Q: Given the graph of a function $$f(x)$$ with domain $$[-4, 5)$$ and range $$[-1, 2)$$, which of the following is the correct interval notation for the domain and range?

$$\text{Domain}: [-4, 5),\ \text{Range}: [-1, 2)$$

Q: Which of the following is the correct definition of the sine function in a right triangle?

$$\sin \theta = \frac{\text{opposite}}{\text{hypotenuse}}$$

Question 1

Given the graph of a function $$f(x)$$ with domain $$[-4, 5)$$ and range $$[-1, 2)$$, which of the following is the correct interval notation for the domain and range?

Accepted Answer

$$	ext{Domain}: [-4, 5),\ 	ext{Range}: [-1, 2)$$

Question 2

Which of the following best describes the range of the function $$f(x)$$ shown in the leftmost graph in the first image?

Accepted Answer

$$[-1, 2)$$

Question 3

For the function $$f(x)$$ shown in the rightmost graph in the first image, what is the domain?

Accepted Answer

$$\mathbb{R}$$

Question 4

Which of the following is the correct set builder notation for the range $$[-1, 2)$$?

Accepted Answer

$$\{y\ |\ -1 \leq y \u003c 2\}$$

Question 5

If a function $$f(x) is $$defined for all real numbers except $$x = 2$$, which of the following is the domain in interval notation?

Accepted Answer

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

Question 6

Which transformation is represented by $$f(x) 	o f(x-3) + 2$$?

Accepted Answer

Shift right by 3 units and up by 2 units

Question 7

Given the transformation $$g(x) = -2f(x)$$, what happens to the graph of $$f(x)$$?

Accepted Answer

It is reflected over the $$x-$$axis and stretched vertically by a factor of 2

Question 8

Which of the following is the correct definition of the sine function in a right triangle?

Accepted Answer

$$\sin 	heta = \frac{	ext{opposite}}{	ext{hypotenuse}}$$

Question 9

On the unit circle, what are the coordinates corresponding to $$	heta = 0$$?

Accepted Answer

$$(1, 0)$$

Question 10

Which quadrant(s) have both sine and cosine values negative?

Accepted Answer

Quadrant III

Question 11

If $$f(x) = |x|$$, what is the effect of the transformation $$f(x) 	o -4|x|$$?

Accepted Answer

Reflection over the $$x-$$axis and vertical stretch by 4

Question 12

Which of the following is the correct reciprocal identity for $$\sec x$$?

Accepted Answer

$$\sec x = \frac{1}{\cos x}$$

Question 13

What is the period of the tangent function $$y = 	an(x)$$?

Accepted Answer

$$\pi$$

Question 14

Which transformation will shift the graph of $$f(x)$$ down by 3 units?

Accepted Answer

$$f(x) - 3$$

Question 15

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

Accepted Answer

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

Foundations of Functions: Domain, Range, and Transformations

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