Question 1

Which of the following best describes a qualitative graph?

Accepted Answer

A graph without scaling (tick marks and their numbers) on the axes.

Question 2

In the context of a graph showing the percentage of children attending college (P) versus parental income (I), which variable is the explanatory variable?

Accepted Answer

I, because it affects the percentage attending college.

Question 3

If a curve on a graph goes upward from left to right, how is the curve described?

Accepted Answer

Increasing

Question 4

Suppose $$n is $$the number of times a person can lift dumbbells that weigh $$w$$ pounds. Which is the response variable?

Accepted Answer

$$n$$, because it depends on $$w.$$

Question 5

What does the A-intercept represent in the graph of average age (A) when men first marry versus years since 1900 (t)?

Accepted Answer

The average age when men first marry at $$t = 0 ($$the year 1900).

Question 6

In a real-world scenario, if $$t is $$the number of hours worked and $$a is $$the amount of money earned, which axis should $$t be $$plotted on?

Accepted Answer

Horizontal axis

Question 7

Which of the following best describes the curve for the cost $$C of a $$Super Bowl ad over years $$t$$ since 1987, given that the annual increase is more than the previous annual increase?

Accepted Answer

A curve that bends upward, showing increasing growth.

Question 8

If a graph shows the number of albums sold ($$n) $$versus advertising dollars ($$a$$), and the curve levels off as $$a$$ increases, what does this indicate?

Accepted Answer

There is a maximum number of albums that can be sold regardless of advertising.

Question 9

Which quadrant would a graph be in if both variables are nonnegative?

Accepted Answer

Quadrant I

Question 10

If a curve goes downward from left to right, how is the curve described?

Accepted Answer

Decreasing

Question 11

Which of the following is a common misunderstanding when identifying explanatory and response variables?

Accepted Answer

Assuming the response variable affects the explanatory variable.

Question 12

In the scenario where $$N is $$the number of people ahead of you in line and $$T is $$your wait time, which statement is correct?

Accepted Answer

$$N is $$the explanatory variable and $$T is $$the response variable.

Question 13

Which of the following best describes the benefit of knowing the concept of explanatory and response variables?

Accepted Answer

It clarifies the cause-and-effect relationship in real-world situations.

Question 14

If a graph has a W-intercept and a t-intercept, what does each intercept represent?

Accepted Answer

The points where the curve crosses the axes.

Question 15

Which of the following is NOT a guideline for writing a good response?

Accepted Answer

Only use technical jargon without explanation.

Question 16

In a scenario where $$a is $$the amount of money spent on advertising and $$n is $$the number of albums sold, why must both $$a$$ and $$n be $$nonnegative?

Accepted Answer

You cannot spend negative money or sell a negative number of albums.

Question 17

Which statement best describes the relationship between the variables in the graph of average age when men first marry versus years since 1900?

Accepted Answer

The average age decreased for a while, then increased.

Question 18

If a curve is sketched in quadrant I, what does this indicate about the variables?

Accepted Answer

Both variables are nonnegative.

Question 19

Which of the following is a real-world example of an explanatory variable affecting a response variable?

Accepted Answer

The number of hours studied ($$t) $$affects the test score ($$s).$$

Question 20

What is the main purpose of using qualitative graphs in algebra?

Accepted Answer

To illustrate general trends and relationships without specific values.

Chapter 1: Linear Equations and Linear Functions – Qualitative Graphs and Variables

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