Q: Find the domain of the function $$f(x) = \sqrt{2 - x} + \frac{x}{x^3$ - 4x}.$$

$$x \u003c 2$$ and $$x \neq 0, x \neq -2$$

Q: If a sprinkler rotates $$120^\circ$$ and waters $$48\pi$$ square feet, what is the perimeter of the region watered if set to $$80^\circ$$?

$$P = 2r + r\theta$$ where $$\theta in $$radians

Q: If $$\cot \theta = -3$$ and $$\cos \theta is $$positive, what is $$\csc \theta$$?

$$\csc \theta = \frac{\sqrt{10}}{1}$$

Question 1

Find the domain of the function $$f(x) = \sqrt{2 - x} + \frac{x}{x^3$ - 4x}.$$

Accepted Answer

$$x \u003c 2$$ and $$x 
eq 0, x 
eq -2$$

Question 2

Given the graph in $$image_1$$, what is the range of the function?

Accepted Answer

$$[-4, 2)$$

Question 3

For the graph in $$image_2$$, what are the local minimum points?

Accepted Answer

$$(0, -4)$$ and $$(\pm 2, -4)$$

Question 4

Which equation best matches the graph in $$image_3$$?

Accepted Answer

$$y = |x| - 2$$

Question 5

Which transformation is represented by $$y = f(-3x) - 1$$?

Accepted Answer

Horizontal compression by $$\frac{1}{3}$$, reflection over y-axis, down 1

Question 6

Determine if $$f(x) = |x| + \sin^2$(x) + 1 is $$even, odd, or neither.

Accepted Answer

Even

Question 7

For the piecewise function $$f(x) = \begin{cases} -x - 1 & x \u003c -1 \ -3 & -1 \leq x \u003c 2 \ \sqrt{x - 2} & x \geq 2 \end{cases}$$, what is $$f(3)$$?

Accepted Answer

$$1$$

Question 8

Find the inverse $$f^{-1}(x$$)$$ for f(x$$) = \frac{3 - 2x}{1 + x}$$.

Accepted Answer

$$f^{-1}(x$$) = \frac{3 - x}{x + 2}$$

Question 9

Convert $$9^\circ to $$radians.

Accepted Answer

$$\frac{9\pi}{180}$$

Question 10

A bicycle travels at 5 m/s with wheels of diameter 0.6 m. What is the angular speed of the wheels?

Accepted Answer

$$\omega = \frac{5}{0.3}$$ rad/s

Question 11

If a sprinkler rotates $$120^\circ$$ and waters $$48\pi$$ square feet, what is the perimeter of the region watered if set to $$80^\circ$$?

Accepted Answer

$$P = 2r + r	heta$$ where $$	heta in $$radians

Question 12

A plane is flying at 25,000 feet and sees the Gateway Arch at an angle of depression of $$24^\circ. $$What is the horizontal distance to the base of the arch?

Accepted Answer

$$d = 25,000 \cdot \cot(24^\circ)$$

Question 13

If $$\cot 	heta = -3$$ and $$\cos 	heta is $$positive, what is $$\csc 	heta$$?

Accepted Answer

$$\csc 	heta = \frac{\sqrt{10}}{1}$$

Question 14

Given the point $$\left(\frac{5}{6}, \frac{\sqrt{11}}{6}\right) on $$the unit circle, what are the coordinates for the angle $$-t$$?

Accepted Answer

$$\left(\frac{5}{6}, -\frac{\sqrt{11}}{6}\right)$$

Question 15

What are the coordinates of the point on a circle of radius 6 at an angle of $$200^\circ$$?

Accepted Answer

$$(6 \cos(200^\circ), 6 \sin(200^\circ))$$

Question 16

For $$f(x) = x^2$ + 4$$ with $$x \leq 0$$, what is the domain of $$f^{-1}(x$$)$$?

Accepted Answer

$$x \geq 4$$

Question 17

Convert $$52^\circ 12' 45'' to $$decimal degrees.

Accepted Answer

$$52.2125^\circ$$

Question 18

For $$h(x) = x^2$ 	an(x)$$, is the function even, odd, or neither?

Accepted Answer

Odd

Analyzing the Domain, Range, and Behavior of a Piecewise Function from Its Graph

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