Question

I need help answering these questions. I have been having some trouble in math lately, It just has not seemed to be interesting at all. If someone can guide me through these that would be amazing! :)

Answer 1

1)
A)
f(x) has a slope of +5 (change with each x step), g(x) of +2 (m of y=mx+b), so f(x) rises 2.5 times faster than g(x)
B)
y intercepts are at x=0
f(x) has its intercept at -10
for g(x) it is the b value of y=mx+b, so 8
so the g(x) intercept is greater/above the one of f(x)

2)
A)
y intercept is at x=0 -> 12

When we started measuring the bird was already 12 miles away from its nest.
B)
average rate=(f(3)-f(1))/(3-1)
=16/2=8 [mph]
The bird moved on average with a speed of 8mph away from the nest.
C)
f(x)=8x+12

insert the 172 miles distance:
172=8x+12
160=8x
20=x

so after 20 hours it would be at a distance of 172 miles
this means we know the value from x=0 to 20 so its domain is/it is defined for x values of [0,20]

3)
A)
f(2)=225
f(5)=480

calculate slope m:
m=(f(5)-f(2))/(5-2)=(480-225)/3=255/3=85$/day

b=f(0)=f(2)-2*m=225-2*85=55
y=85x+55
B)
f(x)=85x+55

C)
Your x label is the amount of days rented, the y label the total cost/rent to pay, because y has larger values decide on some scale and the range of x values you want to draw, which should be x>=0.

Draw the points which were given, (2,225) and (5,480) and draw a line through them from one end of the diagram to the other.