Functions Questions

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Functions Solutions

From the table below, determine whether the data shows an exponential function. Explain why or why not. (1)No; the domain values are at regular intervals and the range values have a common factor 0.25. (2) No; the domain values are not at regular intervals although the range values have a common factor. (3) Yes; the domain values are at regular intervals and the range values have a common factor 4. (4) Yes; the domain values are at regular intervals and the range values have a common factor 0.25.

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Several ordered pairs from a continuous exponential function are shown in the table. What are the domain and range of the function? x y 0 4 1 5 2 6.25 3 7.8125 (1)The domain is the set of integers, and the range is > 4. (2) The domain is the set of integers, and the range is Y>O. (3) The domain is the set of real numbers, and the range is y> 0. (4)The domain is the set of real numbers, and the range is y> 4.

Math

Functions Solutions

Consider a function that describes how a particular car's gas mileage depends on its speed. What would an appropriate domain for this function be? Choose the correct answer below. (A) An appropriate domain would be 0 to 50 miles per gallon because the gas mileage is the independent variable of the function, and the domain consists of all reasonable values of the independent variable. (B) An appropriate domain would be times from 0 to 10 minutes because the time is the dependent variable of the function, and the domain consists of all reasonable values of the dependent variable. (C) An appropriate domain would be 0 to 50 miles per gallon because the gas mileage is the dependent variable of the function, and the domain consists of all reasonable values of the dependent variable. (D) An appropriate domain would be 0 to 100 miles per hour because the speed is the dependent variable of the function, and the domain consists of all reasonable values of the dependent variable. (E) An appropriate domain would be 0 to 100 miles per hour because the speed is the independent variable of the function, and the domain consists of all reasonable values of the independent variable.

Math

Functions Solutions

Use the leading coefficient test to determine the end behavior of the graph of the function. ƒ(x) = 2x⁵ + 4x³ + 7x² +5 ○ Up to the left and down to the right ○Up to the left and up to the right ○Down to the left and down to the right ○Down to the left and up to the right

Math

Functions Solutions

The function below gives the cost in dollars to manufacture x items: C (x) = 10,000 + 5x-x^2/10,000 Find the average cost per item over the interval [1,000, 1,010].

Math

Functions Solutions

(a) If N is the population of the colony and t is the time in days, express N as a function of t. Consider N₀ is the original amount at t= 0 and k≠0 is a constant that represents the growth rate. N(t) = □ (Type an expression using t as the variable and in terms of e.)

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Let f(x) =– 4x² +5/1 +x² The graph of f is given below. Use the graph of f to determine the given limits. Enter DNE if a limit fails to exist, except in case of an infinite limit. If an infinite limit exists, enter ∞, or -∞, as appropriate. lim f(x)=________ x->-∞ lim f(x)=________ x->∞

Math

Functions Solutions

If f(x) = -4|3x - 2| and g(x) = -20, solve the following. (a) f(x) = g(x) (b) f(x) >g(x) (c) f(x) = g(x) (a) Solve f(x) = g(x). Select the correct choice below and, if necessary, fill in the answer box to complete your answer. O A. The solution set is {□ }. (Simplify your answer. Use a comma to separate answers as needed.) O B. The solution set is {x| □} . (Simplify your answer. Type a compound inequality.) O C. The solution set is {x|x≤□ or x≥□}. (Simplify your answer. Type inequalities.) O D. The solution set is the empty set.

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Use a graphing calculator to solve the nonlinear system. y =e^(X+1) X+y =1 Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A). The solution set is (Type an ordered pair. Use a comma to separate answers as needed. Type an integer or decimal rounded to the nearest hundred) B). There are infinitely many solutions. C). There is no solution.

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Lillian is in the business of manufacturing phones. She must pay a daily fixed cost to rent the building and equipment, and also pays a cost per phone produced for materials and labor. Let C represent the total cost, in dollars, of producing p phones in a given day. The table below has select values showing the linear relationship between p and C. Determine the fixed cost for rent and equipment. p C 2 1200 4 1600 6 2000

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Find the (a) period, (b) phase shift (if any), and (c) range of the following function. y = 3csc⅓x (a) The period of y = 3csc⅓x is (Type an exact answer, using a as needed. Use integers or fractions for any numbers in the expression.) (b) The phase shift of y = 3csc⅓x is (Type an exact answer, using π as needed. Use integers or fractions for any numbers in the expression.)

Math

Functions Solutions

Function r(t) gives the amount of rainfall accumulated in inches, when it is t hours after the rain started. Which statement represents the meaning of the equation r(5) = 2.5 in this situation? ○ 2.5 hours after the rain started, it has rained 5 inches ○ 5 days after the rain started, it has rained 2.5 inches ○ 5 hours after the rain started, it has rained 2.5 inches ○ It has rained 5 inches for 2.5 hours