Q: Which of the following best describes when a function $$f(x) is $$increasing on an interval?

$$f(x_1$) \u003c f(x_2$)$$ whenever $$x_1$$ \u003c $$x_2$$ \text{ for any } $$x_1$$, $$x_2$$ \text{ on the interval}$

Q: A function $$f(x) is $$said to be constant on an interval if:

$$f(x_1$) = f(x_2$)$$ \text{ for any } $$x_1$$, $$x_2$$ \text{ on the interval}$

Q: Which of the following is the correct definition of a relative maximum of a function $$f at$$ $$x = a$$?

$$f(a) \u003e f(x)$$ \text{ for all } x \neq a \text{ in some open interval containing } a$

Q: Suppose a function $$f(x) is $$decreasing on an interval. Which of the following must be true?

$$f(x_1$) \u003e f(x_2$)$$ \text{ whenever } $$x_1$$ \u003c $$x_2$$ \text{ for any } $$x_1$$, $$x_2$$ \text{ on the interval}$

Q: A function $$f(x) is $$said to be even if:

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

Q: Given the function $$f(x) = 2x - 5$$, which of the following statements is true?

$$f(x)$$ \text{ is increasing on its entire domain}$

Q: Which of the following describes the symmetry of the function $$y = x^4$?

$$y = x^4$ \text{ is symmetric with respect to the } y\text{-axis}$

Q: If $$f(x) is an $$even function, which of the following must also be true?

$$f(-x) = f(x)$$ \text{ for all } x$

Q: Which of the following is the correct test for symmetry with respect to the origin for a function $$f(x)$$?

$$f(-x) = -f(x)$$ \text{ for all } x$

Q: A function $$f(x)$$ has a relative minimum at $$x = 2 if$$:

$$f(2) \u003c f(x)$$ \text{ for all } x \neq 2 \text{ in some open interval containing } 2$

Question 1

Which of the following best describes when a function $$f(x) is $$increasing on an interval?

Accepted Answer

$$f(x_1$) \u003c f(x_2$)$$ whenever $$x_1$$ \u003c $$x_2$$ 	ext{ for any } $$x_1$$, $$x_2$$ 	ext{ on the interval}$

Question 2

A function $$f(x) is $$said to be constant on an interval if:

Accepted Answer

$$f(x_1$) = f(x_2$)$$ 	ext{ for any } $$x_1$$, $$x_2$$ 	ext{ on the interval}$

Question 3

Which of the following is the correct definition of a relative maximum of a function $$f at$$ $$x = a$$?

Accepted Answer

$$f(a) \u003e f(x)$$ 	ext{ for all } x 
eq a 	ext{ in some open interval containing } a$

Question 4

Suppose a function $$f(x) is $$decreasing on an interval. Which of the following must be true?

Accepted Answer

$$f(x_1$) \u003e f(x_2$)$$ 	ext{ whenever } $$x_1$$ \u003c $$x_2$$ 	ext{ for any } $$x_1$$, $$x_2$$ 	ext{ on the interval}$

Question 5

Which of the following equations represents a function that is symmetric with respect to the $$y-$$axis?

Accepted Answer

$$y = x^2$

Question 6

A function $$f(x) is $$said to be even if:

Accepted Answer

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

Question 7

Which of the following is an example of an odd function?

Accepted Answer

$$f(x) = x^3$

Question 8

Given the function $$f(x) = 2x - 5$$, which of the following statements is true?

Accepted Answer

$$f(x)$$ 	ext{ is increasing on its entire domain}$

Question 9

Which of the following describes the symmetry of the function $$y = x^4$?

Accepted Answer

$$y = x^4$ 	ext{ is symmetric with respect to the } y	ext{-axis}$

Question 10

A real-world scenario: The height $$h (in $$meters) of a ball thrown upward from a bridge is given by $$h(t) = -4.9t^2$ + 20t + 15. $$For what value of $$t$$ does the ball reach its maximum height?

Accepted Answer

$$t = 2.04$$

Question 11

Which of the following functions is neither even nor odd?

Accepted Answer

$$f(x) = x + 1$$

Question 12

If $$f(x) is an $$even function, which of the following must also be true?

Accepted Answer

$$f(-x) = f(x)$$ 	ext{ for all } x$

Question 13

Which of the following is the correct test for symmetry with respect to the origin for a function $$f(x)$$?

Accepted Answer

$$f(-x) = -f(x)$$ 	ext{ for all } x$

Question 14

Suppose $$f(x) is $$constant on the interval $$[2, 5]$$ and $$f(3) = 7. $$What is $$f(4)$$?

Accepted Answer

$$7$$

Question 15

Which of the following functions is decreasing on its entire domain?

Accepted Answer

$$f(x) = -3x + 2$$

Question 16

A function $$f(x)$$ has a relative minimum at $$x = 2 if$$:

Accepted Answer

$$f(2) \u003c f(x)$$ 	ext{ for all } x 
eq 2 	ext{ in some open interval containing } 2$

Question 17

Which of the following is true about the function $$y = |x|$$?

Accepted Answer

$$y = |x|$$ 	ext{ is even}$

Question 18

A real-world application: The temperature $$T (in$$ $$^\circC) in a $$laboratory is modeled by $$T(t) = -2t^2$ + 8t + 20$$, where $$t is $$the number of hours after midnight. What is the maximum temperature reached, and at what time does it occur?

Accepted Answer

$$T = 28 at$$ $$t = 2$$ hours

Question 19

Which of the following statements is true about the function $$y = 2x$$?

Accepted Answer

$$y = 2x$$ 	ext{ is odd}$

Precalculus Study Notes: Functions, Continuity, and Symmetry

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