Question 1

Which of the following sets contains only non-negative real numbers?

Accepted Answer

$$(0, \infty)$$

Question 2

Given the function $$f(x) = \sqrt{x}$$, what is the domain of $$f$$?

Accepted Answer

$$[0, \infty)$$

Question 3

Which of the following intervals is a closed interval?

Accepted Answer

$$[a, b]$$

Question 4

A function $$f is $$defined by $$f(x) = \frac{2x^2$ - 4x + 3}{x - 2}. $$For which value of $$x is$$ $$f(x)$$ undefined?

Accepted Answer

$$x = 2$$

Question 5

Which of the following statements about the vertical line test is correct?

Accepted Answer

A curve passes the vertical line test if no vertical line crosses it more than once.

Question 6

Consider the function $$f(x) = |x|. $$Which of the following is true about $$f(x)$$?

Accepted Answer

It is a piecewise defined function

Question 7

If $$f(x) = x^2$ and g(x) = x + 1$, what is the domain of the composition (f$$ \circ g)(x)$$?

Accepted Answer

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

Question 8

Which of the following is the correct range of the function $$f(x) = x^2$ for x$$ \in [-1, 1]$$?

Accepted Answer

$$[0, 1]$$

Question 9

Given $$f(x) = \sqrt{x - 1}$$, what is the range of $$f$$?

Accepted Answer

$$[0, \infty)$$

Question 10

Suppose $$f(x) = x^2$ + 2x - 3. $$What is the minimum value of $$f(x)$$ and at which $$x$$ does it occur?

Accepted Answer

Minimum is $$-4 at$$ $$x = -1$$

Question 11

If $$f(x) = \sqrt{x}$$ and $$g(x) = x^2$ + 3$$, what is the domain of the composition $$(f \circ g)(x)$$?

Accepted Answer

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

Question 12

Which of the following is NOT a function?

Accepted Answer

The mapping defined by the circle $$x^2$$ + $$y^2 = 9$

Question 13

Given $$f(x) = \frac{1}{x}$$, what is the domain of $$f$$?

Accepted Answer

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

Question 14

If $$f(x) = \sqrt{x - 2}$$ and $$g(x) = \sqrt{x - 3}$$, what is the domain of $$f(x)g(x)$$?

Accepted Answer

$$[3, \infty)$$

Question 15

Which of the following best describes the range of $$f(x) = \frac{x}{x+1}$$?

Accepted Answer

Question 16

If $$f(x) = \sin x$$ and $$g(x) = x - 1$$, what is the domain of the product $$f(x)g(x)$$ for $$x \in (2, 5)$$?

Accepted Answer

$$(2, 5)$$

Question 17

Which of the following is the correct definition of the absolute value function $$|x|$$?

Accepted Answer

$$|x| = x$$ for $$x \geq 0$$, $$|x| = -x$$ for $$x \u003c 0$$

Question 18

If $$f(x) = x^2$ and g(x$$) = \sqrt{x}$$, what is the domain of the composition (g$$ \circ f)(x)$$?

Accepted Answer

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

Question 19

Which of the following is the correct range of the function $$f(x) = 2 + \sqrt{x - 1}$$?

Accepted Answer

$$[2, \infty)$$

Mathematical Functions and Notation for Scientists: Foundations and Applications

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