Pass the WGU Courses and Certificates Applied-Algebra Questions and answers with CertsForce

This question asks for correct function notation. The input x represents the number of properties sold last year, and the output H(x) represents the expected number of property sales this year. Since this year’s number is expected to be 9 more than last year’s number, the function rule is H(x)=x+9. The problem states that 140 properties were sold last year, so the correct input is x=140. Substituting gives H(140)=140+9=149. This means that when last year’s sales were 140, this year’s expected sales are 149. The input must be inside the parentheses, and the output must follow the equals sign. Therefore, the correct answer is B.

The graph shows a decreasing exponential model.

The vertical axis represents:

" Licensed sellers "

The horizontal axis represents:

" Time in years "

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:

y=100

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:

" In the long run, the number of licensed sellers nears 100. "

Therefore, the correct answer is:

▭ ( " C " )

The graph shows a linear relationship between:

w= " water in cups "

and

l= " lemon juice in cups "

The line passes through the origin, so the relationship has the form:

l=mw

where mis the rate of change.

From the graph, a clear point on the line is approximately:

(8│5)

This means when there are 8 cups of water, there are 5 cups of lemon juice.

The rate of change is:

m= " change in lemon juice " / " change in water "

m=5/8

So the relationship is:

l=5/8 w

This means the amount of lemon juice must be:

5/8

of the amount of water.

The maximum value of a polynomial graph is found at the highest point of the curve. In this problem, P(t) represents yearly profit in millions of dollars, and t represents years since opening. The graph reaches its highest point at approximately t=10.5, so the maximum yearly profit occurs about 10.5 years after opening. The vertical value at that point is about 2.25, but because the profit is measured in millions of dollars, this means 2.25 million dollars. Converting gives 2.25×1,000,000=2,250,000. Therefore, the correct interpretation must include both the correct time and the correct dollar amount. The correct answer is C.

This problem asks for an average yearly rate of change over a time interval. Since x represents years since 2005, the year 2013 corresponds to x=8, and the year 2015 corresponds to x=10. Use the average rate of change formula:

10−8

f(10)−f(8)

​

Evaluating the model gives f(8)=240(1.12)

8

≈594.23 and f(10)=240(1.12)

10

≈745.40. The total change is approximately 151.17 dollars over 2 years. Dividing by 2 gives about 75.59 dollars per year. Since the question asks for the average yearly rate, not the total increase, the correct answer is B.

This question asks us to interpret a value from a graph.

The horizontal axis represents:

Days

The vertical axis represents:

Practice duration in minutes

We need to find the practice duration on day 8.

To do this:

Locate 8 on the horizontal axis.

Move vertically until you reach the blue graph.

Read the corresponding value on the vertical axis.

From the graph, when:

x=8

the blue graph is at:

y=115

So the musician practiced for:

115 minutes

This is a linear function evaluation problem. The function G(x)=24+47x gives the drone’s distance from the operator after x minutes. The constant 24 is the starting distance, and 47 is the rate of change in yards per minute. To evaluate G(1.9), substitute 1.9 for x. Then compute G(1.9)=24+47(1.9). Multiplying first gives 47×1.9=89.3. Adding 24 gives 113.3. Because the function measures distance in yards, the result means the drone is 113.3 yards from the operator after 1.9 minutes. The other options do not result from correctly substituting 1.9 into the function. Therefore, the correct answer is D.

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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:

" the regression model fits the data reasonably well "

and the predicted x-values are not too far outside the observed data.

From the scatterplot, the data points appear to run approximately from:

x=3 " to " x=15

So the observed data range is about:

15-3=12

A reasonable extrapolation range extends a little beyond the data, but not too far. The interval:

x=0 " to " x=18

extends about 3 units beyond each side of the observed data, which is reasonable.

The interval:

x=-3 " to " x=21

extends much farther beyond the data and would be less reliable.

Also, r^2does 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:

▭ ( " A " )

We are told that computer B completes 12 more tasks than computer A.

Let:

x= " number of tasks completed by computer A "

and

F(x)= " number of tasks completed by computer B "

The phrase “12 more than” means add 12 to the original amount:

F(x)=x+12

So, if computer A completes xtasks, computer B completes:

x+12

tasks.

For example, if computer A completed 50 tasks, then computer B completed:

F(50)=50+12=62

Therefore, the correct answer is:

▭ ( " B " )

The value r

2

=0.96 indicates a strong regression fit because it is very close to 1. A strong fit supports prediction better than a weak or moderate fit. However, prediction also depends on whether the x-value is within a reasonable extrapolation range. The prediction is made at x=18.1, which is beyond the maximum observed x-value in the scatterplot. Even though the model fits the data well, the prediction is too far beyond the observed data range. For a strong model, extrapolation should not go more than about 50% of the range beyond the maximum value. Since x=18.1 exceeds that limit, the prediction is not appropriate. Therefore, the correct answer is B.