Question 1

Which of the following equations specifies a function with independent variable $$x$$?

Accepted Answer

$$3y - 2x = 3$$

Question 2

Given the cost function $$C(x) = 156 + 19.7x$$ and the revenue function $$R(x) = x(94.8 - 5x)$$, what is the profit function $$P(x)$$?

Accepted Answer

$$P(x) = 94.8x - 5x^2$ - 156 - 19.7x$$

Question 3

Which of the following is the correct domain for the function $$h(x) = \sqrt{2-x}$$?

Accepted Answer

$$(-\infty, 2]$$

Question 4

A company’s price-demand function is $$p(x) = 2000 - 60x$$ for $$1 \leq x \leq 25 (in $$thousands). What is the expression for the revenue function $$R(x)$$?

Accepted Answer

$$R(x) = 2000x - 60x^2$

Question 5

Which transformation describes the graph of $$g(x) = -4|x+3| - 7$$ relative to $$f(x) = |x|$$?

Accepted Answer

Reflect across the x-axis, stretch vertically by 4, shift left 3 units, and down 7 units

Question 6

Given the quadratic function $$f(x) = -0.25x^2$ - 2x + 2$$, what is the vertex of the parabola?

Accepted Answer

$$( -4, 6 )$$

Question 7

If a line passes through the points $$(2, 5)$$ and $$(6, 13)$$, what is the slope of the line?

Accepted Answer

$$m = 2$$

Question 8

Which of the following is the correct range for the square root function $$f(x) = \sqrt{x}$$?

Accepted Answer

$$[0, \infty)$$

Question 9

A company’s cost function is $$C(x) = 156 + 19.7x (in $$millions of dollars). What is the fixed cost?

Accepted Answer

$$156$$ million

Question 10

Given the quadratic equation $$2x^2 - 5x - 5 = 0$, what are the solutions for x$?

Accepted Answer

$$x = \frac{5 \pm \sqrt{65}}{4}$$

Question 11

Which of the following is the equation of a line in point-slope form passing through $$(-2, 10)$$ with slope $$-3$$?

Accepted Answer

$$y - 10 = -3(x + 2)$$

Question 12

If $$f(x) = x^2$ - 4x + 9$$, what is $$\frac{f(a+h) - f(a)}{h}$$ for $$h 
eq 0$$?

Accepted Answer

$$2a + h - 4$$

Question 13

Which of the following describes a vertical stretch of the parent function $$y = x by a $$factor of 2?

Accepted Answer

$$y = 2x$$

Question 14

Given the price-demand data for emerald-shaped diamonds, which regression technique would best fit the data if the relationship appears linear?

Accepted Answer

Linear regression

Question 15

If the supply and demand for grapefruit are both linear, and at $$p = 12.59$$ the supply is $$595,000$$ boxes and demand is $$650,000$$ boxes, while at $$p = 13.19$$ the supply is $$695,000$$ boxes and demand is $$590,000$$ boxes, what is the equilibrium price (rounded to two decimals)?

Accepted Answer

$$12.89$$

Question 16

Which of the following is the correct vertex form for the quadratic function $$f(x) = -0.25x^2$ - 2x + 2$$?

Accepted Answer

$$f(x) = -0.25(x + 4)^2$ + 6$$

Business Calculus Study Notes: Functions, Graphs, and Applications

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