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Graphs and Functions

Graphing Questions

I have a lot of the attached problems to do. I know how to put points on the graph (for example (4,3)) but I am not sure how to get the information I need to graph on the attached. So I don't need to see these problems actually graphed out, just how to get to the stage before graphing. One: Graph: X ≥ 1 Two:

Parallel Lines

Find the pair of parallel lines: 1: -y=-x+2 2: -2y-2x=2 3:-2x+2y=2 Not sure how to do the above problem.

Continuity Proofs

1. Prove that any function f: Natural Nos. --> R is continuous (N --> R). 2. Prove that if a function f: I --> R is continuous and I is an interval then the image f(I) is an interval.

Equations of Lines, Slopes, Intercepts and Word Problems (15 Problems in Total)

Please see the attached file for the fully formatted problems. 1. Find a linear function perpendicular to the function y= -5x + 12 at the point (2,5) in standard form, point slope form, and slope-intercept form. The orginal line is y = -5x + 12 (slope is -5), so the perpindicular line will be y = 1/5x + ? 5 = (1/5)2 + ?.

Find the Vector Equation for the Line of Intersection of Two Planes

Consider the planes 1x + 4y +3z = 1 and 1x + 3z = 0 (A) Find the unique point P on the y-axis which is on both planes. (0,1/4 ,0 ) (B) Find a unit vector with positive first coordinate that is parallel to both planes. .94869 i + 0 j + -.3162 k (C) Use parts (A) and (B) to find a vector equation for the line of

Vector Equation for Line

Find a vector equation for the line through the point P = (-4, -1, 1) and parallel to the vector v = (1, 4, 3). Assume r(0) = -4i -1j +1k and that v is the velocity vector of the line.

Functions : Domain, Intercepts, Symmetry, Asymptotes and Graphing

Given the function R(x) = X^2 + x -12 / X^2 - 4 1. Give the domain 2. Give the X - intercepts 3. Give the Y - intercepts 4. Does it have symmetry with respect to the Y-axis, the origin or neither? 5. Give the vertical asymptotes 6. Give the horizontal asymptotes 7. Graph the function by dividing the axis and te


What is the y coordinate of the point on the curve y = 2x^2 - 3x at which the slope of the tangent line is the same as that of the secant line between x = 1 and x = 2?

Differentiability of Functions

Let f(x) be differentiable for a < x < b. Which of the following statements must be true? A. f is increasing on (a,b) B. f is continuous on (a,b) C. f is bounded on [a,b] D. f is continuous on [a,b] E. f is decreasing on [a,b]

Differentiability of Functions

5. Let f be twice differentiable on (a,b). If g is an antiderivative of f" on (a,b), then then g ' (x) must equal : A. f(x) B. f(x) C. f"(x) D. f(x) + C, for some C not necessarily 0 E. f"(x) + C, for some C not necessarily 0

Continuous Functions

4. Let f(x) = g(x)/h(x), where g and h are continuous functions on the open interval (a,b). Which of the following statements is true for a < x < b? A. f is continuous at all x for which x is not zero. B. f is continuous at all x for which g(x) = 0. C. f is continuous at all x for which g(x) is not equal to zero. D. f is c

Rational function, graph

Suppose that for a particular person enrolled in a typing class, f(x)=55(x+1)/(x+8), for x greater than 0, where f(x) is the number of words per minute the person is able to type after x weeks of lessons. (A) What does f(x) approach as x increases? (B) Sketch a graph of the function f, including any vertical or hor

Limit of Trigonometric Function

Find the limit: lim as x approaches 0 of sin 4x/sin 6x Please provide a detailed explanation of what you are doing in each step of the problem. I am not looking for just an answer.....I would like to be able to do similar problems on my own afterwards! Thanks!

What is the difference between functions and relations?

The question ask - in the real world, what might be a situation where it is preferable for the data to form a relation but not a function? Also, if the variables in an equation were reversed, what would happen to the graph of the equation? This was the example I was given, how would the graph of y = x² relate to the graph o

Linear functions, graphs, slope

As one descends into the ocean, pressure increases linearly. The pressure is 15 pounds per square inch on the surface and 30 pounds per square inch 33 feet below the surface. (A) If p is the pressure in pounds per square inch and d is the depth below the surface in feet, write an equation that expresses p in terms of d. [Hint

Depreciation: linear functions, graphs, slope

Office equipment was purchased for $20,000 and is assumed to have a scrap value of $2,000 after 10 years. If its value is depreciated linearly (for tax purposes) from $20,000 to $2,000: (A) Find the linear equation that relates value (V) in dollars to time (t) in years. (B) What would be the value of the equipment after 6 yea

Simple interest: linear functions, graphs and slopes

The simple interest formula says that if $1,000 is invested at 7.5% (r=0.075), then A=75t+1000, t>=0. (A) What will $1,000 amount to after 5 years? After 20 years? (B) Sketch a graph of A=75t+1000 for t between 0 and 20. (C) Find the slope of the graph and interpret verbally.