Applied-Algebra WGU Applied Algebra FXO2 PFXP C957 Question and Answers

The graph shows the temperature of an object decreasing over time.

The horizontal axis represents:

The vertical axis represents:

The curve decreases and approaches the horizontal axis as time increases.

A horizontal asymptote is a horizontal line that the graph approaches but may not reach. Horizontal lines have equations of the form:

From the graph, the curve approaches:

So the horizontal asymptote is:

The options and are vertical lines, not horizontal asymptotes.

Therefore, the correct answer is:

The graph represents the number of user accounts over time.

The horizontal axis represents:

The vertical axis represents:

We need to find when the number of user accounts reached:

On the vertical axis, is halfway between:

and

So we look for the point where the blue curve reaches that height.

From the graph, the curve reaches approximately user accounts at:

That means the website had about user accounts after approximately:

The function is:

This is a linear function in the form:

where:

and

In this function:

The negative sign means the fish population is decreasing .

The number tells us the amount of decrease per month.

So the fish population is decreasing by:

The value is not the rate of change. It represents the starting fish population at the beginning of the year, when :

Therefore, the correct interpretation is:

So the correct answer is:

The function gives the number of workers at the job site hours after 6:00 a.m.

We need to find the difference between:

and

Because represents workers, the difference will be measured in workers , not hours.

First, evaluate :

Now evaluate :

Now find the difference:

This is approximately:

This graph represents a logistic growth function , which has an S-shaped curve.

Key behavior of logistic functions:

Initial phase (early time) → growth is slow

Middle phase → growth speeds up (increasing rate)

Later phase → growth slows down as it approaches a maximum

Analyze the interval from day 1 to day 17:

This interval is in the early part of the graph .

The curve is increasing and getting steeper over this range.

That means the rate of increase is growing over time .

So, the number of comments is:

The graph shows a linear relationship between the amount of red dye, , and the amount of yellow dye, .

The rate of change of a line is the slope:

From the graph, the line goes through the origin and rises steeply. A clear point on the line is approximately:

This means when the amount of red dye is gallons, the amount of yellow dye is gallons.

So the rate of change is:

That means for every gallons of red dye, the factory uses gallons of yellow dye.

The relationship can be written as:

So the correct interpretation is:

Therefore, the correct answer is:

The graph shows population in thousands, and the horizontal axis represents:

Point is located at approximately:

Since represents years since 1995:

So point corresponds to the year:

The instantaneous rate of change at point is:

Because the vertical axis is measured in thousands, this means:

Convert thousands to actual animals:

So in 2007, the population was increasing by approximately:

The table gives the percent of customers with fiber internet for each year since 2020.

Since 2023 is:

2023−2020=3

we use the row where:

Years since 2020=3

From the table, the percent of customers with fiber internet in 2023 is:

57%

The company has approximately:

1,050

customers each year.

Now find 57% of 1,050:

0.57×1,050=598.5

The closest answer choice is:

598

So approximately 598 customers had fiber internet in 2023.

Therefore, the correct answer is:

C

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This question is about reading an ordered pair from a graph.

An ordered pair has the form:

where:

and

From the graph:

Point is at approximately

Point is at

Point is at

Point is at

Point is at approximately

Point is at

Now compare these graph points with the answer choices.

Choice A says:

This matches point on the graph exactly.

The other choices do not match the graph:

is incorrect because at , the graph shows about , not .

is incorrect because at , the graph is about , not .

is incorrect because at , the graph shows about , not .

The function is:

This is an exponential growth function because the base is greater than 1:

We need to find the population after 25 minutes, so substitute:

into the function:

Evaluate the exponent and multiply:

Since the population is a number of bacteria cells, round to the nearest whole number:

The graph shows:

where:

The graph is a downward-opening curve, so it has a maximum value at its highest point. In Applied Algebra, the highest point of this kind of polynomial graph is called the vertex .

To answer the question, we need the -value of the vertex because the question asks when the store had its maximum weekly profit.

From the graph, the highest point occurs between:

and

More specifically, it is approximately:

So the store had its maximum weekly profit approximately:

The average rate of change tells us how much the output changes, on average, for each 1-unit increase in the input.

Here:

and

From the graph, point is approximately:

and point is approximately:

Now use the average rate of change formula:

Substitute the values:

Rounded to two decimal places:

The negative sign means the estimated wait time is decreasing from point to point .

So the average rate of change is approximately:

The graph shows , where:

and

The graph is a downward-opening curve, so its maximum value occurs at the highest point of the graph, also called the vertex .

