sat-dog

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

1. $f\left(x\right)=33{\left(0.4\right)}^{x+3}$
2. $g\left(x\right)=33\left(0.16\right){\left(0.4\right)}^{x-2}$

A rubber ball bounces upward one-half the height that it falls each time it hits the ground. If the ball was originally dropped from a distance of 20.0 feet above the ground, what was its maximum height above the ground, in feet, between the third and fourth time it hit the ground?

The function $f$ is defined by $f\left(x\right)=6+\sqrt{x}$. What is the value of $f\left(36\right)$?

The number of bacteria in a liquid medium doubles every day. There are $\mathrm{44,000}$ 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? 

$f\left(x\right)=x^2-18x-360$

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

The quadratic function graphed above models a particular measure of plant diversity as a function of the elevation in a region of Switzerland. According to the model, which of the following is closest to the elevation, in meters, at which plant diversity is greatest?

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

The surface area of a cube is , where a is a positive constant. Which of the following gives the perimeter of one face of the cube?

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

According to Moore’s law, the number of transistors included on microprocessors doubles every 2 years. In 1985, a microprocessor was introduced that had 275,000 transistors. Based on this information, in which of the following years does Moore’s law estimate the number of transistors to reach 1.1 million?

The function $f$ is defined by $f\left(x\right)=270{\left(0.1\right)}^x$. What is the value of $f\left(0\right)$?

The function $g$ is defined by $g\left(x\right)=x^2+9$. For which value of $x$ is $g\left(x\right)=25$?

The function f is defined as shown. Which of the following graphs in the xy-plane could be the graph of ?

The function $f\left(x\right)=206{\left(1.034\right)}^x$ models the value, in dollars, of a certain bank account by the end of each year from $1957$ through $1972$, where $x$ is the number of years after $1957$. Which of the following is the best interpretation of “$f\left(5\right)$ is approximately equal to $243$” in this context?

The function above models the height h, in feet, of an object above ground t seconds after being launched straight up in the air. What does the number 72 represent in the function?

A model predicts that the population of Springfield was $\mathrm{15,000}$ in $2005$. The model also predicts that each year for the next $5$ years, the population $p$ increased by $4\text{\%}$ of the previous year's population. Which equation best represents this model, where $x$ is the number of years after $2005$, for $x\le 5$?

The function N defined above can be used to model the number of species of brachiopods at various ocean depths d, where d is in hundreds of meters. Which of the following does the model predict?

The function $h$ is defined by $h\left(x\right)=a^x+b$, where $a$ and $b$ are positive constants. The graph of $y=h\left(x\right)$ in the $xy$-plane passes through the points ($0$, $10$) and ($-2$, $\frac{325}{36}$). What is the value of $ab$?

The table shows three values of $x$ and their corresponding values of $y$, where $y=f\left(x\right)+4$ and $f$ is a quadratic function. What is the y-coordinate of the y-intercept of the graph of $y=f\left(x\right)$ in the xy-plane?

$g\left(x\right)=11{\left(\frac{1}{12}\right)}^x$

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

The area A, in square centimeters, of a rectangular painting can be represented by the expression $w\left(w+29\right)$, where $w$ is the width, in centimeters, of the painting.  Which expression represents the length, in centimeters, of the painting?

A quadratic function models the height, in feet, of an object above the ground in terms of the time, in seconds, after the object is launched off an elevated surface. The model indicates the object has an initial height of $10$ feet above the ground and reaches its maximum height of $\mathrm{1,034}$ feet above the ground $8$ seconds after being launched. Based on the model, what is the height, in feet, of the object above the ground $10$ seconds after being launched?

A company opens an account with an initial balance of $\$\mathrm{36,100.00}$. The account earns interest, and no additional deposits or withdrawals are made. The account balance is given by an exponential function $A$, where $A\left(t\right)$ is the account balance, in dollars, $t$ years after the account is opened. The account balance after $13$ years is $\$\mathrm{68,071.93}$. Which equation could define $A$?

The table above gives the values of the function f for some values of x. Which of the following equations could define f ?

Function $f$ is defined by $f\left(x\right)=\left(x+6\right)\left(x+5\right)\left(x+1\right)$. Function $g$ is defined by $g\left(x\right)=f\left(x-1\right)$. The graph of $y=g\left(x\right)$ in the xy-plane has x-intercepts at $\left(a,0\right)$, $\left(b,0\right)$, and $\left(c,0\right)$, where $a$, $b$, and $c$ are distinct constants. What is the value of $a+b+c$?