Question 1

Given $$f(x) = x^2$ - 2x$$, find and simplify the difference quotient $$\frac{f(x+h) - f(x)}{h}.$$

Accepted Answer

$$2x + h - 2$$

Question 2

Which of the following transformations, when reversed in order, may produce a different result?

Accepted Answer

Vertical shift followed by reflection in the x-axis

Question 3

What is the domain and range of the function $$s(x) = \sqrt{2-x}$$?

Accepted Answer

Domain: $$(-\infty, 2]$$; Range: $$[0, \infty)$$

Question 4

Find all real numbers $$a$$ such that $$a^2$$ = $$a^{-2}. $$Why does this not violate the exponential function property?

Accepted Answer

$$a = 1, -1$$; Both values violate the property since $$a$$ must be positive and not equal to 1.

Question 5

Evaluate $$\log_8$ 64$$ without a calculator.

Accepted Answer

$$3/2$$

Question 6

Which of the following is NOT a function?

Accepted Answer

A vertical line

Question 7

Given the graph of $$f(x) = -x^2$ - 4x - 4$$, what are the coordinates of the vertex?

Accepted Answer

$$(-2, 0)$$

Question 8

Find the equations of any vertical asymptotes for $$f(x) = \frac{x^2$ - 100}{(x-3)(x+1)}.$$

Accepted Answer

$$x = 3, x = -1$$

Question 9

Solve the inequality $$x^2 + 9x$$ \u003e 0$$ and write the solution set in interval notation.

Accepted Answer

$$(-\infty, -9) \cup (0, \infty)$$

Question 10

Write $$\log_8$ (XY) in $$terms of simpler forms.

Accepted Answer

$$\log_8$ X + \log_8$ Y$$

Question 11

Given points $$(2,6)$$ and $$(5,8)$$, what is the slope of the line passing through them?

Accepted Answer

$$\frac{2}{3}$$

Question 12

Which of the following best describes the transformation $$y = -f(x) + k$$?

Accepted Answer

Reflection in the x-axis, then vertical shift up by $$k$$

Question 13

Which of the following is the lowest-degree polynomial function that could have the graph shown with 5 turning points?

Accepted Answer

Degree 6

Question 14

If the leading coefficient of a degree 6 polynomial is negative, what is the end behavior as $$x 	o \infty$$?

Accepted Answer

$$y 	o -\infty$$

Question 15

Given the exponential regression model $$y = 22.2887 \cdot (1.0929)^x$$ for convention costs, what does the base $$1.0929$$ represent?

Accepted Answer

The annual growth factor of the cost

Question 16

Which of the following is the correct point-slope form for the line through $$(2,6)$$ with slope $$\frac{2}{3}$$?

Accepted Answer

$$y - 6 = \frac{2}{3}(x - 2)$$

Question 17

Which of the following is the correct standard form for the line through $$(2,6)$$ with slope $$\frac{2}{3}$$?

Accepted Answer

$$2x - 3y = -14$$

Question 18

Which of the following is the correct slope-intercept form for the line through $$(2,6)$$ with slope $$\frac{2}{3}$$?

Accepted Answer

$$y = \frac{2}{3}x + \frac{14}{3}$$

Business Calculus Test 1 Study Guidance (Spring 2024)

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