WGU C957 APPLIED ALGEBRA OA EXAM
2026 | 180 ACTUAL REAL EXAM
QUESTIONS AND ANSWERS | 100% PASS
GUARANTEED | GRADED A+
1. A local business is looking to become a franchise. The company wants to predict the
number of franchises, F, given a certain number of years, Y. This prediction is modeled by
the function F(Y). What can be concluded by F(5) = 10?
A. Every 5 years, 10 stores will be opened.
B. Every 10 years, 5 stores will be opened.
C. In 5 years, there will be 10 open stores.
D. In 10 years, there will be 5 open stores.
Correct Answer: C
Explanation: In function notation F(Y), Y is the input (years) and F(Y) is the output (number of
franchises). F(5) = 10 means when Y = 5, the number of franchises is 10. The input value of 5
years corresponds to the output value of 10 stores. Choice A misinterprets the function as a rate
of change rather than a direct mapping. Choices B and D incorrectly swap the input and output
values.
2. A bank begins a marketing campaign to increase its number of customers. Each month,
all new customers are put into a drawing. One customer then receives a $50 credit in a
checking account. The amount of money given away in the drawing, G, is a function of
the number of months, M, the drawing has been going on for. What is the correct
function notation to represent the amount of money given away after the drawing has
been going on for 5 months?
A. G(5) = 10
B. G(5) = 250
C. G(250) = 5
D. G(10) = 5
Correct Answer: B
Explanation: Each month, $50 is given away. After 5 months, the total given away is 5 × $50 =
$250. In function notation, G(5) = 250, where M = 5 months is the input and G(5) = 250 is the
,output in dollars. Choice A incorrectly assumes only $10 per month. Choices C and D swap the
input and output values.
3. The volume of calls, V(h), at a particular customer service center can be written as a
function of the number of hours after opening each day, h. What would the ordered pair
(6,8) represent for this function?
A. There were 8 calls 6 hours after opening.
B. There were 6 calls 8 hours after opening.
C. There were h calls 6 hours after opening.
D. There were 8 calls V hours after opening.
Correct Answer: A
Explanation: In an ordered pair (h, V(h)), the first coordinate is the input (hours after opening)
and the second coordinate is the output (volume of calls). Therefore, (6,8) means at h = 6 hours,
V(6) = 8 calls. Choice B reverses the input and output. Choices C and D contain variables in place
of actual values.
4. A company has developed two functions, L(t) and M(t), that determine the least amount
and most amount, respectively, of revenue it will make in any given month in dollars
(with t = 1 corresponding to January). What can the company reasonably conclude if L(2)
= 3,000 and M(2) = 5,000?
A. In February, it will make $2,000.
B. In February, it will make between $3,000 and $5,000.
C. It will make more money in February if it uses M.
D. It will make exactly $4,000 in February.
Correct Answer: B
Explanation: L(t) gives the lowest expected revenue and M(t) gives the highest expected revenue
for a given month. With L(2) = 3,000 and M(2) = 5,000, February revenue is expected to be
between $3,000 and $5,000. Choice A incorrectly subtracts the bounds. Choice C misunderstands
the purpose of the functions as options rather than bounds. Choice D assumes a midpoint value
that is not guaranteed.
5. The function d(x) = 14 + 65x represents the distance, in meters, from a tower to an
object at time x, in seconds. What is the value of d(1.5)?
A. 0
, B. 0.19
C. 1
D. 111.5
Correct Answer: D
Explanation: We are given the function d(x) = 14 + 65x. This is a linear function where 65 is the
rate of change and 14 is the starting value. Substituting x = 1.5: d(1.5) = 14 + 65(1.5) = 14 + 97.5
= 111.5. Choices A, B, and C result from arithmetic errors or misinterpreting the function
structure.
6. A bakery models daily revenue R as a function of the number of cakes c sold. What does
R(24) = 720 mean?
A. The bakery sold 720 cakes in 24 days.
B. Selling 24 cakes produces $720 in revenue.
C. Revenue increases by $720 per cake.
D. The bakery sells cakes for $24 each.
Correct Answer: B
Explanation: The input is cakes sold and the output is revenue. Therefore, input 24 maps to an
output of $720. Choice A confuses the function with a time-based rate. Choice C misinterprets
the output as a rate of change. Choice D incorrectly divides the output by the input.
