Question 1

Which of the following equations represents the graph of a semicircle of radius 2 centered at the origin in the $$xy-$$plane?

Accepted Answer

$$y = \sqrt{4 - x^2$}$$

Question 2

A function $$f(x) is $$defined as $$f(x) = \sqrt{x}. $$Which of the following best describes its domain?

Accepted Answer

$$x \geq 0$$

Question 3

Which of the following graphs represents the function $$f(x) = |x|$$?

Accepted Answer

A 'V' shaped graph opening upwards with vertex at the origin

Question 4

Given the piecewise function $$f(x) = \begin{cases} 1, & x \geq 0 \ -1, & x \u003c 0 \end{cases}$$, what is the range of $$f(x)$$?

Accepted Answer

$$\{-1, 1\}$$

Question 5

Which of the following equations represents a parabola that opens downward?

Accepted Answer

$$y = -x^2$

Question 6

A real-world scenario: The height $$h (in $$meters) of a ball thrown upward from the ground is given by $$h(t) = -4.9t^2$ + 20t$$, where $$t is $$time in seconds. What is the maximum height reached by the ball?

Accepted Answer

$$20.41$$ meters

Question 7

Which of the following is the graph of the function $$f(x) = x^3$ - 3x$$?

Accepted Answer

A cubic curve with two turning points, passing through the origin

Question 8

Given the function $$f(x) = \sqrt{9 - x^2$}$$, what is the range of $$f(x)$$?

Accepted Answer

$$[0, 3]$$

Question 9

Which of the following best describes the graph of $$f(x) = \lfloor x \rfloor ($$the greatest integer function)?

Accepted Answer

A step function with jumps at every integer value of $$x$$

Question 10

If $$f(x) = x^2$ and g(x) = x + 1$, what is (f$$ \circ g)(2)$$?

Accepted Answer

$$9$$

Question 11

Which of the following is the equation of a line passing through the points $$(1,2)$$ and $$(3,6)$$?

Accepted Answer

$$y = 2x$$

Question 12

A function $$f is $$even if $$f(-x) = f(x)$$ for all $$x in $$its domain. Which of the following functions is even?

Accepted Answer

$$f(x) = x^2$

Question 13

Which of the following best describes the transformation of the graph of $$y = x^2$ to y$$ = $$(x-3)^2 + 2$?

Accepted Answer

Shift right by 3 units and up by 2 units

Question 14

Which of the following is the solution set for $$|x - 2| = 5$$?

Accepted Answer

$$\{7, -3\}$$

Question 15

Given the function $$f(x) = \frac{1}{x}$$, which of the following statements is true?

Accepted Answer

The function is undefined at $$x = 0$$

Question 16

Which of the following graphs represents a function that is not one-to-one?

Accepted Answer

A parabola opening upwards

Question 17

If $$f(x) = 2x + 1$$ and $$g(x) = x^2$, what is f(g(3$$))$$?

Accepted Answer

$$19$$

Question 18

Which of the following best describes the end behavior of the function $$f(x) = -x^4$ + 2x^2$ as x$$ 	o \infty$$?

Accepted Answer

$$f(x) 	o -\infty$$

Question 19

A piecewise function is defined as $$f(x) = \begin{cases} x+2, & x \u003c 0 \ 2x-1, & x \geq 0 \end{cases}. $$What is $$f(-3) + f(2)$$?

Accepted Answer

$$2$$

Fundamental Graphs and Properties of Precalculus Functions

Guida di studio - Domande di pratica

Study guide - Flashcard