WGU C957 Applied Algebra OA (pdf) | 2026/2027 | Algebra Q&A |
Mathematics
1. Which of the following best describes the difference between a
quantitative variable and a qualitative variable?
A) A quantitative variable is measured on a number scale, while a qualitative
variable describes categories
B) A quantitative variable describes categories, while a qualitative variable is
measured on a number scale
C) A quantitative variable can only take integer values, while a qualitative
variable can take any value
D) A quantitative variable is always continuous, while a qualitative variable is
always discrete
Correct Answer: A quantitative variable is measured on a number scale,
while a qualitative variable describes categories
Rationale: Quantitative variables have numeric values that can be measured
and described numerically (e.g., cost, time, speed). Qualitative (categorical)
variables describe qualities or categories (e.g., color, type). The distinction is
fundamental to determining which algebraic and statistical methods apply.
2. What is the primary purpose of function notation in algebra?
A) To represent the relationship between an input and an output in a clear,
standardized way
B) To make equations more difficult to understand for beginning students
C) To replace all variable names with the letter f
D) To eliminate the need for graphing in algebraic problems
Correct Answer: To represent the relationship between an input and an
output in a clear, standardized way
,Rationale: Function notation, typically written as f(x), clearly identifies the
independent variable (input) and the dependent variable (output). It provides
a standardized way to express relationships and evaluate functions at
specific values, making algebraic reasoning more systematic.
3. A student is given the function f(x) = 3x + 7. What is the value of f(4)?
A) 12
B) 15
C) 19
D) 21
Correct Answer: 19
Rationale: To evaluate f(4), substitute x = 4 into the function: f(4) = 3(4) + 7
= 12 + 7 = 19. Function notation requires replacing the variable with the
given input value and simplifying.
4. Which term refers to a function that has an extremely rapid increase or
decrease in proportion to its current value?
A) Linear function
B) Polynomial function
C) Exponential function
D) Logistic function
Correct Answer: Exponential function
Rationale: An exponential function has the form f(x) = b^x (or with a
coefficient) and exhibits rapid growth or decay proportional to its current
value. Linear functions change at a constant rate, polynomial functions have
powers of x, and logistic functions model growth with a carrying capacity.
,5. Which of the following is the slope-intercept form of a linear equation?
A) y = mx + b
B) ax + by = c
C) y - y₁ = m(x - x₁)
D) x = a
Correct Answer: y = mx + b
Rationale: The slope-intercept form is y = mx + b, where m represents the
slope and b represents the y-intercept. The standard form is ax + by = c, and
the point-slope form is y - y₁ = m(x - x₁). Slope-intercept form is most useful
for graphing and identifying key features.
6. A line passes through the points (2, 3) and (5, 11). What is the slope of
this line?
A) 8/3
B) 3/8
C) 2
D) 4
Correct Answer: 8/3
Rationale: Slope is calculated as (y₂ - y₁) / (x₂ - x₁) = (11 - 3) / (5 - 2) = 8/3.
This represents the rate of change of y with respect to x. The other options
represent incorrect calculations or different values.
7. What is the most accurate definition of the y-intercept of a linear function?
A) The point where the line crosses the y-axis
, B) The point where the line crosses the x-axis
C) The slope of the line at the origin
D) The average rate of change of the function
Correct Answer: The point where the line crosses the y-axis
Rationale: The y-intercept is the value of y when x = 0, representing where
the graph intersects the y-axis. In slope-intercept form y = mx + b, b is the
y-intercept. The x-intercept is where the line crosses the x-axis.
8. A car rental company charges $30 per day plus $0.20 per mile. Which
equation correctly gives the total cost C for d days and m miles?
A) C = 30d + 0.20m
B) C = 30m + 0.20d
C) C = 30 + 0.20(d + m)
D) C = 30dm
Correct Answer: C = 30d + 0.20m
Rationale: The total cost equals the daily rate ($30) times the number of
days (d) plus the per-mile rate ($0.20) times the number of miles (m). This is
a linear function with two variables representing a real-world application.
9. Which of the following best describes the domain of a function?
A) The set of all possible input values (x-values) for which the function is
defined
B) The set of all possible output values (y-values) produced by the function
C) The point where the function crosses the y-axis
D) The rate at which the function changes
Mathematics
1. Which of the following best describes the difference between a
quantitative variable and a qualitative variable?
