Graphs and Functions

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What are the critical points for f(x) = x/(1 + x^2)?

Find the critical points, determine their nature (maxima, minima, inflection, etc.) and sketch the function: f(x) = x/(1 + x^2)

For each system of linear equations shown below...

For each system of linear equations shown below, classify the system as "consistent dependent," "consistent independent," or "inconsistent," and answer the question about its solutions. a) Line one y=2x+8 Line two y=-2x - 4 b) line one y=-2x+1 line two y= -2x+4 c) line one y= 1/3x-1 line two - x +

Graphing Parabolas

Graph the parabola: y=(x+5)^2 + 3 To graph the parabola, plot the vertex and four additional points, two on each side of the vertex, and then click on the graph icon

Solving Equations

Solve the following equation for x by using the quadratic formula: 4x^2 - 7x - 1=0 (If there is more than one solution, separate them with commas.)

On which interval is the function below decreasing

On which interval is the function below decreasing? f(x) = x2 - 6x + 5 Please show this answer in inequality notation. Thanks

Finding the Average of a Function

Find the averages of the function f(x) = x2 + 1 on the interval [1, 10], and for integer values of x. Compare the results.

Locus of Points that Satisfy the Equation of a Line

In the following problems determine the set of Z satisfying the given equations 1. |Z|=|Z-i| 2. |Z|^2 + Im(z)= 16 3. |Z-i|+|Z| = 9 Where: Z = x+yi __ Z = x-yi.

Completing a Function Table

The function g is defined by the following rule: g(x)=3x-1 . Complete the function table x g(x) -5 0 2 3 4

To calculate the world grain demand be in 2010 and the range of the car selling price

1.WORLD GRAIN DEMAND Freeport McMoran projects that in 2010 world grain supply will be 1.8 trillion metric tons and the supply will be only 3/4 of world grain demand. What will world grain demand be in 2010? 2. CAR SELLING Ronald wants to sell his car through a broker who charges a commission of 10% of the selling price. R

Graphing

The function g is defined by the following function table. Graph the function. x g(x) -3 -4 -2 4 -1 3 2 2 3 -1

Completing a function table.

The function h is defined by the following rule: h(x) = x+2 x -2 0 3 4 5 .

Example of Completing a Function Table

The function g is defined by the following rule: g(x) = 5x - 3 x g(x) -5 0 1 2 5.

Complete the Function Tables

The function g is defined by the following rule: g(x)= 5x+ 2 complete the table below x g(x) -2 0 1 2 3

Graph the Set

Graph the set {x|-7<x<1} on the number line below, and also write the set using interval notation. Graph the set {x | -5 x -2} on a number line, and also write the set using interval notation.

Domain of a square root function

On a number line, graph the domain of the function v defined by v(x) = sqrt( -8x - 8)

Function g

The function g is defined by the following function table. Graph the function. x g(x) -4 -2 -2 2 0 -4 2 2 3 4

Function table

The function h is defined by the following rule: . h (x)=-3x - 3 Complete the function table. x h -4 0 3 4 5

Graphing Absolute Values

Graph each absolute value function and state its domain and range. y=|x - 1| + 2

Graphing absolute value functions (domain and range).

Graph each absolute value function and state its domain and range. g(x) =|x| - 3

Determine whether each table expresses the second variable as a function of the first variable.

Determine whether each table expresses the second variable as a function of the first variable. C h 345 0.3 350 0.4 355 0.5 360 0.6 365 0.7 370 0.8 389 0.9

Are Relations Functions?

Determine whether each relation is a function. {(2, -5), (2, 5), (3, 10)}.

Using a Parabola: Maximum Height Reached by a Soccer Ball

If a soccer ball is kicked straight up from the ground with an initial velocity of 32 feet per second, then its height above the earth in feet is given by s(t) = -16t^2 + 32t where t is time in seconds. Graph this parabola for 0 < or equal to t < or equal to 2. What is the maximum height reached by the ball?

Parabola

Determine whether the graph of each parabola opens upward or downward. y= -1/2x^2+3

Use the product rule to find the slope of the line tangent to the graph of the function.

Use the product rule to find the slope of the line tangent to the graph of the function. f (x) = x^2 (1 + 3x3) at the point (1, 4)

Find five numbers with a mean of 16, a median of 15, a mode of 21 and a range of 11.

Find five numbers with a mean of 16,a median of 15, a mode of 21 and a range of 11.

Graphing Parabolas

How does one graph the following? 5 y= - --- x^2 4

Parabolas

1. State the key features (vertex, focus, directrix, direction of opening, and axis of symmetry) of each parabola, and sketch the graph. a) ysquared-2x+4y-7=0 2. Find the equation of each parabola. a) parabola with focus (-2,-1) and directrix y=5 b) ysquared=-6x translated according to ((x,y)arrow(x-2, y+4)

Imaginary solution

Find the imaginary solutions to each equation. 3y^2 + 8=0

Find f

(See attached file for full problem description) Let f (x) = x2 + 3x - 17. Find f ′ (4).

Find the interval on which the function

See attached file for full problem description. Find the interval on which the function 2 2 ( ) ( 2) ( 3) f x x x = − + is increasing and decreasing. Sketch the graph of y = f(x), and identify any local maxima and minima. Any global extrema should also be identified.