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Graphs and Functions

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.

Graphing Functions and Descartes' Rule of Signs

1. Use Descartes` Rule of Signs to determine the possible number of positive real zeros of the function. F(x)=3x cube-4x squared-2x-4 ***************x squared +11x+28 2. Graph: f (x)= ------------------------ ***************x squared +8x+16 ****************3x squared -3x-1 3. Graph: f (x)= ------------------------ ***

Graphs : Y as a Function of X

1. Which equation defines y as a function of x? answers a. y=-3x+4 b.y=-3 c.-6x second power -3y second power=4 d.x=10 2. m=-4/5,(5,7) answers a.5x=4y=-15 b.5x=4y=55 c.4x=5y=55 d.4x=5y=-15

Exponential function

Why does the graph of the basic exponential function lie entirely above the x-axis?

Horizontal asymptotes and costs

How could you interpret infinity in the y values for costs, a negative x value for time, or a horizontal asymptote in y values for profits?

Graphing question

What is the solution to a system of 2 equations represented by 2 parallel lines in the same plane?