Question 1

Given the function $$g(z) = -2 - \sqrt{z}$$, what is the domain and range of $$g(z)$$?

Accepted Answer

$$D: [0, \infty),\ R: (-\infty, -2]$$

Question 2

For the function $$F(t) = \sqrt{t}$$, which of the following best describes its domain and range?

Accepted Answer

$$D: [0, \infty),\ R: [0, \infty)$$

Question 3

What is the range of the function $$f(x) = -7 - x^2$?

Accepted Answer

$$(-\infty, -7]$$

Question 4

Given $$g(z) = \frac{-7}{z+1}$$, what is the domain of $$g(z)$$?

Accepted Answer

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

Question 5

For the function $$f(x) = \frac{3}{3 + x}$$, which of the following is the correct range?

Accepted Answer

$$(-\infty, 1)$$

Question 6

What is the domain of the function $$g(z) = \sqrt{9 - z^2$}$$?

Accepted Answer

$$[-3, 3]$$

Question 7

Which of the following graphs represents a function of $$x$$?

Accepted Answer

A graph of a straight line passing through the origin (Image 1)

Question 8

Which of the following graphs is NOT a function of $$x$$?

Accepted Answer

A graph of a circle (Image 4)

Question 9

Given the function $$G(t) = \frac{1}{t-3}$$, what is its domain?

Accepted Answer

$$(-\infty, 3) \cup (3, \infty)$$

Question 10

Consider the function $$y = 1 - \frac{1}{x}. $$Can $$x be$$ $$0$$?

Accepted Answer

No

Question 11

What is the domain of the function $$y = 1 - \frac{1}{x}$$?

Accepted Answer

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

Question 12

A chemical reaction rate is modeled by $$R(t) = \frac{t-3}{t-3}. $$What is the domain of $$R(t)$$?

Accepted Answer

$$(-\infty, 3) \cup (3, \infty)$$

Question 13

Which of the following best describes the range of $$f(x) = -5x - 7$$?

Accepted Answer

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

Question 14

A medical dosage is modeled by $$D(t) = \sqrt{t-3}. $$What is the domain of $$D(t)$$?

Accepted Answer

$$[3, \infty)$$

Question 15

Which of the following is the correct range for $$g(z) = \sqrt{9 - z^2$}$$?

Accepted Answer

$$[0, 3]$$

Question 16

A function $$f(x) is $$defined as $$f(x) = -5 - x$$ for $$x \u003c 1$$ and $$f(x) = 3$$ for $$x \geq 1. $$Which of the following describes its graph?

Accepted Answer

A line with negative slope for $$x \u003c 1$$ and a constant value for $$x \geq 1$$

Question 17

Which of the following is the domain of $$f(x) = \frac{1}{x+2}$$ for $$x \u003c -2$$ and $$f(x) = x$$ for $$x \geq -2$$?

Accepted Answer

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

Question 18

A real-world scenario: The height $$h (in $$meters) of a projectile is given by $$h(t) = -4.9t^2$ + 20t + 1.5. $$What is the domain of $$t$$ for which $$h(t) \geq 0$$?

Accepted Answer

$$[0, t_1$]$$ where $$t_1 is $$the positive root of $$h(t) = 0$$

Question 19

Suppose a function $$f(x) is $$defined for all real numbers except $$x = 2. $$Which of the following is the domain of $$f(x)$$?

Accepted Answer

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

Guidance on Identifying Functions from Graphs

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