From the graph, the highest point occurs at approximately:

So the maximum daily profit happened approximately:

The vertical value at this maximum point is approximately:

But the graph measures profit in hundreds of dollars , so:

Therefore, the maximum daily profit was approximately:

So the correct interpretation is:

The graph shows a linear relationship between:

and

The cost of each additional board is the rate of change , or slope, of the line.

From the graph, two labeled points are:

and

This means:

When 0 boards are ordered, the total cost is .

When 10 boards are ordered, the total cost is .

Now calculate the slope:

So each additional board costs:

Therefore, the correct answer is:

From the graph, the horizontal axis represents:

The vertical axis represents:

Point is approximately at:

Point is approximately at:

The average rate of change from point to point is calculated using:

Substitute the values:

Rounded to two decimal places:

So, the wait time decreases by about:

We are told that the number of property sales this year is expected to be 8 times the number of property sales last year.

Let:

and

Since this year’s sales are 8 times last year’s sales, the function rule is:

The question says that last year’s property sales were:

Substitute into the function:

So the correct notation is:

This means: if 360 properties were sold last year, then 2,880 property sales are expected this year.

Therefore, the correct answer is:

The graph shows a decreasing exponential function .

In Applied Algebra, a decreasing exponential function may approach a fixed value over time. This fixed value is called the horizontal asymptote .

The horizontal asymptote represents the long-term value that the function gets closer and closer to, but does not necessarily cross or reach exactly.

From the graph, the curve decreases quickly at first, then begins to level off near:

This means that as time continues, the number of letters processed per day approaches:

So the long-term trend is that the mail center will process about:

Since represents the number of years since 2004:

so:

Also:

so:

The average yearly rate of change from 2013 to 2018 is:

Now evaluate the function:

Now calculate the average rate of change:

So the painting’s value increased by an average of about:

Therefore, the correct answer is:

The graph shows the total value of an investment account as time increases.

The horizontal axis represents:

The vertical axis represents:

We need to find the value of the account after:

From the graph, when , the curve is slightly above . The closest answer choice is:

So the value of the account after 8 years is approximately:

Therefore, the correct answer is:

This question asks us to interpret a graph showing cost and revenue .

In Applied Algebra, the break-even point is where:

On a graph, this happens where the revenue line and the cost line intersect.

From the graph:

The solid blue line represents revenue .

The dashed blue line represents cost .

The break-even point occurs where these two lines cross.

Looking carefully at the graph, the two lines intersect at approximately:

The horizontal axis represents the number of units , meaning the number of down quilts sold.

So the person needs to sell about:

to break even.

After selling more than 6 quilts, the revenue line is above the cost line, meaning the person begins making a profit.

The graph shows a decreasing exponential model.

The vertical axis represents:

The horizontal axis represents:

The graph starts near 700 licensed sellers and decreases over time. However, it does not appear to decrease all the way to 0. Instead, it levels off near:

That horizontal line is the horizontal asymptote .

A horizontal asymptote represents the long-term value the function approaches as time continues.

So the correct interpretation is:

Therefore, the correct answer is:

The function is:

This is an exponential decay function because the base is between 0 and 1:

So the number of registered voters is decreasing over time.

Since represents the number of years since 2001:

To determine the fastest average decrease , compare the average rates of change. A faster decrease means the average rate of change is more negative.

For 2001 to 2007:

So from 2001 to 2007, the number of registered voters decreased by about:

For 2007 to 2008:

For 2008 to 2021:

For 2009 to 2012:

Now compare the decreases:

The most negative rate is:

That means the fastest average decrease happened from:

The function gives the number of active shopping carts on a website.

Because represents active carts, the difference between and will be measured in:

not hours.

First evaluate :

Now evaluate :

Now find the difference:

This is approximately:

Therefore, the correct answer is:

The function is:

Because represents the number of years since 2005:

The average yearly rate of change from 2006 to 2011 is:

First, find :

Now find :

Now calculate the average rate of change:

Rounded to two decimal places:

So the average yearly rate of change of the artifact’s value from 2006 to 2011 is approximately:

Therefore, the correct answer is:

This situation can be modeled with a linear relationship because each box has the same weight.

We are given:

and

The weight increases because more boxes are added.

First, find the change in total weight:

Then find the change in the number of boxes:

Since 5 additional boxes increased the total weight by 45 pounds, the weight of each box is:

So each box weighs:

Check:

If each box weighs 9 pounds, then adding 5 more boxes adds:

This matches the given information.