SMILE

A salesperson makes a base salary of $40,000 a year plus 3% commission on all sales up to (and including) $225,000 . If they exceed $225,000 in sales for a calendar year, the salesperson’s commission jumps to 7% for all their remaining sales over $225,000 . The salesperson’s total salary S for a given year is based on their total sales x . Write the piecewise-defined function S(x) .

(This is the only equation that I did not get correct)

The function h(a)=0.9(200−a) is used to calculate the handicap for a bowler (a bowling handicap is a percentage of the difference between your average and a basis average). In the function h(a)=0.9(200−a) , a bowler’s average a is used to determine their handicap h. How can we undo this original function to express a new function that tells us a bowler’s average a based on their handicap h.

What would be the inverse function? I tried 10 different answers. None were right. 

A sports agent has the following commission structure for contracts he negotiates:

The agent gets 2% of the first 4,000,000

The agent gets 8.5% of the next 8,000,000

The agent gets 11.5% of the remaining value

j(x)= (x+2)^2-3 if x is less than or equal to -2

               x       if -2<x or less than equal to 2

       -(x-1)^2+5 if x>2

(x+2)^2-3

(-4,1) solid dot (-3,-2) solid dot (-2,-3) solid dot 

x

(-2,-2) empty dot (-1,-1) solid dot (0,0) solid dot (1,1) solid dot (2,2) solid dot

-(x-1)^2+5

(2,4) empty dot (3,1) solid dot (4,-4) solid dot 

 1. Find the range of the piecewise-defined function and enter your answer in interval notation.

2. Find the x-intercept(s)

3. The function is positive when x is in the interval(s): 

4. The function is negative when x is in the interval(s): 

5. Increasing 

6. Decreasing

(Note: I need help with all those questions, but if you don't feel like doing them all could you at least do #1, #2, #3, and #5? TIA)

Given the piecewise function q(x), complete an xy-chart for each piece of the given function. Be sure to use correct inputs based on the domain of each piece of the function, and use solid or open dots to denote whether a point will be part of the graph or not (there is not graph to complete, just the charts).

q(x)= x ,if it is less than or equal to -2

          3x+10 ,if x>-2

(Don't know what I am doing wrong or right, therefore this first part of the answer may be wrong also! The first graph I got (-4,-4) (-3,-3) (-2,-2) with the endpoint as (-2,-2) all solid circles (was not told if this was wrong or not). When I get to the other points I am not able to get the correct endpoint for some reason for an answer).  

The major difference in resource allocation between a one-year old oak seedling and a 50-year old oak tree is that the 50-year old tree will allocate a greater fraction of its resources to produce a,b,c, or d?

a: roots

b: stems

c: leaves

d: seeds

Function g(x)=-x^2+8x-16

vertex=(4,0)

Line of symmetry x=4

Domain (-inf,inf)

Range (-inf,0]

g(x)=0 when x=4

g(x) >0 = when x is in ? : none 

g(x)<0 when x is in ? : ____

Increasing (-inf,4)

Decreasing(4,inf)

j(x)=10x^2-1/4x, find the difference quotient (j(-4+h)-j(-4))/h.

After plugging in for x I got the answer 10h+83/4 and got it wrong. 

Let y=f(x) be a function with domain D =(-inf,inf) and range R= [-5,inf). Find the domain D and range R for the following functions and enter your answers using interval notation. Keep in mind the order of operations. Be sure your intervals are in the correct order, and enter exact answers only. 

a. y=-f(2x)-2

Domain= (-inf,inf)

Range= ?

When solving I got the answer 3 so I put [3,inf) and it was said to be wrong. 

b. y=2/3f(x-4)-1

Domain: (-inf,inf)

Range: 2/3(-5)-1=-13/3

I put [-13/3,inf), it was also wrong

c. y=-3f(-1/3x)

Domain: (-inf,inf)

Range: 3(-5)=-15

I put [-15,inf), was also wrong. 

What am I doing wrong? 

Thanks in advance!

Let y=f(x)be a function with domain D=(-inf,inf) and R=[-5, inf). Find the domain D and range R for the following functions and enter your answers using interval notation. 

a)1/2f(-x)+3

Domain: (-inf,inf)

Range: ?

A newborn baby weighed 11 pounds at birth and was 16 inches tall. After 6 months the baby weighs 15 pounds and is 29 inches tall.

a) Write a linear function W(t) to represent the baby’s weight in pounds (W) at t months of age. Enter exact answers only, no approximations.

b) What will the child’s weight and height be on their first birthday? Round to the nearest whole number.

W(12)= 

A newborn baby weighed 11 pounds at birth and was 16 inches tall. After 6 months the baby weighs 15 pounds and is 29 inches tall.

a) Write a linear function W(t) to represent the baby’s weight in pounds (W) at t months of age. Enter exact answers only, no approximations.

b) What will the child’s weight and height be on their first birthday? Round to the nearest whole number.

W(12)= 

The blueprints for a new bathroom show a raised, rectangular bathtub with an area of 37 ft2. The blueprints show that the raised tub will be surrounded by tile on all four sides; 1.25-foot of tile on each side of the rectangular tub as well as at the bottom of the rectangle, and 2.5-feet of tile at the top of the rectangle (as shown in the diagram below). The total length (the vertical dimension) of the raised tub including the tile will be twice the total width (the horizontal dimension). Find the dimensions of the bathtub only.

F=g(mM/d^2) solve for d

10(3x−2)^2−60=0 Solve for x using the quadratic equations. 

The answer I got was 2/3(+or-)(sqrt6)/3. Was told that the answer was wrong. 

My steps were adding 60, 10(3x-2)^2=60, then divide by 10, (3x-2)^2=6, then sqrt both sides, 3x-2=sqrt6, then add 2 and divide by 3. 

Two pipes can be used to fill a swimming pool. When the first pipe is closed, the second pipe can fill the pool in 14 hours. When the second pipe is closed, the first pipe can fill the pool in 6.5 hours. How long (in hours) will it take to fill the pool if both pipes are open? (Round your answer to two decimal places.)

v=100(1-pq/p+q)  solve for p. 

2x^4-16x^2-2=0

2x^4+20x^2−2=0

A rectangular piece of sheet metal is 6 inches shorter than it is wide. From each corner, a 0.5 x 0.5 inch square is cut out and the flaps are then folded up to form an open box. You are given that volume of the open box is 1736 in3.

What is the length? 

What is the width?