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# Graphs and Functions

### Assistance with Graphing Inequities

Please help knowing what to graph (see the attachment). 1. Graph: Y ≤ 3x-6 2. Graph: -4x ≥ 5y 3. Graph: -8x ≤ 2y.

### How to Get to the Stage Before Graphing

See the attached file. 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: Graph: -8y < 34 Thre

### 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.

### Find Y value of a point given slope of a perpendicular line and another point.

The line through A(4,-5) and B(3,y) is perpendicular to a line with slope 1/3. Find y.

### Minimum Value of Closed, Continuous Analytic Function

5. Use the function f(z) = z to show that in Exercise 4 the condition f(z) does not equal 0 anywhere in P is necessary in order to obtain the result of that exercise. That is, show that |f(z)| can reach its minimum value at an interior point when that minimum value is zero. Please see the attached file for Exercise 4 and the

### Analytic Functions and Closed Contours

Please see the attached file for the fully formatted problems.

### L'Hopital's Rule & Indeterminate Functions

1. lim (as x approaches infinite) of (2^x)/(3^x) 2. lim (as x approaches infinite) of ln(lnx)/xlnx (See attachment for full questions)

### Continuity Proofs of Functions

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.

### Find points of intersection

Find the points of intersection algebraically of the graphs of the equations y= x^2-3x+4, and 2x-2y= -8

### Find the Domain and Range

Find the domain and range of the function f(x) = sqrt(5 - 3x) + 3.

### Find x and y intercepts

Find x and y intercepts of the equation algebraically y=6x^2+7x-5

### Write the equation of the line given two points.

Write the equation of the line that passes through points (4,-1) and (-1,9).

### Find the point of intersection of two lines.

Find the points of intersection algebraically of the graphs of the equations y=x^2-3x+4, and 2x-2y=8

### Equations of Lines, Slopes, Intercepts and Word Problems

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 + ?.

### Analytic Functions : Constancy

7. Let a function f (z) be a analytic in a domain D. Prove that f (z) must be constant throughout D if (a) f (z) is real-valued for all z in D (b) | f (z) | is constant throughout D. (Question also included in attachment)

### Graphing the Rational Function

Please graph the following rational function and show all of the necessary work involved: x^2 + x - 2/ 2x^2 + 1

### How to Graph the Rational Function

Consider the following rational function: x^2-4/ x - 1 Now graph this function.

### Polar coordinates of the point

Rectagular coordinates of a particular point are x=7, y= negative 24. find the polar coordinates of the point

### Proof for Domains with 2 Elements

Please see the attached file for the fully formatted problem. 71. 14b. Given the wff .... Show that W is true for any interpretation whose domain has two elements.

### Find the vector equation for the line of intersection of the two planes.

Consider the planes 1x + 4y +3z = 1 and 1x + 3z = 0 (C) find a vector equation for the line of intersection of the two planes, ? i + 1/4 j + ? k

### Find the vector equation for 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

### 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

### Parametric Equation of a Line and Point of Intersection

A) Find the parametric equations for the line through the point P = (3, -4, 0) that is perpendicular to the plane 2x + 0y+ 5z = 1 Use "t" as your variable, t = 0 should correspond to P, and the velocity vector of the line should be the same as the standard normal vector of the plane. x = 3+2t y = -4 z = 5t (B) At what p

### 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.

### Integrals (Find Area Under Graph of F Over Given Closed Interval)

Let f(x) = {see attachment}. What is the area under the graph of f over the closed interval [-1,1]? **Please see attachment for multiple choice options. Thanks.

### 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

### Arrangement of Block Possibilities

9. A child has 12 blocks, of which 6 are black, 4 are red, 1 is white, and 1 is blue. If the child puts the blocks in a line, how many arrangements are possible?

### Tangent Line Curves

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 Investigated

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