Answer to Question #94189 in Algebra for Joey

Question

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?

Answer 1

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

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

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

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

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

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

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

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

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

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

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

When boss starts paying $40 extra,

the new model will be

$f(x)=20x+40$

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

It has a $y-axis$ 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 $f(x)=30 x$

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