Question 1

Which of the following is the domain of the function $$f(x) = \frac{2x+1}{x^2$-x-2}$$?

Accepted Answer

$$(-\infty, -1) \cup (-1, 2) \cup (2, \infty)$$

Question 2

Given the piecewise function $$f(x) = \begin{cases} x, & x \u003c 0 \ 2, & 0 \leq x \u003c 1 \ 1, & x \geq 1 \end{cases}$$, which of the following statements is true?

Accepted Answer

The function is discontinuous at $$x = 0$$ and $$x = 1.$$

Question 3

Which of the following functions is odd?

Accepted Answer

$$f(x) = x^3$ + x$$

Question 4

For the function $$f(x) = |x-2| - 1$$, which transformation has been applied to the parent function $$y = |x|$$?

Accepted Answer

Shift right by 2 units and down by 1 unit.

Question 5

Which of the following is the correct composite function for $$f(x) = \sqrt{x}$$ and $$g(x) = x^2$ + 1$$?

Accepted Answer

$$f(g(x)) = \sqrt{x^2$ + 1}$$

Question 6

Which of the following is the period of the function $$f(x) = 	an x$$?

Accepted Answer

$$\pi$$

Question 7

If $$\cos x = \frac{5}{13}$$ and $$x is in $$the fourth quadrant, what is $$\sin x$$?

Accepted Answer

$$-\frac{12}{13}$$

Question 8

Which of the following is a property of logarithms?

Accepted Answer

$$\ln(ab) = \ln a + \ln b$$

Question 9

Evaluate $$\lim_{x 	o 0} \frac{\sin x}{x}.$$

Accepted Answer

$$1$$

Question 10

Which of the following is the horizontal asymptote of $$f(x) = \frac{x^2$ - 1}{x^2$ + 1}$$?

Accepted Answer

$$y = 1$$

Question 11

Given $$f(x) = 3x + 4$$, $$g(x) = 2x - 1$$, express $$f(g(x)).$$

Accepted Answer

$$6x + 1$$

Question 12

Which of the following is true about the function $$f(x) = x^2$?

Accepted Answer

It is an even function.

Question 13

If $$f(x) = e^x + 2$$, what is the domain of $$f(x)$$?

Accepted Answer

$$(-\infty, \infty)$$

Question 14

Which of the following is the correct simplification for $$\ln(8x+4) - 2\ln2$$?

Accepted Answer

$$\ln(2x+1)$$

Question 15

For the function $$f(x) = \frac{1}{1-e^x}$$, what is its domain?

Accepted Answer

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

Question 16

Which of the following is the correct inverse of $$f(x) = \frac{1}{2}x + 1$$?

Accepted Answer

$$f^{-1}(x) = 2x - 2$

Question 17

Which of the following is the correct application of the Intermediate Value Theorem?

Accepted Answer

If $$f is $$continuous on $$[a, b]$$ and $$f(a)  0$$, then there exists $$c \in (a, b)$$ such that $$f(c) = 0.$$

Question 18

Evaluate $$\lim_{x 	o \infty} \frac{2x^2$ + 5x + 1}{x^2$ + 3}.$$

Accepted Answer

$$2$$

Question 19

Which of the following is the correct result for $$\lim_{x 	o 0} \frac{1 - \cos x}{\sin 2x}$$?

Accepted Answer

$$0$$

Calculus Chapter 1: Functions, Limits, and Continuity – Study Notes

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