Question 1

Which of the following is the domain of the function $$f(x) = \dfrac{1}{x-3}$$?

Accepted Answer

$$(-\infty, 3) \cup (3, \infty)$$

Question 2

Given the function $$g(x) = \sqrt{5 - 2x}$$, what is the domain of $$g(x)$$?

Accepted Answer

$$(-\infty, 2.5]$$

Question 3

A company’s cost function is $$C(x) = 200 + 5x$$ and its revenue function is $$R(x) = 15x. $$What is the break-even point?

Accepted Answer

$$x = 20$$

Question 4

Which of the following is the equation of a line with slope $$m = -2$$ passing through the point $$(1, 4)$$?

Accepted Answer

$$y - 4 = -2(x - 1)$$

Question 5

Factor the expression $$x^2 - 9$.

Accepted Answer

$$(x - 3)(x + 3)$$

Question 6

Convert $$\sqrt[3]{x^5$} to $$rational exponent form.

Accepted Answer

$$x^{5/3}$$

Question 7

Evaluate $$\displaystyle \lim_{x 	o 2} (3x^2$ - 4x + 1).$$

Accepted Answer

$$5$$

Question 8

Which of the following statements about continuity is TRUE?

Accepted Answer

A function $$f(x) is $$continuous at $$x = a if$$ $$\displaystyle \lim_{x 	o a} f(x) = f(a).$$

Question 9

Given the graph of $$f(x)$$ with a jump at $$x = 1$$, which of the following is TRUE?

Accepted Answer

$$f(x) is $$not continuous at $$x = 1$$

Question 10

Find the average rate of change of $$f(x) = x^2$ from x = 1$ to x = 4$.

Accepted Answer

$$5$$

Question 11

Simplify the difference quotient $$\dfrac{f(x+h) - f(x)}{h}$$ for $$f(x) = 3x + 2.$$

Accepted Answer

$$3$$

Question 12

Which of the following functions is NOT differentiable at $$x = 0$$?

Accepted Answer

$$f(x) = |x|$$

Question 13

Find the derivative of $$f(x) = x^2$ at x = 3$ using the limit definition.

Accepted Answer

$$6$$

Question 14

If $$f(x) = \dfrac{2x+1}{x-1}$$, what is $$\displaystyle \lim_{x 	o 1} f(x)$$?

Accepted Answer

Does not exist (infinite limit)

Question 15

A medication’s concentration in the bloodstream is modeled by $$C(t) = 10 - 2t$$ for $$t \geq 0. $$What is the average rate of change in concentration from $$t = 1 to$$ $$t = 4$$?

Accepted Answer

$$-2$$

Question 16

Which of the following is the correct factorization of $$x^2 + 5x + 6$?

Accepted Answer

$$(x + 2)(x + 3)$$

Question 17

Which of the following is the correct equation for a horizontal line passing through $$(2, -5)$$?

Accepted Answer

$$y = -5$$

Question 18

Evaluate $$\displaystyle \lim_{x 	o 0} \dfrac{x^2$}{x}.$$

Accepted Answer

$$0$$

Question 19

If $$f(x) = \sqrt{x-2}$$, what is the domain of $$f(x)$$?

Accepted Answer

$$[2, \infty)$$

Question 20

Which of the following is the correct rational exponent form for $$\sqrt[4]{x^3$}$$?

Accepted Answer

$$x^{3/4}$$

Calculus Exam 1 Study Guide: Functions, Limits, and the Derivative

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