Applied-Algebra Certification Exam Guide + Practice Questions Updated 2026

Explanation:
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:

Explanation:
The contractor charges a flat rate plus a fixed rate per hour, so this situation is modeled by a linear function:
where:
and
We are given two points:
and
These mean:
A 3-hour job costs . A 5-hour job costs.
First, find the hourly rate using slope:
So the contractor charges:
Now the function has the form:
Use the point to find the flat rate:
So the function is:
Check with:
This matches the given information.

Explanation:
The scatterplot shows data collected over time, and a regression curve is used to model the pattern.
Extrapolation means using a model to make predictions slightly outside the observed data range.
In Applied Algebra, extrapolation can be appropriate when:
and the predicted -values are not too far outside the observed data.
From the scatterplot, the data points appear to run approximately from:
So the observed data range is about:
A reasonable extrapolation range extends a little beyond the data, but not too far. The interval:
extends about 3 units beyond each side of the observed data, which is reasonable.
The interval:
extends much farther beyond the data and would be less reliable.
Also, does not have to equal exactly 1 for extrapolation to be useful. A value less than 1 can still represent a strong model.
Therefore, the correct answer is:

Explanation:
The graph shows a linear relationship between:
and
The line passes through the origin, so the relationship has the form:
where is the rate of change.
From the graph, a clear point on the line is approximately:
This means when there are 8 cups of water, there are 5 cups of lemon juice.
The rate of change is:
So the relationship is:
This means the amount of lemon juice must be:
of the amount of water.

Explanation:
The graph shows a curved, downward-opening function. This type of graph is commonly associated with a quadratic polynomial function.
The maximum value of a downward-opening parabola occurs at its highest point, called the vertex.
From the graph, the highest point occurs at approximately:
This means the museum reaches its maximum daily profit approximately:
The vertical axis represents daily profit in hundreds of dollars. From the graph, the maximum -value is approximately:
Since the profit is measured in hundreds of dollars:
So the maximum daily profit is approximately:
Therefore, the correct interpretation is: