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Graphs and Functions

Identifying Graphs: Domain and Range

Identify the attached graphs and give the domain and range for each graph. See the attached file for the full problem description and diagrams of the graphs.

Derivatives and Rate of Change Word Problems: Motion and Relative Speed

1.A body has an a equation of motion measured in metres after t seconds such that s=4t3-14t2+40t+8. a) When and where is the body momentarily at rest? b) For what time interval is it moving forward? c) During what times is its acceleration negative? d) Draw three separate graphs for acceleration, velocity, and displaceme

Curve Sketching

1. Draw a sign graph to determine where the following function is increasing or decreasing. Identify all stationary points. y=2x^4-4x^2+1 2. Find the intervals where the following curve is concave up or down. Also find the coordinates of any points of inflection. y=2x^3 - x^2 +3x+5 3

Graph Coordinates : Scatterplot

Years (t) A = (1.10)t amount after t years (A) 0 A = (1.10)(0) 1 1 A = (1.10)(1) 1.1 2 A = (1.10)(2) 1.21 3 A = (1.10)(3) 1.331 4 A = (1.10)(4) 1.4641

Graphing Surfaces

Sketching Functions. Only circled questions. See attached file for full problem description.

Comparing Equations of Lines

1.For the pairs of lines defined by the following equations indicate with an "I" if they are identical, a "P" if they are distinct but parallel, an "N" (for "normal") if they are perpendicular, and a "G" (for "general") if they are neither parallel nor perpendicular. 3x + 4y + 5 = 0 and y = - 3 4 x - 54 . x = 2 and y = p

Vectors : Linear Combinations and Spans

Please see the attached file for the fully formatted problems. 1) Determine if b is a linear combination of , . 2) List five vectors in span { }. For each vector, show the weights on used to generate the vector and list the three entries of the vector. Do not make a sketch. a) b) 3) Let For what

Critical Points

Let f(x,y)=((x^(2)y^(2))/(x^(2)+y^(2))), classify the behavior of f near the critical point (0,0).

Graphs : Hyperbolas and Parabolas

Given the graph, identify the graph of the function (line, parabola, hyperbola, or exponential), explain your choice, and give the domain and range as shown in the graph, and also the domain and range of the entire function. See attached file for full problem description.

Vectors and Parametric Equations of Lines

2. Find a vector equation and parametric equations for the line. 3. The line through the point (?2, 4, 10) and parallel to the vector (3, 1, ?8) Find parametric equations and symmetric equations for the line. 8. The line through the points (6, 1, ?3) and (2, 4, 5) 11. The line through (1, ?1, 1) and parallel to the line x +

Trivial, Irregular Graphs

A non - trivial graph g is called irregular, if no two vertices of g have the same degrees. Prove that no graph is irregular.

Equation of a Secant Line

F(x)=x^2+2x-6 X(1)=2 and x(2)=-1 I have to find the secant line of this graph but can not remember how to find the points to graph the equation

Does the parabola open upward or downward?

Determine if the parabola for the equation, y = -2x^2 - 4x + 6, opens upward or downward. Find the vertex, x-intercepts, and y-intercept without graphing. keywords: concave, concae-up, concave-down

Sketch the region bounded by the graph of the function and find the area.

Sketch the region bounded by the graphs of the functions and find the area of the region. f(x) = sin(x), g(x) = cos(2x), -pi/2 <= x <= pi/6 (a) Use a graphing utility to graph the region bounded by the graphs of the equations, (b) find the area of the region and (c) use the integration capabilities of the graphing utility

Sketch regions bounded by graphs of algebraic functions and calculate the areas.

Sketch the region bounded by the graph of the algebraic function. 20. f(x) = -x^2 + 4x + 1, g(x) = x + 1 22. f(x) = -x^2 + 4x + 2, g(x) = x + 2 24. y = 1/(x^2), y = 0, x = 1, x = 5 26. f(x) = 1*sqrt(x - 1), g(x) = x - 1 28. f(x) = y(2 - y), g(y) = -y 30. f(y) = y/(sqrt(16 - y^2)), g(y) = 0, y = 3 32. g(x) = 4/(2 - x),