Functions Questions and Answers

If f(x) = log₂ x and g(x) = 2^x, what is (g — f) (8) ? Round your answer to two decimal places if needed. Upload a picture of your work Your Answer:

1.Given f(x) = x - 1 and g(x) = x + 3, fill out the table below. Sketch h(x), j(x), k(x), and 1(x) in the set of axes below. Make sure to clearly label each function and your axes. Show your work in identifying the domain and range in the space below. the equation (fully simplified) domain range h(x) = f(x) + g(x) i(x) = f(x) = g(x) k(x) = f(x)g(x) 1(x) = f(x)/g(x)

1. As a tornado moves, its speed increases. The function S(d) = 93logd + 65 relates the speed of the wind, S, in miles per hour, near the centre of a tornado to the distance that the tornado has travelled, d, in miles. (a) Calculate the average rate of change for the speed of the wind at the centre of a tornado from: (i) mile 10 to 100 (ii) mile 100 to 1000 (iii) Describe how the two rates above compare with respect to the given information. (b) Estimate the instantaneous rate of change at d = 1000 miles. Use an interval of 0.01. Round your answer to the nearest hundredth. Do not find the instantaneous rate of change using the difference quotient or any Calculus method. Explain what the value represents in this situation.

Find the inverse of the function f(x) = 6x-5/ 2x+3

The function f(x) =8x/x+3 is one-to-one. Find its inverse and check your answer.

The domain of f(t) is [-10,10], and its range is [-3,2]. What are the domain and range of a. f(2t) b. f(t/2) c. 0.2f(t) +3 d. 0.2f(-2t+2)+3

Consider the functions f(x) = |x| and g(x) = 0.1 |x|. (a) Sketch the graph of the pair of functions using a standard window. (b) Describe the transformations used to obtain the graph of the second function from the first function. (a) Graph the functions.

Determine the rate of change of f(x) = x/x-3 on the interval -5≤ x ≤10 Enter you answer in the box below and round to two decimal places.

Give the domain for r(x): x+5/x²-14x+40 in interval notation.

Sketch the graph of y = g(x) by transforming the graph of y = f(x). Next, determine the horizontal asymptote by taking the limit of g(x). Then select the correct horizontal asymptote.* f(x) = 9^x , g(x) = 9(x+10/5) - 3 *This question is worth four points. In order to receive full credit, you must show your work or justify your answer. y=-1 y=-7 y=-3 y = -8 None of these answers are correct.

Give the domain of each of the following functions in interval notation. g(x) = -7 /25-x² p(x) = -3/49 + x²

Find the domain of the function in interval notation: f(x)=√x + 7

Finding the Domain of Radical Functions Determine the domain for each of the following functions. Write your answer in Interval Notation and as an Inequality. Radical Function Domain written in Interval Domain written as Notation an Inequality f(x) = √5x - 7 g(x) = -15√-3x + 15 f(x) = 12 + √8x + 10 p(x) = √-14+ 18x

How many of the following are 1-1 functions: x² + y² = 1 {(2, 1), (-2,3), (5,7), (2,3)} x² = y + 1 x = y² + 1 THREE ALL FOUR ONE NONE TWO

Give the domain of p(x) = - 3x² + 5x/ √-14-x in interval notation.

If f(x) = 6x-9 and g(x)=x+9/6 (a) f(g(x)) = (b) g(f(x)) = (c) Thus g(x) is called an_____function of f(x)

For the 3-CNF f = (x' +y+z)& (x+y+z')&(x+y+z')& (x+y+z)&(x+y+z') &(x+y+z) - give 0-1 assignment to variables such that f=1 - give 0-1 assignment to variables such that f=0 -Draw the corresponding graph and mark the maximum independent set

The function h is defined below. h(x)= x²-x-30/x^2-11x+24 Find all values of x that are NOT in the domain of h. If there is more than one value, separate them with commas.

