Functions Questions and Answers

f(x)= 3/(2x⁴- 3x³ - 3)⁵

Which of the following does not represent a quadratic equation? y = 2x²-4x + 7 y = 2x(7-5x) + 3 y = 1/²x² + 7 y = 3x³-4x -1

y = 0.2(-3)^x is an exponential function. True False

1. A function y = f(x) has a hole whose coordinates occur at (3/2 , 2) and the function y = f(x) has at least one vertical asymptote. Provide the equation of any rational function that satisfies this requirement. Explain how you arrived at your equation. Leave your answer in factored form.

C(3000) = 330 Now interpret the value of C(3000). Choose the correct interpretation below. A The value of C(3000) represents the minutes used that correspond to a monthly charge of $3000. B The value of C(3000) represents the monthly charge if 3000 minutes are used. C The value of C(3000) represents the monthly charge if each person on the plan uses 3000 minutes. (d) What is the domain of C? What does this domain imply in terms of the number of anytime minutes? The domain is The domain implies that there are____anytime minutes____

(a) f(x) =-1/3x g(x) =-1/3x f(g(x)) = g (f(x)) = fand g are inverses of each other fand g are not inverses of each other (b) f(x) = x + 4 g(x) = x + 4 f(g(x)) = g (f(x)) = f and g are inverses of each other f and g are not inverses of each other

The one-to-one functions g and h are defined as follows. g= {(1, 2), (1, 9), (2, 3), (3, -9), (7, 8)} h(x)= x-3/ 11 Find the following. g^-1 (2)= h^-1(x)= (h.h^-1)(0)=

A roast turkey is removed from an oven when its temperature has reached 185°F and is placed on a table in a room where the ambient temperature is 75°F. (Round your answers to the nearest whole number.). (a) If the temperature of the turkey is 150°F after half an hour, what is the temperature (in °F) after 50 minutes? T(50) = (b) After how many minutes will the turkey have cooled to 105°F? t = min

For eac of functions f and g below, find f(g(x)) and g(f(x)). Then, determine whether fand g are inverses of each other. Simplify your answers as much as possible. (Assume that your expressions are defined for all x in the domain of the composition. You do not have to indicate the domain.) (a) f(x)=x+6 g(x)=x-6 f(g(x)) = g (f(x)) = fand g are inverses of each other f and g are not inverses of each other (b) f(x) = ,-1/4x g(x) = 1/4x f(g(x)) = g(f(x)) = f and g are inverses of each other f and g are not inverses of each other

If ƒ(x) =a/1+e^bx and f(0) = 1, ƒ(-1) = 1/1-e , then a= and b= Input your answers as an integer or a real number with two decimals

Use the vertex (h, k) and a point on the graph (x, y) to find the equation of the quadratic function in general form, f(x) = ax²+bx+c. SHOW YOUR WORK IN STEPS. (h, k) = (-4,3), (x,y) = (0,-5)

Evaluate g(x) = In(x) at the indicated value of x without using a calculator. X = e^- 1/4 g(e-¹/4)=

2. For each function, create a table of values, graph the function, and state the domain and range, a. f(x) = 2/3x-4 b. f(x) = 2x-1 c. f(x) = 1/(x-1)

Use f(x) = 6x² and g(x) =x-6/2 to evaluate the expression. a. (fog)(4) b. (gof)(-5) a. (fog)(4) = (Simplify your answer.) b. (gof)(-5) = (Simplify your answer.)

Find (fog)(x) and (gof)(x). f(x) = 7x-10, g(x)=8-5x (fog)(x) = (Simplify your answer.) (gof)(x) = (Simplify your answer.)

Let f(x) =8x-9 / 6 and g(x) = 6x+9/8 (a) Find (fog)(x). (b) Find (gof)(x). (a) (fog)(x) = (b) (gof)(x) =

Let f(x)=x² +4 and g(x) = 2x + 3. Find the following. (a) (f+g)(x) (b) (f-g)(x) (c) (f.g)(x). (d) (f/g)(x) (e) The domain of (a) (f+g)(x) = (Simplify your answer. Do not factor.) (b) (f-g)(x) = (Simplify your answer. Do not factor.) (c) (fog)(x) = (Simplify your answer. Do not factor.) (d)(f/g)(x)= (Simplify your answer. Do not factor.) (e) The domain of f/g is (Type your answer in interval notation.)

Given the function f(x) =-2+x², evaluate the following: a) f(x + 1) = b) f(x) + f(8) =

Determine the domain of the function. Fill in the blank below. f(x) =x-z/ x+y if z = 21 and y = 42 Solution: x ≠

Find the Domain. Include both. Set builder notation and interval notation. X.5 / X-2 * 1/ X.4

Find the cumulative distribution function for the probability density function f(x)=1/9x -1/18 on the interval [2,5] F(x)= (Type an expression using x as the variable) What is the domain? The domain is (Type your answer in interval notation)

Answer the questions about the following function. f(x)=12x²/x4 +36 (a) is the point (-√6,1) on the graph of f? (b) If x=3, what is f(x)? What point is on the graph of f? (c) If f(x) = 1, what is x? What-point(s) is (are) on the graph of f? (d) What is the domain of f? (e) List the x-intercepts, if any, of the graph of f. (f) List the y-intercept, if there is one, of the graph of f.

comment on the pros and cons of social media use in disasters

Find the y-intercept of the function. Give your answer as an ordered pair. g (x) = 2 (4x − 1) (3x + 1)

