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Graphs and Functions

Parametric equation of line equation and equation of plane

See attached for full description. For the points P(1, 2, 1), Q(-2, 3, 1), and R(3, 0, -3): 1) Find the parametric equation for the line segment PQ. 2) Find the equation of the plane through P, Q, and R 3) Find the parametric equation for the line R normal to this plane.


Graph the line y= 5x -4 I do not need the graph only the 3 points for the graph.

Tree diagram

The Knicks won the first game against the Lakers in a basketball playoff. If the first team to win four games is the winner, construct a tree diagram for this playoff. Hint: Some of the branches in the tree diagram will end sooner than the other , as one of the teams would have one four games.

Find the equation of the plane

Find the equation of the plane which contains the points A(1, 1, 0) and B(1, 2, -1) and which does not intersect the line x = 1 + t, y = 2t, z = -1 + t.

Graph a polar curve using the given equations.

Use a graphing device to graph the polar curve. Choose the parameter interval to make sure that you produce the entire curve. 1.)r= square root of 1 - 0.8sin^2 theta (hippopede) 2.)r= 1 + 4cos(theta/3)

Graph the line

I need to graph the line using this equation. Can you tell me the three points I need to use? x+2y-2=0

Graph the slope

Graph the slope -1 passing through the point(5,5) I need to know where the points are on the graph.


Difficulty understanding the process with functions (see attached) 5) Given the function f describe by f(x)=x+10. Find each of the following: f(0)= 7) Find the indicated outputs for f(x)=5x^2 -3x, f(0)= 8) The function H described by H(x)=2.75x+71.48 can be used to predict the height in centimeters of a women whose hume


Given the function described k(x)=4x, find each of the following (a) k(-9) (b) k(4) (c) k(26)


Graph the line 3x -4y=8

Graph parabola

Steps to create a graph in excel (parabola's) Please show with an example


See attached The point A(-1,3) lies in a Cartesian plane. Determine the co-ordinates of the image of A if...

Composition of mappings

A) Let f : R→R be given by x→3x-1 and g:R→R be given by x→x+1. Calculate (i) fοg and ii) gοf. b) Prove that fοg and gοf are both invertible and describe their inverses. c) Demonstrate that (fοg)^-1 = g^-1 ο f^-1

Please see attached problems on domain, range, equations, and asymptotes

1. Write an equation that expresses the relationship. Use k as the constant of variation. d varies directly as the square of y. 2. Find the horizontal asymptote, if any, of the graph of the rational function. f(x) = 8x / (2x^2 + 1) 3. Find the domain of the rational function: g(x) = 6x / [(x-1)(x+7)] 4. Find the vertica

Transformation of the graph of a function

See file for an example from textbook. I plugged in x^2 + 6x + 10 into my calculator and got the required graph and the answer of -3 units parallel to the x-axis. But how does one come to this answer of -3units 'manually' without using a calculator? Thank you.

Right triangle applications - Angle of Elevation and angle of depression

1. From the top of a building 70 meters high, the angles of depression of two objects that are directly east of the observation position are 38° and 25° respectively. find the distance between the objects. 2. The angle of elevation of the top of a flag pole as seen from a window is 40° and the angle of depression of its b

Parametric equations

See attachment please sketch the curve for the following parametric equation and show the table to plot points. Thank you. (ii) For what parameter t does the slope of the line tangent to the graph at the point correspond to the value of the parameter -5? What are the rectangular coordinates at that point? (iii) Writ


Find the range for the group of data items 29, 32, 32, 38 The range is ___?

Truth table

Constructing a truth table for the given statement for 1 and the second is to write a truth table and indicate whether the compound statements is true.

Exponential function

In the formula A=I e^(kt), A is the amount of material remaining from an initial amount I at a given time t and k is negative constant determined by the nature of the material. If it has 53% of the carbon it originally contained, what is the approximate age of the artifact? (carbon decays @ a rate of 0.0125% annually.) Round

Linear cost function

An electrician charges a fee of $60 plus $45 per hour. Let C(x) be the cost in dollars of using the electrician for x hours. Find the linear cost function.