Q: The function $$f(x) = |x|$$ can be written as a piecewise function. Which of the following is correct?

$$f(x) = \\begin{cases} x & x \\geq 0 \\ \\ -x & x \u003c 0 \\end{cases}$$

Q: Which of the following is the correct domain for the function $$h(x) = \\frac{1}{x-1}$$?

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

Question 1

Which of the following represents the interval notation for all real numbers $$x$$ such that $$2 \u003c x \leq 7$$?

Accepted Answer

$$(2, 7]$$

Question 2

Given the function $$f(x) = \sqrt{1 - x^2$}$$, what is the domain of $$f(x) in $$interval notation?

Accepted Answer

$$[-1, 1]$$

Question 3

A box is to be constructed from a $$6 \times 8$$ piece of cardboard by cutting out squares of side $$x$$ from each corner and folding up the sides. Which of the following expressions gives the volume $$V(x) of $$the box as a function of $$x$$?

Accepted Answer

$$V(x) = x(6 - 2x)(8 - 2x)$$

Question 4

For the box construction problem, what is the appropriate domain for $$x$$ based on physical constraints?

Accepted Answer

$$[0, 3]$$

Question 5

Which of the following is the correct interval notation for the set $$\{x \mid x \geq 5\}$$?

Accepted Answer

$$[5, \infty)$$

Question 6

The function $$f(x) = |x|$$ can be written as a piecewise function. Which of the following is correct?

Accepted Answer

$$f(x) = \begin{cases} x & x \geq 0 \ \ -x & x \u003c 0 \end{cases}$$

Question 7

Which of the following is the vertex of the quadratic function $$f(x) = 2x^2$ - 4x + 1$$?

Accepted Answer

$$(1, -1)$$

Question 8

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

Accepted Answer

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

Question 9

Which of the following is the correct domain for the function $$g(x) = \frac{1}{\sqrt{x}}$$?

Accepted Answer

$$(0, \infty)$$

Question 10

A piecewise function is defined as $$f(x) = \begin{cases} 2x + 2 & x \u003c 1 \ \ -3x + 5 & x \geq 1 \end{cases}. $$What is the value of $$f(1)$$?

Accepted Answer

$$2$$

Question 11

Which of the following is the correct interval notation for the set $$\{x \mid x \u003c 0 \}$$?

Accepted Answer

$$(-\infty, 0)$$

Question 12

If $$f(x) = x^2$ + 4x + 5$$, what is the minimum value of $$f(x)$$?

Accepted Answer

$$1$$

Question 13

Which of the following is the correct domain for the function $$h(x) = \frac{1}{x-1}$$?

Accepted Answer

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

Question 14

A polynomial of degree $$n \u003e 2$$ can have which of the following features that a quadratic cannot?

Accepted Answer

Multiple peaks and valleys (local maxima and minima)

Question 15

Which of the following statements about the roots of the quadratic $$f(x) = ax^2$ + bx + c is $$true?

Accepted Answer

There are two distinct real roots if $$b^2 - 4ac$$ \u003e 0$$

Question 16

Suppose a function $$f(x) is $$defined as $$f(x) = \begin{cases} 3x - 1 & x \u003c 2 \ \ x^2$ & x \geq 2 \end{cases}. $$What is the value of $$f(2)$$?

Accepted Answer

$$4$$

Question 17

Which of the following is the correct interval notation for the set of all real numbers?

Accepted Answer

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

Functions, Domains, and Graphs: Foundations for Business Calculus

Guida di studio - Domande di pratica

Study guide - Flashcard