Math 112 Exam 2

Function Notation

100

Write the rule in function notation:
Multiply by 3, then subtract 7

f(x)= 3x-7

200

Write the rule in function notation

First add 9, take the square root, then divide by 6

f(x)= √(x+9)/6

300

Is this a function? if so is it one to one

f(x)=x²

Yes it is a function, no it is not one to one

400

find f(g(x)) if 

f(x)=2x-5

g(x)= 3-x²

1-2x²

500

If f(x)= 1/(x+3), find f^-1(x)

f^-1(x)=(1/x) -3

Piecewise Functions

100

If f(x)= {x²     x<_0

            {x+2  x>0

Find f(-1) 

1

200

Picture 1:

What interval (in interval notation) do the functions occur on?

1. f(x)=1

2. f(x)= x²-3

1. (-inf,1)

2. [-1, inf+)

300

Which graph corresponds f(x)= {1      x<_1

                                              {x+5  x>1

picture 2

400

What is the parent function found on each interval: 

1.(-inf, 1]

2. (1,2]

3. (2,inf+)

1. f(x)= x² (quadratic)

2. f(x)=3 (constant)

3. f(x)= x (linear)

500

What are the functions for the following intervals: 

f(x)= {____   x<-3

         {____ -3<_x<_3

         {____ x>3

1. f(x)= -3

2. f(x)= x

3. f(x)= 3

Domain and Range

100

Find the domain of 

f(x)= 1/(x+4)

(-inf,-4)U(-4,inf+)

200

Find the domain of f(x)=4-7x

(-inf, inf+)

300

Find the domain of 

g(x)=√(6x-36)

[6,inf)

400

Find the domain of 

f(x)=523x-9.8754/√(x-3)

(3,inf)

500

Find the domain of 

m(x)=√(x+6)/x²-16

[-6,-4),(-4,4),(4,inf)

Transformations

100

Which way does f(x)=(x-2)³ shift? 

What is the parent function

right two units

f(x)=x³

200

How does the function f(x)= -|x| transform?

reflects over x axis

300

Transform f(x)= x²

Reflect over y axis, shift down 4, left 2, and vertically shrink by 3

f(x)= -1/3(x+2)²-4

400

What is the equation for the function g?

Picture

g(x)= |x +4|+3

500

Graph the following

f(x)=-√(x-1) + 1

picture

Linear/ Intervals/ROC

100

Determine if the given function is linear. If it is, express in the form f(x)=ax+b. 

f(x)= 1/3(9-12x)

Define the slope and y intercept

f(x)= -4x+3

slope: -4

y intercept: (0,3)

200

A table of values for a linear function h is given

Find the AROC of the function

Write the equation of the function

h(x)=3/2x + 9

AROC is 3/2

300

What is the net change between these two points (-1,0) and (5,4)

What is the average rate of change

picture

net: 4

average: 2/3

400

For this graph, list the increasing and decreasing intervals, and all local maximums and minimums

Increasing: (-inf,-2), (0,2), (3,inf)

Decreasing: (-2,0), (2,3)

Maximums: (-2,8) and (2,3)

Minimums: (0,-3) and (3,2)

500

What is the average rate of change equation? what is the net change equation?

What is the average rate of change of the function between any two points?

f(x)= 56,800x -34

AROC: f(b)-f(a)/b-a

Net: f(b)-f(a)

56,800