graph of a function, as
(e)
To fill: The blanks provided for the statement “The given graph of a function is increasing over the interval(s) _____________”
(f)
To fill: The blanks provided for the statement “The given graph of a function is decreasing over the interval(s) _____________”
(g)
To fill: The blanks provided for the statement “In the given graph of a function, the domain is _____________”
(h)
To fill: The blanks provided for the statement “In the given graph of a function, the range is _____________”
(i)
To fill: The blanks provided for the statement “In the given graph of a function, the vertical asymptote is the line _____________”
(j)
To fill: The blanks provided for the statement “In the given graph of a function, the horizontal asymptote is the line _____________”
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College Algebra
- 4. Working with functions. In this question, we will explore various properties of functions. You may want to review the basic definitions and terminology introduced on pages 15–16 of the course notes. Then, read the following definitions carefully. Definition: A function f : A → B is one-to-one iff no two elements of A have the same image. Symbol- ically, Va1, a2 E A, f(a1) = f(a2) → a1 = a2. (3) Definition: A function f: A → B is onto iff every element of B is the image of at least one element from A. Symbolically, VbE В, За Е А, f (a) — b. (4) Definition: For all functions f : A → B and g : B → C, their composition is the function g o f : A → C defined by: Va e A, (go f)(a) = g(f(a)). (5) (b) Give explicit, concrete definitions for two functions f1, f2 : Z → Z† such that: i. f2 is onto but not one-to-one, ii. fi is one-to-one but not onto, and prove that each of your functions has the desired properties.arrow_forwardPls help ASAParrow_forwardThe derivation of the functionarrow_forward
- 3.3 (1) A) Draw the graphical representation of the function. Show all the steps of your reasoning.arrow_forwardTime (t) 0 1 2 3 4 5 Temperature difference (D) 69 66.3 63.7 61.2 58.8 56.5 a) What type of function models the relationship between D and t. b) Find an explicit rule for the function. c) Find a recursive rule for the functionarrow_forwardA 1.Find the domain of following functions: a. f(x) = {(2,6), (3,9), (7, 11), (4, 0), (–1, 12)} and g(x) = {(9, –1), (6, 3), (11, 32), (4, –1)} (fog)? b.f(x) = 2 ||x|–1|-3arrow_forward
- It indicates the correspondence rule and determines whether or not it is functionarrow_forwardpodasip 6. Let f and g be two arithmetic functions with g(n) = Σd\n f(d). If g is multiplicative, then so is f.arrow_forwardUse the graphs to evaluate the expressions below. 6 5 4 3 2 1 f(x) - 1 +-1 f(g(2)) 1 2 3 4 = g(ƒ(4)) = g(g(0)) ƒ(ƒ(5)) = = = 000 X 5 6-1 6 g(x) 5 4 3 W 2 1 2 3 4 9 -1 1 X 5 6arrow_forward
- Algebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:CengageGlencoe Algebra 1, Student Edition, 9780079039897...AlgebraISBN:9780079039897Author:CarterPublisher:McGraw Hill