A) A quantitative variable is measured on a number scale, while a qualitative
variable describes categories
B) A quantitative variable describes categories, while a qualitative variable is
measured on a number scale
C) A quantitative variable can only take integer values, while a qualitative
variable can take any value
D) A quantitative variable is always continuous, while a qualitative variable is
always discrete
Correct Answer: A quantitative variable is measured on a number scale,
while a qualitative variable describes categories
Rationale: Quantitative variables have numeric values that can be measured
and described numerically (e.g., cost, time, speed). Qualitative (categorical)
variables describe qualities or categories (e.g., color, type). The distinction is
fundamental to determining which algebraic and statistical methods apply.
2. What is the primary purpose of function notation in algebra?
A) To represent the relationship between an input and an output in a clear,
standardized way
B) To make equations more difficult to understand for beginning students
C) To replace all variable names with the letter f
D) To eliminate the need for graphing in algebraic problems
Correct Answer: To represent the relationship between an input and an
output in a clear, standardized way
,Rationale: Function notation, typically written as f(x), clearly identifies the
independent variable (input) and the dependent variable (output). It provides
a standardized way to express relationships and evaluate functions at
specific values, making algebraic reasoning more systematic.
3. A student is given the function f(x) = 3x + 7. What is the value of f(4)?
A) 12
B) 15
C) 19
D) 21
Correct Answer: 19
Rationale: To evaluate f(4), substitute x = 4 into the function: f(4) = 3(4) + 7
= 12 + 7 = 19. Function notation requires replacing the variable with the
given input value and simplifying.
4. Which term refers to a function that has an extremely rapid increase or
decrease in proportion to its current value?
A) Linear function
B) Polynomial function
C) Exponential function
D) Logistic function
Correct Answer: Exponential function
Rationale: An exponential function has the form f(x) = b^x (or with a
coefficient) and exhibits rapid growth or decay proportional to its current
value. Linear functions change at a constant rate, polynomial functions have
powers of x, and logistic functions model growth with a carrying capacity.
,5. Which of the following is the slope-intercept form of a linear equation?
A) y = mx + b
B) ax + by = c
C) y - y₁ = m(x - x₁)
D) x = a
Correct Answer: y = mx + b
Rationale: The slope-intercept form is y = mx + b, where m represents the
slope and b represents the y-intercept. The standard form is ax + by = c, and
the point-slope form is y - y₁ = m(x - x₁). Slope-intercept form is most useful
for graphing and identifying key features.
6. A line passes through the points (2, 3) and (5, 11). What is the slope of
this line?
A) 8/3
B) 3/8
C) 2
D) 4
Correct Answer: 8/3
Rationale: Slope is calculated as (y₂ - y₁) / (x₂ - x₁) = (11 - 3) / (5 - 2) = 8/3.
This represents the rate of change of y with respect to x. The other options
represent incorrect calculations or different values.
7. What is the most accurate definition of the y-intercept of a linear function?
A) The point where the line crosses the y-axis
, B) The point where the line crosses the x-axis
C) The slope of the line at the origin
D) The average rate of change of the function
Correct Answer: The point where the line crosses the y-axis
Rationale: The y-intercept is the value of y when x = 0, representing where
the graph intersects the y-axis. In slope-intercept form y = mx + b, b is the
y-intercept. The x-intercept is where the line crosses the x-axis.
8. A car rental company charges $30 per day plus $0.20 per mile. Which
equation correctly gives the total cost C for d days and m miles?
A) C = 30d + 0.20m
B) C = 30m + 0.20d
C) C = 30 + 0.20(d + m)
D) C = 30dm
Correct Answer: C = 30d + 0.20m
Rationale: The total cost equals the daily rate ($30) times the number of
days (d) plus the per-mile rate ($0.20) times the number of miles (m). This is
a linear function with two variables representing a real-world application.
9. Which of the following best describes the domain of a function?
A) The set of all possible input values (x-values) for which the function is
defined
B) The set of all possible output values (y-values) produced by the function
C) The point where the function crosses the y-axis
D) The rate at which the function changes