Find f[g(x)] and g[f(x)]. f(x) = 5x²-3; g(x) =8/x f(g(x)] =

The graph of the function y = x is transformed to the graph of the function y = -2(x - 3)^4+1 by a)a horizontal stretch by a factor of 2, a reflection in the x-axis, a translation of 3 units to the left, and a translation of 1 unit up b)a vertical stretch by a factor of 2, a reflection in the x-axis, a translation of 3 units to the left, and a translation of 1 unit up c)a vertical compression by a factor of of 3 units to the left, and a translation of 1 unit up a reflection in the x-axis, a translation d) a vertical stretch by factor of 2, a reflection in the x-axis, a translation of 3 units to the right, and a translation of 1 unit up

Which of the following is an odd function? y=2x (x²-3x) y = 2x³ (x² − 2) y = −3x(x − 2)(x+2) y=−5x²(x − 2)

Graph the following function on the axes provided. f(x)=-1/2+3 for ≤-4 -x+10 for x>1

Determine the range of the quadratic function. Give your answer as an inequality- f(x)=7x²-10x+10

The point (19, -12) is on the graph of y = f(x). a) A point on the graph of y = g(x), where g(x) =-f(x) is b) A point on the graph of y = g(x), where g(x) = f(x) + 10 is c) A point on the graph of y = g(x), where g(x) = f(x - 12) is d) A point on the graph of y = g(x), where g(x) = f(-x) is e) A point on the graph of y = g(x), where g(x) = = f(x) is f) A point on the graph of y = g(x), where g(x) = 6 f(x) is

The concentration C of a drug in a patient's bloodstream t hours after injection (for the first 24 hours) is given by C(t)= 100t /2t² + 75 nanograms per millileter (ng/mL). Round your answers to the nearest hundredth ng/mL or hundredth of an hour. (a) What is the concentration after 1 hour? (b) About how many hours will it take for the drug to fall below 2 ng/mL in the patient's bloodstream? (c) How long is the drug above 2 ng/mL in the patient's bloodstream?

Check off all the statements that are true. (check all that apply) if h(c) = 0, then x - c is a factor of h(x) if x is a factor of g(x), then g(0) = 0 when g(x) is divided by jx - k, then g(j/k) = the remainder x - k is a factor of f(x) if and only if f(k) = 0

For the demand function q = D(p) = 219-p, find the following. a) Find the equation for elasticity. b) Find the elasticity at the given price, stating whether the demand is elastic, inelastic or has unit elasticity. Is the demand elastic, inelastic, or does it have unit elasticity? c) Find the value(s) of p for which total revenue is a maximum (assume that p is in dollars). $ (Round to the nearest cent. Use a comma to separate answers as needed.)

1. (a) describe the increasing, decreasing, and constant behavior of the function. (b) find the relative maximum and relative minimum. (c) Find the domain and range of the function. you should sketch the graph using desmos, graph calculator, etc. i) f(x) = x^3 - 3x^2 ii) f(x) = x + 1| + |x − 1| iii) f(x)=x√x + 3

2. Function f(x,y) x³y² + y² + 2x(y + 1). Suppose the initial values are given x 1.yo=0, and the learning rate is set to 0.01. a) Perform one iteration of the gradient descent algorithm. b) Find the Hessian matrix of f(x,y). Provide appropriate justification and explanation to all your answers, detailing the methods used.

If the domain of y = f(x) is -1 ≤ x ≤ 4, determine the domain of y = 3 f(-x-2). Select one: a.-2≤x≤3 b. -6 ≤ x ≤-1 c. -10 ≤x≤5 d. -3 ≤ x ≤ 12

W = -i Z-1/z+1 R: |z|≥ 1,0 ≤ Argz ≤π/2 find the mapping image, I need caculation process

State the leading coefficient of the polynomial function f(x) = -x(-1x-2)(3x + 3)²(-2x-6)^3

True or False: A degree 3 polynomial function may have 0, 1, 2, or 3 real zeroes. True False

Given f(x) = 2(x - 1)(x - 2)(x + 3), a) What quadrant does f(x) start in? b) What quadrant does f(x) end in?

Let g(x)=4x-3. Find g(2.5). g(2.5) = (Type an integer or a decimal.)

Find the domain of f(z) the analytic function, graph on the z-plane.find the Re(f'(1)). ƒ(z) = (z² + 1)^i

Determine the domain of the quadratic function f(x)=-6x² - 6x +5

What is the domain of the function? f(x)=-3x (x - 1) (x - 5) (-∞0,0] (0,3) (1,5) (-∞, ∞) [0, ∞)

Find the domain of each function using inequality notation. f (x) =1/x²+4x-45

For the given function f, evaluate f(-1), ƒ (0), ƒ (2), and ƒ (4). f(x)= x²-2 if x < 2 4+|x-3| if x ≥ 2 f(-1) = f(0) = f(2)= f (4) =

Given f(x) = px + q where p and are constant and p is positive. Find the value of p and q if f^2(x) = 4x + 15.

Enter the interval equivalent to 2 < x < 5 or x > 7

6) g(x) = -3+5csc(4x) Directions: In 5-6, sketch two periods of the graph of the given function. Be sure that the "fab five" points/places clearly represented on each graph

Give functions f: N ---> N that satisfy the following: (a) f is total and 1-1 but not onto (b) f is total and onto but not 1-1. (c) f is total, 1-1, and onto but not the identity. (d) f is not total but is onto.