Answer to Question #94189 in Algebra for Joey

Question #94189
Brian works on commission. For each subscription he sells in a day, Brian earns $20. The function f(x)=20x models this, where x is subscriptions sold and f(x) is the number of dollars Brian earn
A. Is the domain of f(x) all real numbers?
B. List five ordered pairs with x < 10 that satisfy the function?
C. Brian’s boss starts paying him $40 per day in addition to $20 per subscription. How would the graph of f(x) change?
D. Suppose that instead of paying $40 extra per day, Brian’s boss decides to pay him $30 per subscription. How would the graph of f(x) change?
1
Expert's answer
2019-09-11T13:32:05-0400

(a) f(x)=20x \ \

Here "x" represent the number of subscriptions sold which are natural numbers.

Hence as per the question ,domain of f(x)f(x) is xNx \in N

(b) Five ordered pairs for x<10x<10

1.x=1;f(x)=20x=20×1=20    (x,f(x))=(1,20)1. x=1;f(x)=20 x=20 \times 1=20 \implies(x,f(x))=(1,20)

2.x=2;f(x)=20x=20×2=40    (x,f(x))=(2,40)2. x=2;f(x)=20 x=20 \times 2=40 \implies(x,f(x))=(2,40)

3.x=3;f(x)=20x=20×3=60    (x,f(x))=(3,60)3. x=3;f(x)=20 x=20 \times 3=60 \implies(x,f(x))=(3,60)

4.x=4;f(x)=20x=20×4=80    (x,f(x))=(4,80)4. x=4;f(x)=20 x=20 \times 4=80 \implies(x,f(x))=(4,80)

5.x=5;f(x)=20x=20×5=100    (x,f(x))=(5,100)5. x=5;f(x)=20 x=20 \times 5=100 \implies(x,f(x))=(5,100)

(c) Initial model=f(x)=20x=f(x)=20 x

It is a straight line passing through origin with slope +20.

When boss starts paying $40 extra,

the new model will be

f(x)=20x+40f(x)=20x+40

The new graph will also be a straight line with slope 20 but it does not passes through origin.

It has a yaxisy-axis intercept of +20 which means he will get $40 even if he does not sell any subscriptions in a day.

(d) New model will be f(x)=30xf(x)=30 x

It is a straight line passing through origin with slope +30 bisecting the first and third quadrant.


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