Q: Which of the following is the correct piecewise definition of the absolute value function $$f(x) = |x|$$?

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

Question 1

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

Accepted Answer

$$[0, \infty)$$

Question 2

Given the function $$f(x) = x^2$ with a restricted domain x$$ \u003e 0$$, which of the following describes its range?

Accepted Answer

$$[0, \infty)$$

Question 3

Which of the following graphs represents the constant function $$f(x) = b$$?

Accepted Answer

A horizontal line crossing the y-axis at $$y = b$$

Question 4

The greatest integer function $$f(x) = \lfloor x \rfloor$$ assigns to each real number:

Accepted Answer

The largest integer less than or equal to $$x$$

Question 5

Which of the following is the correct piecewise definition of the absolute value function $$f(x) = |x|$$?

Accepted Answer

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

Question 6

For the function $$f(x) = x^3$, which of the following statements is true about its domain and range?

Accepted Answer

Domain: $$(-\infty, \infty)$$, Range: $$(-\infty, \infty)$$

Question 7

A piecewise-defined function is best described as:

Accepted Answer

A function defined by different expressions over different intervals of its domain

Question 8

Given the function $$f(x) = \sqrt{x}$$ with a restricted domain $$x \geq 1$$, what is the range of $$f$$?

Accepted Answer

$$[1, \infty)$$

Question 9

If $$f(x) = x^2$ for x$$ \leq 1$$ and f(x) = 1 - x$ for x$$ \u003e 1$$, what is f(2$$)$$?

Accepted Answer

$$-1$$

Question 10

Which of the following is the correct interval notation for the domain of the function $$f(x) = |x|$$ for $$-2 \u003c x \leq 1$$?

Accepted Answer

$$(-2, 1]$$

Question 11

Suppose you are sketching the graph of $$f(x) = x^2$ for x$$ \u003e 0$$. Which of the following statements is true?

Accepted Answer

The graph is a parabola opening upwards, starting at the origin and extending to the right

Question 12

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

Accepted Answer

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

Question 13

Which of the following is the correct range for the function $$f(x) = \frac{1}{x}$$?

Accepted Answer

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

Question 14

A medical researcher models the concentration of a drug in the bloodstream over time using $$f(t) = \frac{1}{t}$$, where $$t is $$time in hours after administration. What is the domain of this function in the context of the problem?

Accepted Answer

$$t \u003e 0$$

Question 15

Which of the following is true about the graph of the cube root function $$f(x) = \sqrt[3]{x}$$?

Accepted Answer

It is defined for all real numbers and passes through the origin

Question 16

A piecewise function is defined as $$f(x) = \begin{cases} 3x-6 & -2  1 \end{cases}. $$What is $$f(0)$$?

Accepted Answer

$$2$$

Question 17

Which of the following best describes the graph of $$f(x) = |x|$$?

Accepted Answer

A V-shaped graph with its vertex at the origin

Question 18

If $$f(x) = x^2$ for x$$ \u003c 1$$ and f(x) = 1 - x$ for x$$ \geq 1$$, what is the value of f(1$$)$$?

Accepted Answer

$$0$$

Question 19

Which of the following is the correct interval notation for the range of the function $$f(x) = \frac{1}{x}$$?

Accepted Answer

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

Graphing and Analyzing Basic Functions and Restricted Domains in College Algebra

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