Question 1

Which of the following best describes the function shown in the first image (left side, labeled (a)), where the graph is a straight line with a positive slope passing through the origin?

Accepted Answer

A linear function of the form $$y = ax$$ with $$a \u003e 0$$

Question 2

In the second image, the line crosses the y-axis at $$b. $$Which equation represents this function?

Accepted Answer

$$y = ax + b$$

Question 3

The third image shows two parabolas. The left graph (a) opens upwards and the right graph (b) opens downwards. Which of the following statements is correct?

Accepted Answer

Graph (a) represents $$y = ax^2$ + bx + c$$ with $$a \u003e 0$$, and graph (b) represents $$y = ax^2$ + bx + c$$ with $$a \u003c 0$$

Question 4

The fourth image shows a curve that is asymptotic to both axes and passes through the origin. Which type of function does this graph most likely represent?

Accepted Answer

A reciprocal function of the form $$y = \frac{a}{x}$$

Question 5

In the fifth image, the left graph (a) shows a curve increasing rapidly for $$b \u003e 1$$, while the right graph (b) shows a curve decreasing for $$b \u003c -1. $$Which function type is illustrated here?

Accepted Answer

Exponential functions of the form $$y = b^x$$

Question 6

The sixth image shows two graphs: (a) with $$b  1. $$Both pass through the point (1, 0). Which function do these graphs represent?

Accepted Answer

Logarithmic functions of the form $$y = \log_b(x)$$

Question 7

Suppose a country’s national product $$Y is a $$function of investment $$I$$, written as $$Y = f(I). If$$ $$f(I) is $$linear, which of the following is a possible form for this function?

Accepted Answer

$$Y = aI + b$$

Question 8

If the demand function for a good is $$Q = 100 - 2P$$, where $$Q is $$quantity demanded and $$P is $$price, what is the slope of the demand curve?

Accepted Answer

$$-2$$

Question 9

Which of the following statements about the function $$y = ax^2$ + bx + c is $$correct?

Accepted Answer

If $$a \u003e 0$$, the graph is convex (opens upwards)

Question 10

A cost function is given by $$C(x) = 5x + 100. $$What is the fixed cost in this function?

Accepted Answer

$$100$$

Question 11

If a function $$f(x) is $$defined as $$f(x) = \frac{10}{x}$$, what happens to $$f(x) as$$ $$x$$ increases?

Accepted Answer

$$f(x)$$ decreases and approaches zero

Question 12

Which of the following is a property of exponential functions of the form $$y = b^x$$ with $$b \u003e 1$$?

Accepted Answer

The function increases rapidly as $$x$$ increases

Question 13

Given the function $$y = 3x - 4$$, what is the y-intercept?

Accepted Answer

$$-4$$

Question 14

If $$y = ax + b is a $$supply function and $$a \u003c 0$$, what does this imply about the relationship between price and quantity supplied?

Accepted Answer

As price increases, quantity supplied decreases

Question 15

Which of the following best describes a function where each value of $$x is $$associated with exactly one value of $$y$$?

Accepted Answer

A function of one real variable

Question 16

If $$y = \log_b(x)$$ and $$b \u003e 1$$, what is the behavior of $$y as$$ $$x$$ increases?

Accepted Answer

$$y$$ increases slowly as $$x$$ increases

Question 17

Suppose the production function is $$Q = 2L + 3$$, where $$Q is $$output and $$L is $$labor input. What is the marginal product of labor?

Accepted Answer

$$2$$

Question 18

Which of the following is NOT a common functional form found in economics?

Accepted Answer

Circular functions

Question 19

If $$y = ax^3$ + bx^2$ + cx + d is a $$cubic function, which of the following statements is true?

Accepted Answer

The graph can have up to two turning points

Functions of One Variable: Mathematical Foundations for Economic Analysis

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