Functions Questions and Answers

A particular leaf is comprised of 80 thousand cells. As the leaf grows, the number of cells grows at a daily rate of 6.5%. (a) Find a function f(x) = Ae^kx that models the number of cells (in thousands) after x days. (b) Use your function in part (a) to determine how long until the number of cells triples.

Use the piecewise function below to evaluate for each x, which is the number inside the parentheses. f(x) = { 7x – 2 for x ≤ -7 {|3x| for – 5 < x ≤ 4 {–x² + 5 for x > 4 a) f(-8)= _______ b) f(4) = ______ c) f(- 2) =______ d) f(5)= ______ e) f(- 6) = _____ A piecewise function is shown below. 8(x) = {- 3x – 2x +8 for – 4 ≤ x <1 {-2x + 7p for 1 ≤ x ≤ 5 For what value of p will the function be continuous? a) To be a continuous function, where the first function stops the next will start. So the pieces share this point. At what point does the first function stop and the second start? Write as an ordered pair.

Which polynomial must be added to x^3+2x+15 so that the sum is 5x^3+6x+6? A. 6x^3+8X+21 B. 5x^3+4x+21 C. 5x^3+4x-9 D. 4x^3+4x-9 E. 4x^3+8X-9

Which value, to the nearest tenth, is the smallest solution of f (x) = g(x) if f (x) = 3 sin(1/2 x) - 1 and g (x) = x3- 2x + 1?

Consider the quadratic equation y= -4x^2 - 48x + 6. Complete the square to express the quadratic in standard form y = a(x – h)^2 + k. a= h= k=

Solve the equation x^2 - 2x -8 =0 by completing the square. Solutions (separate by commas): x=

Solve the equation 9x^2 + 36x + 27 = 0 by completing the square. The solutions are x1= _______________ and x2 = ________________ with x1 ≤ x2.

Find domain, range, roots/zeros/solutions, intercepts, maximum, minimum, increasing/decreasing intervals of a quadratic function and use to graph and solve application problems 1. Use the function f(x)= 2x2 + 20x +48 to identify each of the following: Domain: Range: x-intercept(s): y-intercept: vertex: root(s): interval(s) where graph is increasing: 2.Graph f(x) on the grid below interval(s) where graph is decreasing:

What is the most a store can pay for a tie for a line of ties that sell for $20 if the markup must be 32% of the selling price?

A TV set was originally priced at $2000. Last week, it went on a 4% off sale. (That means that the price of the TV set was reduced by 4%). What is the current price of the TV? (Enter your answer without the dollar sign.)

Raise the complex number to a power as indicated, and give your answer in standard a +bi form. [2(cos 5° + i sin 5°)}^6 A ship at point A is sailing directly north. The navigator a lighthouse on some rocks at point R. The bearing from point A to the rocks is 24 degrees, as shown. The ship then sails 4.7 km north to point B. From point B, the bearing to the rocks is 57 degrees, as shown. Find the distance from B to R.

Find the period of y=-2 sin (4x + π/2) A) π B) 4 C) π/2 D) 2

Given g(x) = -4sin( x/2 ) (a) Determine the amplitude. (b) Find the period. (c) Write the equation of the midline. (d) Identify 5 key points for one period. x g(x)

Find two linearly independent solutions of 2x²y" - xy + (5x + 1)y = 0, x > 0 of the form y₁ = x¹(1+ a₁x + a₂x² + a3x³ + ...) y₂ = x²(1 + b₁x + b₂x² + b3x³ + ...) where r₁ > r2. Enter r1 = a1 = a2 = a3 = r2 = b₁ = b₂ = b3 =

Graph the ellipse. Be sure to label the center, vertices and foci. (x² /16)+(y + 3)²/4=1

Find the Laplace transform, Y(s), of the function y(t)=1-3t³-5cos(5t) Find the inverse Laplace transform, y(t), of the function. Y(s) =24/(s+5) + 7/(s²+49)

Find the vertical asymptotes, if any, of the graph of the following rational function. f(x) ={(x+3)(4x-4)}/{(x-7)(x+8)} Select the correct choice below and fill in the answer boxes within your choice, if necessary. (A.) The vertical asymptote(s) is/are _________ (Type an equation. Use a comma to separate answers as needed.) (B.) The graph has no vertical asymptotes.

Given f(x) = (2/5)X -3 determine f^-1(x). f^-1(x) = (5/2)(x+3) f^-1(x) =(5/2)x+3 f^-1(x) = -(2/5)(x-3) f^-1(x)= -(5/2)x-1

1) Alex and Ryan had 37 points together in a basketball game. Ryan had 21 points. Which equation will tell us how many points Alex had? a +21=37 37+21=a 21+a=37 21- a=37

Suppose you have the following functions. f(x)=√(x-1)+1 g(x) = x³ + x - 3 Which of the following is an approximate solution for f(x) = g(x)? x= 1.69 x = 1.476 x= 1.286 x = 2.98

Draw a graph of f(x)=-2x/-x+3 by first placing the horizontal and vertical asymptotes, then plotting an additional point on the graph

Find two asymptotes for the following function: y = tan (x + π/6)

show that f'(x) = 2/4x-x^2 when g(f(x)) = x-2 and g'(x) = 2 -[f(x)]^2

A parabola has focus (5, 1) and directrix y=-3. Where is the parabola's vertex?