Suppose that the relation T is defined as follows. T= {(-5, -3), (-9, -6), (-5,5)} Give the domain and range of T. Write your answers using set notation. domain range

The function f is defined as follows. f(x) = -5x²+2 If the graph of fis translated vertically downward by 5 units, it becomes the graph of a function h. Find the expression for h (x). Note that the ALEKS graphing_calculator may be helpful in checking your answer. h(x) =

The functions u and w are defined as follows. u(x) = -4x+1 w (x) = 5x-4 Find the value of w (u (-2)). w (u(-2)) =

Which of the following is the range of the exponential function f(x) = a^x, a>0 and a ≠1? Choose the correct answer below. (-∞,∞) (0,∞) (-∞,∞) (-∞,0)U(0,∞)

Given the function f(x)=-5-2/3x (a) Slope: (b) y-intercept: (c) Is this function increasing, decreasing or constant? (d) Solve the inequality: f(x)≥ -1 Use interval notation. Use Int for positive infinity and in for negative infinity. Use for union. Don't include any spaces in your solution. (e) Average rate of change

2. Make a table for r = 2 cos(30) with 0=15° +30°k with k going from 0 to 11 along with = 90°k with k going from 0 to 4 and plot these points (by hand). Use these points to help you sketch a graph of r = 3 sin(20).

Let f (x) = 4^-x-1. Find the domain and range of f (x). Domain: (-∞, ∞) Range: (-∞, -1) Domain: (-∞, ∞) Range: (0, ∞) O Domain: (-∞, ∞) Range: (-1, ∞) Domain: (-∞, ∞) Range: (-∞0,0) Domain: (-1, ∞) Range: (-∞, ∞)

Find the domain and intercepts. f(x)=√x+1 Find the domain. Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The domain of the function f(x) is (Type your answer in interval notation.) B. The domain is all real numbers. Find the x-intercept(s). Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The x-intercept(s) of the graph is (are) x = (Simplify your answer. Type an integer or a decimal. Use a comma to separate answers as needed.) B. There is no x-intercept. Find the y-intercept(s). Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The y-intercept(s) of the graph is (are) y = (Simplify your answer. Type an integer or a decimal. Use a comma to separate answers as needed.) B. There is no y-intercept.

A set of exam scores is normally distributed with a mean = 80 and standard deviation = 9. Use the Empirical Rule to complete the statements below. 95% of the data values lie between ___and___ ___% of the exam scores are between 71 and 80. ___% of the exam scores are between 80 and 98. ___% of the exam scores are between 89 and 98. ___% of the exam scores are greater than or equal to 71.

The parabola y = x² is compressed vertically by a factor of 0.3, translated up 1 unit and to the right 3 units. Write the equation of the new parabola in the form y = a(x - h)² + k.

The function y = sin x has been transformed. It now has amplitude of 7.8, a period of 22, a phase shift of 10 units to the right, a vertical translation of 4.5 units down, and is reflected over the x-axis. Given that (π/6, 1/2) is a point in the parent function, use mapping notation to determine the x-coordinate of its image point in the transformed function. Enter the numerical value of the x-coordinate only in the box below rounded to two decimals. Upload a picture of your work.

Determine the domain of the following function. f(x) =x+6/x-4

Rewrite the equation of the circle (x-2)^2 + y^2 =3 in general form. x²+y²-4x+1=0 x²+y²-4x+7=0 x²+y²-2x+1=0 x²+y²-2x+7=0

I understand that I have to derive both sides however I don't understand how the integral on the right side of the equation turns into a negative (-xf(x))

How is the graph of log (x + 3) - 4 translated from the graph of log x? shifted right 4 units and down 3 units shifted right 3 units and up 4 units shifted left 4 units and up 3 units shifted left 3 units and down 4 units

Is the function f(x) = 4x^4 - 5x³ + 12x² even, odd, or neither. Explain your answer.

How is the graph of y = 9(3)x+² + 6 translated from the graph of y = 9(3)x? 6 units right and 2 units down 2 units right and 6 units up 6 units left and 2 units down 2 units left and 6 units up

Which of the following describes the graph of f-¹(x)? The graph of f-1(x) is the reflection of the graph of f(x) in the y-axis. The graph of f-¹(x) is the reflection of the graph of f(x) in the x-axis. The graph of f-1(x) is the reflection of the graph of f(x) in the line y = x. The graph of f-1(x) is the reflection of the graph of f(x) in the line y = -x.

