Q: If $$f(x) = 3x + 2$$ and $$g(x) = x^2$, what is (f$$ \circ g)(2)$$?

$$f(g(2)) = 3 \times 4 + 2 = 14$$

Q: Which of the following is the correct definition of an even function?

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

Question 1

Which of the following is the correct factored form of the polynomial $$18x^3y^2$ - 12x^3$y - 24x^2$y$?

Accepted Answer

$$6x^2y(3xy - 2y - 4$$)$$

Question 2

A quadratic equation in standard form is given by $$ax^2 + bx + c = 0$. If a = 2$, b = -4$, and c = -6$, what is the discriminant and what does it tell you about the solutions?

Accepted Answer

$$	ext{Discriminant} = 16$$, two real and distinct solutions

Question 3

Which of the following is the correct application of the Zero-Factor Property?

Accepted Answer

If $$ab = 0$$, then $$a = 0 or$$ $$b = 0 or $$both

Question 4

A projectile is launched upward from the ground with an initial velocity of $$73.5 m/s. $$Its height $$s (in $$meters) after $$t$$ seconds is given by $$s = -4.9t^2$ + 73.5t. $$After how many seconds will the projectile return to the ground?

Accepted Answer

$$t = 15$$ seconds

Question 5

Which of the following is the correct formula for the sum of a finite geometric series with first term $$a_1$$ and common ratio $$r ($$where $$r 
eq 1$$)?

Accepted Answer

$$S_n = a_1$ \frac{1 - r^n}{1 - r}$$

Question 6

Given the function $$f(x) = 2x^2$ - 4x + 1$$, what is the vertex of the parabola?

Accepted Answer

$$(1, -1)$$

Question 7

Which of the following statements about the graph of $$y = \frac{1}{x} is $$true?

Accepted Answer

It has a vertical asymptote at $$x = 0$$ and a horizontal asymptote at $$y = 0$$

Question 8

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

Accepted Answer

$$f(g(2)) = 3 	imes 4 + 2 = 14$$

Question 9

Which of the following is the correct definition of an even function?

Accepted Answer

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

Question 10

A system of equations is given by $$\begin{cases} 2x + 3y = 7 \ 4x - y = 5 \end{cases}. $$What is the solution $$(x, y)$$?

Accepted Answer

$$(2, 1)$$

Question 11

Which of the following is the correct formula for the distance between two points $$(x_1$, y_1$)$$ and $$(x_2$, y_2$) in $$the coordinate plane?

Accepted Answer

$$\sqrt{(x_2$ - x_1$)^2$$ + ($$y_2$$ - $$y_1)^2$}$$

Question 12

If $$\log_2$ x = 5$$, what is the value of $$x$$?

Accepted Answer

$$x = 32$$

Question 13

Which of the following is the correct formula for the midpoint of the segment joining $$(x_1$, y_1$)$$ and $$(x_2$, y_2$)$$?

Accepted Answer

$$\left( \frac{x_1$ + x_2$}{2}, \frac{y_1$ + y_2$}{2} \right)$$

Question 14

If $$f(x) = x^2$ - 4x + 3$$, what are the $$x-$$intercepts of the graph of $$f$$?

Accepted Answer

$$x = 1$$ and $$x = 3$$

Question 15

Which of the following is the correct formula for the future value $$A of an $$investment of $$P$$ dollars at an annual interest rate $$r$$, compounded $$n$$ times per year for $$t$$ years?

Accepted Answer

$$A = P \left(1 + \frac{r}{n}\$$right)^{nt}$$

Question 16

Which of the following is the correct formula for the $$nth $$term of an arithmetic sequence with first term $$a_1$$ and common difference $$d$$?

Accepted Answer

$$a_n = a_1$ + (n-1)d$$

College Algebra: Structured Study Notes and Visuals

스터디 가이드 - 연습 문제

학습 가이드 - 플래시카드