7. A taxi fare is F(m), where m is miles traveled. Which correctly identifies the independent
and dependent variables?
A. m is dependent; F(m) is independent.
B. m is independent; F(m) is dependent.
C. Both m and F(m) are independent.
D. Both m and F(m) are dependent.
Correct Answer: B
Explanation: Miles are the input selected first; the fare depends on miles. Thus m is the
independent variable and F(m) is the dependent variable. Choices A, C, and D incorrectly
describe the relationship between input and output.
8. A gym charges C(n) = 35 + 12n dollars for n training sessions. What is the cost for 5
sessions?
A. $47
, B. $60
C. $95
D. $175
Correct Answer: C
Explanation: C(5) = 35 + 12(5) = 35 + 60 = 95. The $35 is a fixed fee and $12 is charged per
session. Choice A incorrectly adds only the fixed fee to a partial session charge. Choice B omits
the fixed fee. Choice D incorrectly multiplies the wrong values.
9. What is the domain of h(x) = 1/(x − 4)?
A. All real numbers
B. All real numbers except x = 4
C. All real numbers except x = 0
D. All real numbers greater than 4
Correct Answer: B
Explanation: The function is undefined when the denominator equals zero. Setting x − 4 = 0
gives x = 4. Therefore, the domain excludes 4. Choice A ignores the restriction. Choice C
incorrectly identifies the excluded value. Choice D incorrectly restricts the domain to only values
greater than 4.
10. A parking garage records P(h), the price after h hours. How would you write the price
after 3.5 hours using function notation?
A. P(3.5)
B. P(h) = 3.5
C. h(P) = 3.5
D. P = 3.5
Correct Answer: A
Explanation: Function notation places the input inside parentheses. The input is 3.5 hours, so
P(3.5) is correct. Choice B incorrectly sets the function equal to the input. Choice C swaps the
function and variable. Choice D omits the function notation entirely.
11. If f(x) = 2x + 1 and g(x) = x², what is g(f(3))?
A. 7
B. 36
2026 | 180 ACTUAL REAL EXAM
QUESTIONS AND ANSWERS | 100% PASS
GUARANTEED | GRADED A+
1. A local business is looking to become a franchise. The company wants to predict the
number of franchises, F, given a certain number of years, Y. This prediction is modeled by
the function F(Y). What can be concluded by F(5) = 10?
A. Every 5 years, 10 stores will be opened.
B. Every 10 years, 5 stores will be opened.
C. In 5 years, there will be 10 open stores.
D. In 10 years, there will be 5 open stores.
Correct Answer: C
Explanation: In function notation F(Y), Y is the input (years) and F(Y) is the output (number of
franchises). F(5) = 10 means when Y = 5, the number of franchises is 10. The input value of 5
years corresponds to the output value of 10 stores. Choice A misinterprets the function as a rate
of change rather than a direct mapping. Choices B and D incorrectly swap the input and output
values.
2. A bank begins a marketing campaign to increase its number of customers. Each month,
all new customers are put into a drawing. One customer then receives a $50 credit in a
checking account. The amount of money given away in the drawing, G, is a function of
the number of months, M, the drawing has been going on for. What is the correct
function notation to represent the amount of money given away after the drawing has
been going on for 5 months?
A. G(5) = 10
B. G(5) = 250
C. G(250) = 5
D. G(10) = 5
Correct Answer: B
Explanation: Each month, $50 is given away. After 5 months, the total given away is 5 × $50 =
$250. In function notation, G(5) = 250, where M = 5 months is the input and G(5) = 250 is the
,output in dollars. Choice A incorrectly assumes only $10 per month. Choices C and D swap the
input and output values.
3. The volume of calls, V(h), at a particular customer service center can be written as a
function of the number of hours after opening each day, h. What would the ordered pair
(6,8) represent for this function?
A. There were 8 calls 6 hours after opening.
B. There were 6 calls 8 hours after opening.
C. There were h calls 6 hours after opening.
D. There were 8 calls V hours after opening.
Correct Answer: A
Explanation: In an ordered pair (h, V(h)), the first coordinate is the input (hours after opening)
and the second coordinate is the output (volume of calls). Therefore, (6,8) means at h = 6 hours,
V(6) = 8 calls. Choice B reverses the input and output. Choices C and D contain variables in place
of actual values.
