Question 1

Which of the following best describes the process of mathematical modeling in business calculus?

Accepted Answer

Applying mathematics to solve real-world problems through constructing, solving, and interpreting mathematical models.

Question 2

Given the cost function $$C(x) = 175 + 4.75x$$ and the revenue function $$R(x) = 12x$$ for selling custom t-shirts, how many shirts must be sold to break even?

Accepted Answer

$$x = 24$$

Question 3

Which equation represents a line with an undefined slope?

Accepted Answer

$$x = a$$

Question 4

If a line passes through the points $$(2, 5)$$ and $$(4, 11)$$, what is its slope?

Accepted Answer

$$m = 2$$

Question 5

Which of the following is the vertex form of a quadratic function?

Accepted Answer

$$y = a(x - h)^2$ + k$$

Question 6

A farmer has 20 trees per acre, each producing 300 peaches. For each additional tree, yield per tree drops by 10. What quadratic function models the total yield $$Y(x) if$$ $$x$$ additional trees are planted?

Accepted Answer

$$Y(x) = (300 - 10x)(20 + x)$$

Question 7

Given the quadratic function $$f(x) = -x^2$ + 5x + 3$$, what is the interval of $$x$$ values for which $$f(x) \u003e 0$$?

Accepted Answer

$$(-0.541, 5.541)$$

Question 8

Which of the following statements about the graph of $$f(x) = a(x-h)^2$ + k is $$true if $$a \u003c 0$$?

Accepted Answer

The parabola opens downward and the vertex is a maximum.

Question 9

A company’s revenue and cost functions for $$x$$ million cameras are $$R(x) = x(94.8 - 5x)$$ and $$C(x) = 156 + 19.7x. $$What equation must be solved to find the break-even points?

Accepted Answer

$$x(94.8 - 5x) = 156 + 19.7x$$

Question 10

Which interval notation represents all real numbers $$x$$ such that $$x \u003e a$$?

Accepted Answer

$$(a, \infty)$$

Question 11

If the best-fit line for a data set is $$y = 0.15x + 45.2$$ with $$r^2 = 0.014$, what does this indicate about the fit?

Accepted Answer

The linear model is a poor fit for the data.

Question 12

Which of the following is NOT a property of the graph of a quadratic function $$f(x) = a(x-h)^2$ + k$$?

Accepted Answer

The graph is always a straight line.

Question 13

A horizontal line has which of the following equations and slope?

Accepted Answer

$$y = b$$, 	ext{ slope } 0$

Question 14

Which of the following best describes the solution set to the inequality $$-x^2 + 5x + 3$$ \u003e 0$$?

Accepted Answer

All $$x$$ values between the x-intercepts.

Question 15

If a scatter plot of data appears to follow a curved pattern, which regression model is likely to provide a better fit?

Accepted Answer

Quadratic regression

Question 16

Given the quadratic regression model $$y = -0.52x^2$ + 33.29x - 480.94$$ with $$R^2 = 0.95$, what does the R^2$ value indicate?

Accepted Answer

The model fits the data very well.

Question 17

Which of the following is the correct point-slope form for a line with slope $$m$$ passing through $$(x_1$, y_1$)$$?

Accepted Answer

$$y - y_1$ = m(x - x_1$)$$

Question 18

If the graph of a quadratic function opens upward, which of the following must be true?

Accepted Answer

$$a \u003e 0$$

Question 19

Which of the following is the correct standard form of a linear equation in two variables?

Accepted Answer

$$Ax + By = C$$

Functions and Graphs: Linear and Quadratic Functions in Business Calculus 1.3

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