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

$$f(x_1$) = f(x_2$)$$ \text{ for all } $$x_1$$, $$x_2$$ \in [a, b]$

$$x = 0$$ \text{ is a relative minimum.}

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

Question 1

A function $$f(x) is $$defined as follows: $$f(x) = x^2$ - 4x + 3. On $$which interval is the function decreasing?

Accepted Answer

$$(-\infty, 2)$$

Question 2

Given the function $$f(x) = -x^3$ + 3x^2$ + 1$$, use the graph to determine the $$x-$$value where $$f$$ has a relative maximum.

Accepted Answer

$$x = 2$$

Question 3

Which of the following functions is even?

Accepted Answer

$$f(x) = x^4$ - 2x^2$ + 7$$

Question 4

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

Accepted Answer

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

Question 5

Which of the following equations is symmetric with respect to the $$y-$$axis?

Accepted Answer

$$y = x^2$ + 1$$

Question 6

Consider the piecewise function $$f(x) = \begin{cases} 2x + 1 & x \u003c 0 \ x^2$ & x \geq 0 \end{cases}. $$What is $$f(-3)$$?

Accepted Answer

$$-5$$

Question 7

Which of the following is the correct difference quotient for $$f(x) = x^2$?

Accepted Answer

$$\dfrac{(x+h)^2$ - x^2$}{h}$$

Question 8

A function $$f(x) is $$constant on the interval $$[a, b] if$$:

Accepted Answer

$$f(x_1$) = f(x_2$)$$ 	ext{ for all } $$x_1$$, $$x_2$$ \in [a, b]$

Question 9

Suppose a chemical reaction's rate is modeled by $$R(t) = -2t^2$ + 8t + 3. At $$what time $$t$$ does the reaction rate reach its maximum?

Accepted Answer

$$t = 2$$

Question 10

Which of the following statements is true about the function $$f(x) = x^3$?

Accepted Answer

$$f(x) is $$odd and symmetric with respect to the origin.

Question 11

A function $$f(x) is $$defined as $$f(x) = |x|. $$Which of the following is true?

Accepted Answer

$$f(x) is $$even and symmetric with respect to the $$y-$$axis.

Question 12

Given the function $$f(x) = x^2$ - 4$$, what is the simplified form of its difference quotient?

Accepted Answer

$$2x + h$$

Question 13

Which of the following real-world scenarios best models a piecewise function?

Accepted Answer

A taxi fare that charges a flat rate for the first mile and a different rate for each additional mile.

Question 14

If $$f(x) is $$decreasing on $$(-\infty, 0)$$ and increasing on $$(0, \infty)$$, what can you conclude about $$x = 0$$?

Accepted Answer

$$x = 0$$ 	ext{ is a relative minimum.}

Question 15

Which test would you use to determine if the graph of $$y = x^2$ - 3 is $$symmetric with respect to the $$y-$$axis?

Accepted Answer

Substitute $$-x$$ for $$x$$ and check if the equation is unchanged.

Question 16

A hospital monitors a patient's temperature $$T(t)$$ over time $$t. If$$ $$T(t) is $$constant on $$[2, 6]$$, what does this mean?

Accepted Answer

The patient's temperature did not change between $$t = 2$$ and $$t = 6.$$

Question 17

Which of the following is neither even nor odd?

Accepted Answer

$$f(x) = x^2$ + x$$

Question 18

If a function $$f(x) is $$symmetric with respect to the origin, which of the following must be true?

Accepted Answer

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

Question 19

Given the piecewise function $$g(x) = \begin{cases} 5 & x \u003c 2 \ 2x & x \geq 2 \end{cases}$$, what is $$g(2)$$?

Accepted Answer

$$4$$

Functions and Their Graphs: Key Concepts in Precalculus

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