Q: Which of the following describes an even function?

$$f(-x) = f(x)$$ \text{ for every } x \text{ in the domain of } f$

Q: Which of the following describes an odd function?

$$f(-x) = -f(x)$$ \text{ for every } x \text{ in the domain of } f$

Question 1

What is the domain of the function $$g(x) = \frac{2x}{x^2$ - 81}$$?

Accepted Answer

$$(-\infty, -9) \cup (-9, 9) \cup (9, \infty)$$

Question 2

If the point $$(4, -1) is on $$the graph of $$f$$, what is $$f(4)$$?

Accepted Answer

$$-1$$

Question 3

Given the function $$f(x) = \frac{5x}{|x|}$$, determine whether it is even, odd, or neither.

Accepted Answer

Odd

Question 4

Let $$f(x) = 4x - 5. $$What is the average rate of change of $$f$$ from $$x = 4 to$$ $$x = 6$$?

Accepted Answer

$$4$$

Question 5

Let $$f(x) = 4x - 5. $$What is the equation of the secant line containing $$(4, f(4))$$ and $$(6, f(6))$$?

Accepted Answer

$$y = 4x - 21$$

Question 6

Which of the following describes an even function?

Accepted Answer

$$f(-x) = f(x)$$ 	ext{ for every } x 	ext{ in the domain of } f$

Question 7

Which of the following describes an odd function?

Accepted Answer

$$f(-x) = -f(x)$$ 	ext{ for every } x 	ext{ in the domain of } f$

Question 8

Given the piecewise function $$f(x) = \begin{cases} -x + 3 & 	ext{if } x \u003c 2 \ 2x - 3 & 	ext{if } x \geq 2 \end{cases}$$, what is $$f(2)$$?

Accepted Answer

$$1$$

Question 9

Find the function that results after applying the following transformations to $$y = \sqrt{x} in $$order: (1) vertical stretch by a factor of 2, (2) shift down 1 unit, (3) shift left 3 units.

Accepted Answer

$$y = 2\sqrt{x+3} - 1$$

Question 10

A person rows a boat from an island 4 miles from the nearest point P on a straight shoreline to a town 11 miles down the shore from P. If the person rows at 2 miles per hour and walks at 3 miles per hour, what is the time $$T(x) to $$travel from the island to the town as a function of $$x$$, the distance from P where the boat lands?

Accepted Answer

$$T(x) = \frac{\sqrt{x^2$ + 16}}{2} + \frac{11 - x}{3}$$

Question 11

Using the function $$T(x) = \frac{\sqrt{x^2$ + 16}}{2} + \frac{11 - x}{3}$$, what is $$T(3)$$?

Accepted Answer

$$5.16$$ hours

Question 12

A wire 28 meters long is cut into two pieces. One piece forms a square, the other a circle. If $$x is $$the length used for the square, what is the domain for $$A(x) = x^2$ + \pi \left( \frac{28 - 4x}{2\pi} \$$right)^2$$?

Accepted Answer

$$(0, 7)$$

Question 13

For the function $$A(x) = x^2$ + \pi \left( \frac{14 - 2x}{\pi} \$$right)^2$$, what value of x$ minimizes A(x$$)$$?

Accepted Answer

$$x \approx 3.92$$

Question 14

Given the graph of a function with domain $$[-6, 6]$$ and range $$[-2, 6]$$, which of the following statements is true?

Accepted Answer

The function is symmetric with respect to the y-axis.

Question 15

If a function passes the vertical line test, what does this indicate?

Accepted Answer

The graph represents a function.

Question 16

Which of the following is the correct formula for the area of a circle in terms of its circumference $$C$$?

Accepted Answer

$$A = \frac{C^2$}{4\pi}$$

Question 17

If $$f(x) = x^2$, which transformation results in g(x) = (x$$ - $$3)^2 + 2$?

Accepted Answer

Shift right 3 units, then up 2 units

Precalculus Concepts: Domain, Symmetry, Transformations, and Applications

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