Objective 1: Graph Exponential Functions
For Exercises 9–12, evaluate the functions at the given values of x. Round to 4 decimal places if necessary.
a.
b.
c.
d.
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College Algebra (Collegiate Math)
- In Exercises 11–18, graph each function by making a table of coordinates. If applicable, use a graphing utility to confirm your hand-drawn graph. 11. f(x) = 4" 13. g(x) = ()* 15. h(x) = (})* 17. f(x) = (0.6) 12. f(x) = 5" 14. g(x) = () 16. h(x) = (})* 18. f(x) = (0.8)* %3!arrow_forwardIn Exercises 7–12, describe the relationship between the two quantities.arrow_forwardIn Exercises 1–6, solve for x.arrow_forward
- In Exercises 63–65, find the domain and range of each composite function. Then graph the composition of the two functions on separate screens. Do the graphs make sense in each case? Give reasons for your answers. Comment on any differences you see. 63. a. y = tan-1 (tan x) b. y = tan (tan-1 x) 64. a. y = sin-1 (sin x) b. y = sin (sin-1 x) 65. a. y = cos-1 (cos x) b. y = cos (cos-1 x)arrow_forward1–2 Classify each function as a power function, root function,polynomial (state its degree), rational function, algebraic function,trigonometric function, exponential function, or logarithmicfunction.arrow_forwardBirths to Unmarried Mothers The percent of livebirths to unmarried mothers for the years 1970–2007can be modeled by the logistic functiony = 44.742/1 + 6.870e-0.0782xwhere x is the number of years after 1960.a. Use this model to estimate the percent in 1990 andin 1996.b. What is the upper limit of the percent of teenmothers who were unmarried, according to thismodel?arrow_forward
- (3.1) #10arrow_forwardFor Exercises 49–52, rewrite the equation so that the coefficient on x is positive.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_forward
- Your cardiac index is your heart's output, in liters of blood per minute, divided by your body's surface area, in square meters. The cardiac index, C(x), can be modeled by 7.644 C(x) = 10 s xs 80, where x is an individual's age, in years. The graph of the function is shown. Use the function to solve Exercises 95–96. 7.644 C(x) = %3D 10 20 30 40 50 60 70 80 90 Age 95. a. Find the cardiac index of a 32-year-old. Express the denominator in simplified radical form and reduce the fraction. b. Use the form of the answer in part (a) and a calculator to express the cardiac index to the nearest hundredth. Identify your solution as a point on the graph. 96. a. Find the cardiac index of an 80-year-old. Express the denominator in simplified radical form and reduce the fraction. Cardiac Index liters per minute squar e met ers 654 32arrow_forwardGraphing Inverse Functions Each of Exercises 11–16 shows the graph of a function y = ƒ(x).Copy the graph and draw in the line y = x. Then use symmetry withrespect to the line y = x to add the graph of ƒ -1 to your sketch. (It isnot necessary to find a formula for ƒ -1.) Identify the domain andrange of ƒ -1.arrow_forwardThe function f is exponential. Its graph contains the points (0, 5) and (1.5, 10). a.) Find f (3) Use the value of f(3) to find f(1)arrow_forward
- Algebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:Cengage