13. Graph the rational function y=x/2x+2.Which quadrant does neither branch of the rational function pass through? Quadrant 3 Quadrant 1 Quadrant 2 Quadrant 4

8. Find the y-axis intercepts for the function f(x)=1/x does not exist (1,1) (0,0) (0, 1)

14. For the function f(x) = 4x-3, evaluate and simplify the expression: f(a+h)-f(a)/h f(a+h)-f(a)/h =4 ƒ(a+h)-f(a)/h = 4a+4h+3 f(a+h)-f(a)/h= 4a+4h-3 f(a+h)-f(a)/h= 4h

15. Evaluate the function f(x) = -x²-1 and simplify at the indicated value: f(-a) = ? f(-a)=-a² f(-a)= a(a + 1) f(-a)= -a²-a f(-a)=-a²-1

What is the multiple zero and multiplicity of f(x) = (x + 8)(x + 8)(x − 3)(x + 8)? multiple zero = 3; multiplicity = -8 multiple zero = 3; multiplicity = 8 multiple zero = 8; multiplicity = 3 multiple zero = -8; multiplicity = 3

Solve the equation in the real number system: (x^5) - 4(x^4) +4(x^3)+2x² -5x+2=0. x = -1,1,2 x = -2,-1,1 x = -5,-4,1,2,4 x=-5,-4,1,2

State the various transformations applied to the base function f(x) = (x^2) to obtain a graph of the function (x) = -2[(x - 1)² +31 A reflection about the y-axis, a vertical stretch by a factor of 2, a horizontal shift of 2 units to the right, and a vertical shift downward of 6 units. A reflection about the x-axis, a vertical stretch by a factor of 2, a horizontal shift of 2 units to the right, and a vertical shift downward of 6 units. A reflection about the y-axis, a vertical stretch by a factor of 2, a horizontal shift of 1 unit to the right, and a vertical shift downward of 6 units. A reflection about the x-axis, a vertical stretch by a factor of 2, a horizontal shift of 1 unit to the right, and a vertical shift downward of 6 units.

28. State the various transformations applied to the base function f(x) = x² to obtain a graph of the function g(x) = -2[(x - 1)² +3]. A reflection about the y-axis, a vertical stretch by a factor of 2, a horizontal shift of 2 units to the right, and a vertical shift downward of 6 units. A reflection about the x-axis, a vertical stretch by a factor of 2, a horizontal shift of 2 units to the right, and a vertical shift downward of 6 units. A reflection about the y-axis, a vertical stretch by a factor of 2, a horizontal shift of 1 unit to the right, and a vertical shift downward of 6 units. A reflection about the x-axis, a vertical stretch by a factor of 2, a horizontal shift of 1 unit to the right, and a vertical shift downward of 6 units.

In this module assignment, many of your answers will involve monetary values, that is, dollars and cents. In WeBWork, you must remember to begin any monetary value with a dollar sign ($) and always round to the nearest penny, unless the instructions on a particular problem call for something else. Practice by inputting the value $10,314.76 in the blank below. (You'll get credit for one homework question for doing so!) Note that you can either include the comma separator for the thousands place or not, WeBWork will accept either notation.

Complete the statement. If a function f has an inverse and f(π) = -1, then f¯¹(− 1) =_

Evaluate the polynomial function for x = -6 and x = -3. f(x) = x³ - 16x f(-6)= f(-3) = Based on the results and the Intermediate Value Theorem, which statement is correct? Because f(-6) is negative and f(-3) is positive, f has at most one real zero between x= -6 and x= -3 Because f(-6) is negative and f(-3) is positive, f has at least one real zero between x = -6 and x= -3 Because both f(-6) and f(-3) are negative, f has no real zeros between x = -6 and x = -3 Because f(-6) < f(-3), f has at least one real zero between x = -6 and x = -3. Because f(-6) is negative and f(-3) is positive, f has exactly one real zero between x = -6 and x = -3.

Solve the following equation. (2x + 1) (x² + 1) = 0

The one-to-one function f is defined below. f(x)=8-x³ Find f⁻¹(x), where f⁻¹ is the inverse of f.

f(x)= 3/(2x⁴- 3x³ - 3)⁵