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A rectangle has a length of $x$ units and a width of $\left(x-15\right)$ units. If the rectangle has an area of $76$ square units, what is the value of $x$?

A scientist initially measures $\mathrm{12,000}$ bacteria in a growth medium. $4$ hours later, the scientist measures $\mathrm{24,000}$ bacteria. Assuming exponential growth, the formula $P=C{\left(2\right)}^{rt}$ gives the number of bacteria in the growth medium, where $r$ and $C$ are constants and $P$ is the number of bacteria $t$ hours after the initial measurement. What is the value of $r$?

A quadratic function models a projectile's height, in meters, above the ground in terms of the time, in seconds, after it was launched. The model estimates that the projectile was launched from an initial height of $7$ meters above the ground and reached a maximum height of $51.1$ meters above the ground $3$ seconds after the launch. How many seconds after the launch does the model estimate that the projectile will return to a height of $7$ meters?

$y=x^2-14x+22$

The given equation relates the variables $x$ and $y$. For what value of $x$ does the value of $y$ reach its minimum?

The function $f$ is defined by $f\left(x\right)=\frac{1}{6x}$. What is the value of $f\left(x\right)$ when $x=3$?

Function $f$ is defined by $f\left(x\right)=-a^x+b$, where $a$ and $b$ are constants. In the xy-plane, the graph of $y=f\left(x\right)-15$ has a y-intercept at $\left(0,-\frac{99}{7}\right)$. The product of $a$ and $b$ is $\frac{65}{7}$. What is the value of $a$?

$g\left(x\right)=x^2+55$

What is the minimum value of the given function?

$f\left(x\right)=\left(x-14\right)\left(x+19\right)$

The function $f$ is defined by the given equation. For what value of $x$ does $f\left(x\right)$ reach its minimum?

What is the y-intercept of the graph shown?

What is the x-intercept of the graph shown?

$f\left(x\right)=\left(x+6\right)\left(x-4\right)$

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

Immanuel purchased a certain rare coin on January 1. The function $f\left(x\right)=65{\left(1.03\right)}^x$, where $0\le x\le 10$, gives the predicted value, in dollars, of the rare coin $x$ years after Immanuel purchased it. What is the best interpretation of the statement “$f\left(8\right)$ is approximately equal to $82$” in this context?

A model estimates that at the end of each year from $2015$ to $2020$, the number of squirrels in a population was $150\%$ more than the number of squirrels in the population at the end of the previous year. The model estimates that at the end of $2016$, there were $180$ squirrels in the population. Which of the following equations represents this model, where $n$ is the estimated number of squirrels in the population $t$ years after the end of $2015$ and $t\le 5$?

$f\left(x\right)=\left(59-2x\right)$

The function $f$ is defined by the given equation. For which of the following values of $k$ does $f\left(k\right)=3k$?

From 2005 through 2014, the number of music CDs sold in the United States declined each year by approximately 15% of the number sold the preceding year. In 2005, approximately 600 million CDs were sold in the United States. Of the following, which best models C, the number of millions of CDs sold in the United States, t years after 2005?

If during this time the population of the city decreases by a fixed percent each year, which of the following must be true?

The graph of $y=f\left(x\right)$ is shown in the xy-plane. What is the value of $f\left(0\right)$?

The graph gives the estimated number of catalogs $y$, in thousands, a company sent to its customers at the end of each year, where $x$ represents the number of years since the end of $1992$, where $0\le x\le 10$. Which statement is the best interpretation of the y-intercept in this context?

$f\left(x\right)=(x+6)(x+5)(x-4)$

The function $f$ is given. Which table of values represents $y=f\left(x\right)-3$?

The product of two positive integers is $546$. If the first integer is $11$ greater than twice the second integer, what is the smaller of the two integers?

$f\left(x\right)=\mathrm{5,470}{\left(0.64\right)}^{\frac{x}{12}}$

The function $f$ gives the value, in dollars, of a certain piece of equipment after $x$ months of use. If the value of the equipment decreases each year by $p\%$ of its value the preceding year, what is the value of $p$?

In the xy-plane, the y-coordinate of the y-intercept of the graph of the function f is c. Which of the following must be equal to c ?

$y=0.25x^2-7.5x+90.25$

The equation gives the estimated stock price $y$, in dollars, for a certain company $x$ days after a new product launched, where $0\le x\le 20$. Which statement is the best interpretation of $\left(x,y\right)=\left(1,83\right)$  in this context?

For the function f defined above, what is the value of ?

Which of the following is the graph in the xy-plane of the given equation?