The function $f$ is defined by $f(x)=7x^{3}$. In the xy-plane, the graph of $y=g(x)$ is the result of shifting the graph of $y=f(x)$ down 2 units. Which equation defines function $g$?

The surface area of a cube is $6\left(\dfrac{a}{4}\right)^{2}$, where $a$ is a positive constant. Which of the following gives the perimeter of one face of the cube?

$$y=2x^{2}-21x+64$$ $$y=3x+a$$

In the given system of equations, $a$ is a constant. The graphs of the equations in the given system intersect at exactly one point, $(x,y)$, in the $xy$-plane. What is the value of $x$?

Square P has a side length of $\bm{x}$ inches. Square Q has a perimeter that is $\bm{176}$ inches greater than the perimeter of square P. The function $\bm{f}$ gives the area of square Q, in square inches. Which of the following defines $\bm{f}$?

$$f(x)=x^{2}-18x-360$$

If the given function $f$ is graphed in the $xy$-plane, where $y=f(x)$, what is an $x$-intercept of the graph?

Which of the following is equivalent to $\left(a+\frac{b}{2}\right)^{2}$?

Which of the following expressions is equivalent to $2a^{2}(a+3)$?

$$x-29=(x-a)(x-29)$$

Which of the following are solutions to the given equation, where $a$ is a constant and $a>30$?

I. $a$

II. $a+1$

III. 29

The number of bacteria in a liquid medium doubles every day. There are $44,000$ bacteria in the liquid medium at the start of an observation. Which represents the number of bacteria, $y$, in the liquid medium $t$ days after the start of the observation?

$$D=T-\frac{9}{25}\left(100-H\right)$$

The formula above can be used to approximate the dew point $D$, in degrees Fahrenheit, given the temperature $T$, in degrees Fahrenheit, and the relative humidity of $H$ percent, where $H>50$. Which of the following expresses the relative humidity in terms of the temperature and the dew point?

Which expression is equivalent to $9x^{2}+5x$?

$P=\frac{W}{t}$

The power $P$ produced by a machine is represented by the equation above, where $W$ is the work performed during an amount of time $t$. Which of the following correctly expresses $W$ in terms of $P$ and $t$?

Blood volume, $V_{B}$, in a human can be determined using the equation $V_{B}=\dfrac{V_{P}}{1-H}$, where $V_{P}$ is the plasma volume and $H$ is the hematocrit (the fraction of blood volume that is red blood cells). Which of the following correctly expresses the hematocrit in terms of the blood volume and the plasma volume?

The given equations define the functions $f$ and $g$, where $x\geq 0$. Which of the following equations displays, as a constant or coefficient, the maximum value of the function it defines, where $x\geq 0$?

I. $f(x)=33(0.4)^{x+3}$

II. $g(x)=33(0.16)(0.4)^{x-2}$

The function $f(x)=200,000(1.21)^{x}$ gives a company's predicted annual revenue, in dollars, $x$ years after the company started selling light bulbs online, where $0<$x$\leq 10$. What is the best interpretation of the statement "$f(5)$ is approximately equal to 518,748" in this context?

A certain college had 3,000 students enrolled in 2015. The college predicts that after 2015, the number of students enrolled each year will be 2% less than the number of students enrolled the year before. Which of the following functions models the relationship between the number of students enrolled, $f(x)$, and the number of years after 2015, $x$ ?

$M=1,800(1.02)^{t}$

The equation above models the number of members, $M$, of a gym $t$ years after the gym opens. Of the following, which equation models the number of members of the gym $q$ quarter years after the gym opens?

Which of the following is equivalent to $2x^{3}+4$? 

Which expression is equivalent to $a^{\frac{11}{12}}$, where $a>0$?

In the $xy$-plane, the graph of $y=x^{2}-9$ intersects line $p$ at $(1,a)$ and $(5,b)$, where $a$ and $b$ are constants. What is the slope of line $p$?

Which of the following is equivalent to $2(x^{2}-x)+3(x^{2}-x)$?

$$P(t)=290(1.04)^{(\frac{4}{6})t}$$

The function $P$ models the population, in thousands, of a certain city $t$ years after 2005. According to the model, the population is predicted to increase by $n\%$ every 18 months. What is the value of $n$?

Sara opened a savings account at a bank. The table shows the exponential relationship between the time $t$, in years, since Sara opened the account and the total amount $d$, in dollars, in the account. If Sara made no additional deposits or withdrawals, which of the following equations best represents the relationship between $t$ and $d$?

$\frac{1}{7b}=\frac{11x}{y}$

The given equation relates the positive numbers $b$, $x$, and $y$. Which equation correctly expresses $x$ in terms of $b$ and $y$?

Which expression is equivalent to $6x^{8}y^{2}+12x^{2}y^{2}$?