Evaluate the function h at the given values. h(x) = -x² +5 a).h(4) = b). h(-2): C).h(0) =

For each of the following relation tables answer T if the relation is a function and F if it is not. 1 1.8 | 1 4.9 | 1 1.4 | 1 1.6 2 2.2 | 2 2.9 | 2 2.1| 2 2.7 3 3.5 | 3 2.9 | 2 3.5| 1 2.7 4 4.4 | 4 1.9 | 4 4.1 | 3 2.7

Evaluate the function H at the given values. H(t) = t² +9 a) H(4) = b).H(-1) = c). H (0) =

Evaluate the function h at the given values. h(x)= -x +3 a). h(1) = b). h(-1) = c). h(0) =

Evaluate the function G at the given values. G(x) = -5x + 5 a). G(1) = b.____ C.___

Let f(x) = x + 4. Find and simplify: a) ƒ (4) = ____ b) f(0) = ____ c) f(-2)= ____ d) f(2a) = ____ e) f(a + 4) = ____

Evaluate the function g(x)=4/√(x² + 2). x = √(23) without using a calculator. Simplify your answer as much as possible. g(√23)=___

Use the algebraic tests to check for symmetry with respect to both axes and the origin. (Select all that apply.) y = x⁹ x-axis symmetry y-axis symmetry origin symmetry no symmetry Use the algebraic tests to check for symmetry with respect to both axes and the origin. (Select all that apply.) y=x²-x² + 4 x-axis symmetry y-axis symmetry origin symmetry no symmetry Use the algebraic tests to check for symmetry with respect to both axes and the origin. (Select all that apply.) y =x/x² + 8 x-axis symmetry y-axis symmetry origin symmetry no symmetry

The diameter of a Window-Pane oyster (in mm) as a function of its mass (in grams) can be modeled by the function, y=d(x). Write a sentence describing what is known from d-¹(23)=1.7 regarding an oyster.

According to data from the American Hospital Association, the rate of change in the number of hospital outpatient visits, in millions, in the United States each year from 1980 to the present can be approximated by f'(t) = 0.0014831(t - 1980) 0.75, where it is the year. Source: Hospital Statistics. a. Using the fact that in 1980 there were 262,951,000 outpatient visits, find a formula giving the approximate number of outpatient visits as a function of time.

An open bed truck is moving at 20 m s and comes to a stop. A 100 kg crate sitting in the back of the truck remains at rest in the truck bed. How much work was done by friction to keep the crate from moving as the truck came to a stop?

Suppose the graph of the rational function k(x) has the lines x = -2 andx = 3 as vertical asymptotes, x = 1 and x= 4 as x-intercepts, and a horizontalasymptote at y =1/2. Sketch a possible graph of k. Write an equation for your graph.

If f(x) = 3x + 2 and g(x) = 2x - 2, what is (f- g)(x)? A. x+4 B. x-2 C. X D. 5x-2 E. X-4

Find the linear speed ∨ for the following. the tip of a propeller 3 m long, rotating 900 times per min (Hint: r=1.5m) The linear speed ∨ for the tip of a propeller 3 m long, rotating 900 times per min is______. (Simplify your answer. Type an exact answer, using as needed. Use integers or fractions for any numbers in the expression.)

An adult human at rest inhales and exhales approximately 450 mL of air (called the tidal volume) in approximately 5 sec. However, at the end of each exhalation, the lungs still contain a volume of air, called the functional residual capacity (FRC), which is approximately 2100 mL. (a) What volume of air is in the lungs after inhalation? The volume of air in the lungs after inhalation is mL.

Rhea stated that the equation f(x) = x5 - 4x³ + x²-4 has 3 zeros because the graph only crosses the x-axis three times as pictured. Is she correct or incorrect? Explain to her why you think so.

A 90% confidence interval for the proportion of twelfth-grade students who chose math as their favorite subject is (0.43, 0.51). What was the point estimate or sample proportion used to calculate the interval?

Determine whether the relation represents y as a function of x. Domain, x Range, y -2 0 -1 1 0 2 1 2

Does the table describe x as a function of y? Does the table describe x as a function of y? A Yes, each output y is assigned to exactly one input x. B. Yes, exactly one output x is assigned to each input y. C. No, more than one output value x is assigned to the input y-value D. No, more than one output value y is assigned to the input x-value

In 4-card poker, each player is dealt 4 cards (go figure) from a standard deck of 52 cards. A total of _____ different hands can be dealt.

Tell whether the statement is true or false. If false, tell why. The tangent and secant functions are undefined for the same values. Choose the correct answer below. a. True. b. False. Tangent values are undefined when x=(2n + 1)π/2, while secant values are undefined when x=nπ c. False. Tangent values are undefined when x = nπ, while secant values are undefined when x=(2n+1)π/2 d. False. Tangent values are undefined when x = 2nπ, while secant values are undefined when x = (2n+1)π/2

Construct a truth table for ~p<--> q. Use T for true and F for false. p q ~p<--> q T T T F F T F F

Evaluate and write your answer in a + bi form. [2(cos 50° + i sin 50°)]6 =

Rewrite the Cartesian equation x = -5 as a polar equation. r(θ) = Enter theta for θ if needed.

The flux of the vector filed F=xi+ yj + zk flowing out through the surface of the ellipsoid x2/a2 + y2/b2 + z2/c2 = 1 a>b>c>Ois (a) πabc (b) 3πabc (c) 2πabc (d) 4πabc

Problem 1. A function f is given, and the indicated transformations are applied to its graph. • Write an equation for the final transformed graph. • Graph the function after the transformation 1. f(x) = x², stretch vertically by a factor of 2, shifted down 2 units and shift 3 units to the right. 2. f(x)=√x, reflect over x- axis, stretch horizontally by a factor of 4, and shift up 2 units.