4. A company has developed two functions, L(t) and M(t), that determine the least amount
and most amount, respectively, of revenue it will make in any given month in dollars
(with t = 1 corresponding to January). What can the company reasonably conclude if L(2)
= 3,000 and M(2) = 5,000?
A. In February, it will make $2,000.
B. In February, it will make between $3,000 and $5,000.
C. It will make more money in February if it uses M.
D. It will make exactly $4,000 in February.
Correct Answer: B
Explanation: L(t) gives the lowest expected revenue and M(t) gives the highest expected revenue
for a given month. With L(2) = 3,000 and M(2) = 5,000, February revenue is expected to be
between $3,000 and $5,000. Choice A incorrectly subtracts the bounds. Choice C misunderstands
the purpose of the functions as options rather than bounds. Choice D assumes a midpoint value
that is not guaranteed.
5. The function d(x) = 14 + 65x represents the distance, in meters, from a tower to an
object at time x, in seconds. What is the value of d(1.5)?
A. 0
, B. 0.19
C. 1
D. 111.5
Correct Answer: D
Explanation: We are given the function d(x) = 14 + 65x. This is a linear function where 65 is the
rate of change and 14 is the starting value. Substituting x = 1.5: d(1.5) = 14 + 65(1.5) = 14 + 97.5
= 111.5. Choices A, B, and C result from arithmetic errors or misinterpreting the function
structure.
6. A bakery models daily revenue R as a function of the number of cakes c sold. What does
R(24) = 720 mean?
A. The bakery sold 720 cakes in 24 days.
B. Selling 24 cakes produces $720 in revenue.
C. Revenue increases by $720 per cake.
D. The bakery sells cakes for $24 each.
Correct Answer: B
Explanation: The input is cakes sold and the output is revenue. Therefore, input 24 maps to an
output of $720. Choice A confuses the function with a time-based rate. Choice C misinterprets
the output as a rate of change. Choice D incorrectly divides the output by the input.
7. A taxi fare is F(m), where m is miles traveled. Which correctly identifies the independent
and dependent variables?
A. m is dependent; F(m) is independent.
B. m is independent; F(m) is dependent.
C. Both m and F(m) are independent.
D. Both m and F(m) are dependent.
Correct Answer: B
Explanation: Miles are the input selected first; the fare depends on miles. Thus m is the
independent variable and F(m) is the dependent variable. Choices A, C, and D incorrectly
describe the relationship between input and output.
8. A gym charges C(n) = 35 + 12n dollars for n training sessions. What is the cost for 5
sessions?
A. $47
, B. $60
C. $95
D. $175
Correct Answer: C
Explanation: C(5) = 35 + 12(5) = 35 + 60 = 95. The $35 is a fixed fee and $12 is charged per
session. Choice A incorrectly adds only the fixed fee to a partial session charge. Choice B omits
the fixed fee. Choice D incorrectly multiplies the wrong values.
9. What is the domain of h(x) = 1/(x − 4)?
A. All real numbers
B. All real numbers except x = 4
C. All real numbers except x = 0
D. All real numbers greater than 4
Correct Answer: B
Explanation: The function is undefined when the denominator equals zero. Setting x − 4 = 0
gives x = 4. Therefore, the domain excludes 4. Choice A ignores the restriction. Choice C
incorrectly identifies the excluded value. Choice D incorrectly restricts the domain to only values
greater than 4.
10. A parking garage records P(h), the price after h hours. How would you write the price
after 3.5 hours using function notation?
A. P(3.5)
B. P(h) = 3.5
C. h(P) = 3.5
D. P = 3.5
Correct Answer: A
Explanation: Function notation places the input inside parentheses. The input is 3.5 hours, so
P(3.5) is correct. Choice B incorrectly sets the function equal to the input. Choice C swaps the
function and variable. Choice D omits the function notation entirely.
11. If f(x) = 2x + 1 and g(x) = x², what is g(f(3))?
A. 7
B. 36
