WESTERN GOVERNORS UNIVERSITY
APPLIED ALGEBRA FXO1 PRACTICE
SCRIPT 2026 FULL ANSWERS GRADED A+
⩥ The amount of gasoline remaining in your gas tank, G(h)
, is a linear function of driving time, h, in hours. At time h = 0 (before
any driving), you have 10 gallons in your tank. After driving 3 hours,
you have 5.5 gallons in your tank. Find the equation of G(h)
.
G(h) = 1.5x + 10
G(h) = -0.67x + 10
G(h) = 0.67x + 10
G(h) = -1.5x + 10.
Answer: G(h) = -1.5x + 10
Correct! The slope is y2−y1/x2−x1=5.5−10/3−0=−4.5/3=−1.5
and the y-intercept is 10, the starting value.
⩥ Is the point (50, 4500) on P(c)=30c+1500
?.
Answer: No, because P(50)=30(50)+1500=1500+1500=3000.
⩥ Which lines have the fastest rate of increase?
,f(x)=3x−100
h(x)=0.5x+6
g(x)=x+5.
Answer: f(x)=3x−100
Correct! The slopes for the functions f, g, and h are 3, 1, and 0.5,
respectively. This means f(x)
has the fastest rate of increase.
⩥ Which line decreases the fastest?
h(x)=−0.5x+6
f(x)=−3x−100
g(x)=−x+5.
Answer: f(x)=−3x−100
⩥ Tostle Auto's Series A model can hold 10 gallons of gas, and it
consumes 0.04 gallons of gas per mile; Series B model can hold 12
gallons of gas, and it consumes 0.03 gallons of gas per mile. Let A(m)
model the amount of gas, in gallons, in a Series A model's tank, and
B(m)
in a Series B model's tank, where m is the number of miles to drive.
Assuming both functions start with a full tank.
Which statement is correct?
A(m)'s line decreases faster than B(m)
,. It implies the gas in a Series A auto decreases more slowly.
B(m)'s line decreases faster than A(m)
. It implies the gas in a Series A auto decreases faster.
B(m)'s line decreases faster than A(m)
. It implies Series B holds more gas than Series A.
A(m)'s line decreases faster than B(m)
. It implies the gas in a Series A auto decreases faster..
Answer:
⩥ Sarah has $50 in her piggy bank, and she spends $3.75 to purchase ice
cream every day. How much money is left after 8 days?.
Answer: $50−3.75(8)=20$ dollars
⩥ By the end of Julian's 8-hour shift at 5:00 p.m., he has cleaned a total
of 100 shirts. What is the average number of shirts Julian cleaned per
hour for those 8 hours?.
Answer: 100/8 = 12.5
⩥ For the function: f(x)=0.25x+20
, can you explain why the function's average rate of change at any two
given points equals the instantaneous rate of change at any given point?.
Answer: Because the function is a linear function.
, ⩥ A cell phone company charges a flat fee of $94 per month. A
customer's cost for service is given by the function: C(m)=94m
, where m represents the number of months. After 3 months of service,
the cost totals $282. After 4 months of service, the total cost is $376.
What is the instantaneous rate of change at the end of the third month?
$282
$94 per month
$94
−$94 per month.
Answer: $94 per month
Correct! The instantaneous rate of change at any point on the line is
simply the line's slope.
⩥ Alain generates a report that displays monthly advertising cost and
monthly revenue increase for Hot PC Fix. If the company spends $5,000
on advertising, the revenue is expected to increase by $10,000. If the
company spends $6,000 on advertising, the revenue is expected to
increase by $15,000. Let the linear function R(a)
, where a is the amount spent on advertising, model revenue increase.
Which statement is correct?
The company's average rate of change at a = 5,000 is 5, implying $5
increase in revenue for each dollar spent in advertising.
The company's instantaneous rate of change at a = 5,000 is smaller than
that at a = 6,000.
APPLIED ALGEBRA FXO1 PRACTICE
SCRIPT 2026 FULL ANSWERS GRADED A+
⩥ The amount of gasoline remaining in your gas tank, G(h)
, is a linear function of driving time, h, in hours. At time h = 0 (before
any driving), you have 10 gallons in your tank. After driving 3 hours,
you have 5.5 gallons in your tank. Find the equation of G(h)
.
G(h) = 1.5x + 10
G(h) = -0.67x + 10
G(h) = 0.67x + 10
G(h) = -1.5x + 10.
Answer: G(h) = -1.5x + 10
Correct! The slope is y2−y1/x2−x1=5.5−10/3−0=−4.5/3=−1.5
and the y-intercept is 10, the starting value.
⩥ Is the point (50, 4500) on P(c)=30c+1500
?.
Answer: No, because P(50)=30(50)+1500=1500+1500=3000.
⩥ Which lines have the fastest rate of increase?
,f(x)=3x−100
h(x)=0.5x+6
g(x)=x+5.
Answer: f(x)=3x−100
Correct! The slopes for the functions f, g, and h are 3, 1, and 0.5,
respectively. This means f(x)
has the fastest rate of increase.
⩥ Which line decreases the fastest?
h(x)=−0.5x+6
f(x)=−3x−100
g(x)=−x+5.
Answer: f(x)=−3x−100
⩥ Tostle Auto's Series A model can hold 10 gallons of gas, and it
consumes 0.04 gallons of gas per mile; Series B model can hold 12
gallons of gas, and it consumes 0.03 gallons of gas per mile. Let A(m)
model the amount of gas, in gallons, in a Series A model's tank, and
B(m)
in a Series B model's tank, where m is the number of miles to drive.
Assuming both functions start with a full tank.
Which statement is correct?
A(m)'s line decreases faster than B(m)
,. It implies the gas in a Series A auto decreases more slowly.
B(m)'s line decreases faster than A(m)
. It implies the gas in a Series A auto decreases faster.
B(m)'s line decreases faster than A(m)
. It implies Series B holds more gas than Series A.
A(m)'s line decreases faster than B(m)
. It implies the gas in a Series A auto decreases faster..
Answer:
⩥ Sarah has $50 in her piggy bank, and she spends $3.75 to purchase ice
cream every day. How much money is left after 8 days?.
Answer: $50−3.75(8)=20$ dollars
⩥ By the end of Julian's 8-hour shift at 5:00 p.m., he has cleaned a total
of 100 shirts. What is the average number of shirts Julian cleaned per
hour for those 8 hours?.
Answer: 100/8 = 12.5
⩥ For the function: f(x)=0.25x+20
, can you explain why the function's average rate of change at any two
given points equals the instantaneous rate of change at any given point?.
Answer: Because the function is a linear function.
, ⩥ A cell phone company charges a flat fee of $94 per month. A
customer's cost for service is given by the function: C(m)=94m
, where m represents the number of months. After 3 months of service,
the cost totals $282. After 4 months of service, the total cost is $376.
What is the instantaneous rate of change at the end of the third month?
$282
$94 per month
$94
−$94 per month.
Answer: $94 per month
Correct! The instantaneous rate of change at any point on the line is
simply the line's slope.
⩥ Alain generates a report that displays monthly advertising cost and
monthly revenue increase for Hot PC Fix. If the company spends $5,000
on advertising, the revenue is expected to increase by $10,000. If the
company spends $6,000 on advertising, the revenue is expected to
increase by $15,000. Let the linear function R(a)
, where a is the amount spent on advertising, model revenue increase.
Which statement is correct?
The company's average rate of change at a = 5,000 is 5, implying $5
increase in revenue for each dollar spent in advertising.
The company's instantaneous rate of change at a = 5,000 is smaller than
that at a = 6,000.
