Question 1

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

Accepted Answer

$$x \geq 2$$

Question 2

Given the function $$f(x) = x^2$, which transformation results in the graph of f(x-3) + 2$?

Accepted Answer

Shift right by 3 units and up by 2 units

Question 3

Which of the following is the inverse function of $$f(x) = 2x + 5$$?

Accepted Answer

$$f^{-1}(x$$) = \frac{x-5}{2}$$

Question 4

If $$f(x) = x^3$ and g(x$$) = \sqrt{x}$$, what is (f$$ \circ g)(x)$$?

Accepted Answer

$$(f \circ g)(x) = (\sqrt{x})^3$

Question 5

Which of the following describes the range of the exponential function $$f(x) = e^x$$?

Accepted Answer

$$(0, \infty)$$

Question 6

A population of bacteria doubles every hour. If the initial population is $$P_0$$, which function models the population after $$t$$ hours?

Accepted Answer

$$P(t) = P_0$ \cdot 2^t$$

Question 7

Which of the following is the correct summation notation for the sum $$1 + 2 + 3 + \ldots + n$$?

Accepted Answer

$$\sum\limits_{k=1}^{n} k$$

Question 8

Given $$f(x) = x^2$ and g(x) = x + 1$, what is the difference function h(x) = f(x) - g(x$$)$$?

Accepted Answer

$$h(x) = x^2$ - x - 1$$

Question 9

Which of the following is the correct formula for the sum of the first $$n$$ terms of an arithmetic sequence with first term $$a_1$$ and common difference $$d$$?

Accepted Answer

$$S_n = \frac{n}{2} [2a_1 + (n-1)d]$$

Question 10

Which property of functions states that $$f(-x)$$ reflects the graph of $$f(x)$$ over the $$y-$$axis?

Accepted Answer

Even/Odd symmetry

Question 11

If $$f(x) = \frac{1}{x}$$, which of the following describes its graph?

Accepted Answer

It has a vertical asymptote at $$x=0$$ and a horizontal asymptote at $$y=0$$

Question 12

Which of the following is the correct formula for the sum of the first $$n$$ terms of a geometric sequence with first term $$a_1$$ and common ratio $$r 
eq 1$$?

Accepted Answer

$$S_n = a_1$ \frac{1 - r^n}{1 - r}$$

Question 13

Which function is always increasing for all real $$x$$?

Accepted Answer

$$f(x) = e^x$$

Question 14

If $$f(x) = x^2$ is an even function, which of the following is true?

Accepted Answer

$$f(-x) = f(x)$$

Question 15

Which of the following is the correct expression for the logarithmic function with base $$a$$?

Accepted Answer

$$f(x) = \log_a(x)$$

Question 16

A radioactive substance decays according to $$N(t) = N_0$ e$$^{-kt}$$. What does k$ represent?

Accepted Answer

Decay constant

Question 17

Which of the following is the correct formula for the $$nth $$term of an arithmetic sequence?

Accepted Answer

$$a_n = a_1$ + (n-1)d$$

Question 18

If $$f(x) = x^3$ and g(x) = 2x$, what is the composition (g$$ \circ f)(x)$$?

Accepted Answer

$$(g \circ f)(x) = 2x^3$

Question 19

Which of the following is true about the function $$f(x) = \ln(x)$$?

Accepted Answer

Its domain is $$(0, \infty)$$

Foundations of Functions and Sequences in Calculus I

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