Concept explainers
For Exercises 53–58,
a. Identify the power function of the form
b. In order, outline the transformations that would be required on the graph of
c. Match the function with the graph of i–vi.
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COLLEGE ALGEBRA CUSTOM -ALEKS ACCESS
- In Exercises 11–18, use the function f defined and graphed below toanswer the questions. (a) Does f (-1) exist?arrow_forward4. 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_forward1.2.4arrow_forward
- 14) Determine the equation of the piecewise function shown on the right. -1 -1 0arrow_forward3.3 (1) A) Draw the graphical representation of the function. Show all the steps of your reasoning.arrow_forwardExercise 3: You challenge yourself and graph the given functions on your own 1. y = 2() -3 -2 -1 3.arrow_forward
- Graph the functionarrow_forwardGraph the given parent function after the set of transformations (7,4) (2,2) * (4,-2) (-3,5) 1)-f(x-3)+2 2) F(x+1)-2arrow_forward2. Use the picture below (on the left) and the function f(x) = ab* to answer the following questions: a. Which graph has the largest value for b? b. Which graph has the smallest value for b? c. Which graph has the largest value for a? d. Which graph has the smallest value for a? BA CA 5+ 4 E 3 2- A 12 3 4 5 -1- -5 4 3 2 "2 -4+ 3. Match each function with its graph in the picture above (on the right). a. log,(-x+ 2) b. - log,(x + 2) c. log,(x + 2) to 3.arrow_forward
- 12. Consider the function f(x) = = -3 x 2x a) Construct a table of values for the function. Use an image or transformation table. b) Graph the function on the grid provided. Use at least four points. 10 8 6 4 2 -10 -8 -6 -4 -2 4 6 8 10 -2 -4 -6 -8 -10 to 2arrow_forwardIntroduction 1. Determine whether the function is even, odd, or neither a. f(x) = 5 – 3x b. f(x) = x* – x² – 1 c. f(x) = 2x³ + 3x Domain, Range and Graphing 2. Find the domain, range for f(x) = x² + 4x + 4 and graph 3. Find the domain, range for f(x) = 2x-3 5-4x and graph 4. Find the domain, range for f(x) = V9x2 – 16 and graph 5. Find the domain for f(x) = log2(x + 2) – 3 Transformation of Graph 6. Use graph of f(x) = x³ to sketch the graph of each function a. f(x) = x3 – 1 b. f(x) = (x + 2)³ +1 7. Sketch the graph for f(x) = -5sinx + 3 Composite Function 8. Solve the following set of function (please simplify): x3 + x2 + 2x f(x) = -,g(x) = 2x² + 2, h(x) = v6x +3 %3D x +1 a. (f • g)x b. (g o h)x Piecewise Defined Function 9. Find the domain, range of the set of piecewise defined function and graph h(x) = {2, x 3 10. Find the domain, range of the set of piecewise defined function and graph x< 2 x2 2 4-x, 1 + 2x, f(x) =arrow_forwardSuppose that Af is the function given by the graph below and that da and a + ha + h are the input values as labeled on the bex – axis. Use the graph in Figure 1.3.2 to answer the following questions. Locate and label the points (a, f(a))(a, f(a)) and Ka + h, f(a+h)X(a +h, f(a + h)) on the graph. D. Construct a right triangle whose hypotenuse is the line segment from (a, f(a))(a, f (a)) to Ka + h, f(a + h)Xa + h, f(a + h)). what are the lengths of the respective legs of this triangle? C What is the slope of the line that connects the points (a, ƒ (a))(a, ƒ (a)) an Ka + h, f(a+ h))Xa +h, f(a+ h))?arrow_forward
- Algebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:CengageBig Ideas Math A Bridge To Success Algebra 1: Stu...AlgebraISBN:9781680331141Author:HOUGHTON MIFFLIN HARCOURTPublisher:Houghton Mifflin Harcourt