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# Graphs and Functions

### 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 &#8242; (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 = &#8722; + 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.

### Square the Given Function

Expand the square (4z - 4)^2.

### WEIRD Mathematical System

In a "WEIRD" Mathematical system, the following is true: 11+1=1 11+2=2 5+2=2 3+5=8 5+10=4 12+9=10 9+8=6 18+28=2 27+13=7 10+9=8 11+11=11 33+7=7 22+16=5 15+12=5 15+7=11 23+10=11 22+1=1 35+12=3 These are clues! After figuring out the system answer this problem: 152+46=? It can be a combination of anything,

### Evaluate limf(x) for the Function Given

(See attached file for full problem description). Evaluate lim f(x) for the function given below - X0+ x + 1 x ≤0 f(x) = { x - 2 x > 0.

### Graph: How to Graph Appropriately

Question Please select all the situations below that are POSSIBLE and do not mark those that are IMPOSSIBLE. Each list of numbers is a degree list (list of the degrees of all the vertices) of a graph. If there are extra restrictions - the graph is simple, or a tree, etc - it will be noted in the question. a. Graph, degre

### Problem set

Question 1 Consider the functions f(x) = x^2 and g(x) = square root of x, both with domain and co-domain R+, the set of positive real numbers. Are f and g inverse functions? Give a brief reason. Question 2 Given the Hamming distance function f: A X A -> Z defined on pairs of 8-bit strings, (where A is the set o

X+y<1 or y<4

X>3 or x<-3

### Exponential, logarithmic functions, etc

Refer to the graph given (attached) and identify the graph that represents the corresponding function. Justify your answer. y = 2x y = log2x

### Solving and Graphing Compound Inequalities

-1&#8804; 3 -2x<11 keywords: inequality

### Solve equations with radicals and exponents

Solve equations with radicals and exponents and create graphs of functions. See attached file for full problem description.

### Measurable Functions

Show that a function f is measurable IF AND ONLY IF there exists a sequence (f_m) of set functions such that f(x)=lim f_m(x) for almost all x. Please make sure to show the proof in both directions.

### Measurable functions

If f is measurable and almost everywhere nonzero, show that 1/f is measurable.

### Graphing, Domain and Range

Given the table below, graph the function, 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. x -2 -1 0 1 2 y .111 .333 1 3 9 See attachment

### Value of function at a given point

1. The number of 4-year college, public and private, in the period 1980-1996 can be modeled by f(x)=0.0003x^3 - 0.007x^2+0.058x+1.957 0 less than or equal to X less then or equal to 16 Where X is the number of years since 1980 and f(x) is the number of 4-year colleges measured in thousands. Determine the average number

### graph the functions with data points

For the function, y = ___1____ x - 2 a) Give the y values for x = -2, -1, 0, 1, 2, 3. Answer: Show work in this space. b) Using these points, draw a curve. Show graph here.