$$f(x) = x^2$ \, \text{on} \, \mathbb{R}$

Question 1

Which of the following best describes a function $$f$$ from set $$X to $$set $$Y$$?

Accepted Answer

For every $$x \in X$$, there exists exactly one $$y \in Y$$ such that $$f(x) = y.$$

Question 2

Given the function $$f(x) = (x-3)^2$ + 1$$, what is the range of $$f$$?

Accepted Answer

$$[1, \infty)$$

Question 3

Which of the following is NOT a one-to-one function?

Accepted Answer

$$f(x) = x^2$ \, 	ext{on} \, \mathbb{R}$

Question 4

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

Accepted Answer

$$[0, \infty)$$

Question 5

Suppose $$f(x) = \sin x$$ and $$g(x) = \sin(x^2$). $$Which of the following correctly expresses $$(f+g)(x)$$?

Accepted Answer

$$\sin(x) + \sin(x^2$)$$

Question 6

Given $$f(x) = x^2$ and g(x$$) = \frac{1}{x}$$, what is the domain of f$$ \cdot g$$?

Accepted Answer

$$\mathbb{R} \setminus \{0\}$$

Question 7

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

Accepted Answer

$$(x+1)^2$$

Question 8

For the quadratic function $$f(x) = ax^2$ + bx + c$$, what is the formula for the $$x-$$coordinate of the vertex?

Accepted Answer

$$x = \frac{-b}{2a}$$

Question 9

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

Accepted Answer

$$(0, \infty)$$

Question 10

Which of the following statements about the symmetry of $$f(x) = x^2$ is correct?

Accepted Answer

$$f(x) is $$even

Question 11

If $$f(x) = x^2$ and g(x) = x-2$, what is the domain of f/g$?

Accepted Answer

$$\mathbb{R} \setminus \{2\}$$

Question 12

A function $$f is $$called one-to-one if:

Accepted Answer

For any $$x_1$$, $$x_2$$ \in X$$, f$$($$x_1) = f$$($$x_2$$)$$ implies x_1$ = x_2$

Question 13

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

Accepted Answer

$$[0, \infty)$$

Question 14

If $$f(x) = \frac{3}{4x+2}$$, for which value of $$x is$$ $$f(x)$$ not defined?

Accepted Answer

$$x = -\frac{1}{2}$$

Question 15

Which of the following is the correct formula for the range of $$f(x) = \sqrt{x}$$?

Accepted Answer

$$[0, \infty)$$

Question 16

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

Accepted Answer

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

Question 17

Suppose $$f(x) = x^2$ and g(x$$) = \frac{1}{x-2}$$. What is the domain of f$$ \circ g$$?

Accepted Answer

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

Question 18

Which of the following is true about the graph of $$f(x) = (x-3)^2$ + 1$$?

Accepted Answer

It is a parabola opening upwards with vertex at $$(3, 1)$$

Question 19

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

Accepted Answer

$$(0, \infty)$$

Functions: Definitions, Representations, and Operations in Calculus

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