sat-dog

A rectangle has a length that is $15$ times its width. The function $y=\left(15w\right)\left(w\right)$ represents this situation, where $y$ is the area, in square feet, of the rectangle and $y>0$. Which of the following is the best interpretation of $15w$ in this context?

The quadratic function h is defined as shown. In the xy-plane, the graph of intersects the x-axis at the points and , where t is a constant. What is the value of t ?

The function $f$ is defined by $f\left(x\right)=\left(-8\right){\left(2\right)}^x+22$. What is the y-intercept of the graph of $y=f\left(x\right)$ in the xy-plane?

The graph shows the height above ground, in meters, of a ball $x$ seconds after the ball was launched upward from a platform. Which statement is the best interpretation of the marked point $\left(1.0,4.8\right)$ in this context?

$f\left(x\right)=\mathrm{9,000}{\left(0.66\right)}^x$

The given function $f$ models the number of advertisements a company sent to its clients each year, where $x$ represents the number of years since $1997$, and $0\le x\le 5$. If $y=f\left(x\right)$ is graphed in the xy-plane, which of the following is the best interpretation of the y-intercept of the graph in this context?

The first term of a sequence is $9$. Each term after the first is $4$ times the preceding term. If $w$ represents the $n$th term of the sequence, which equation gives $w$ in terms of $n$?

What is the $y$-intercept of the graph shown?

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

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 $y=f\left(x\right)-12$ has a y-intercept at $\left(0,-\frac{75}{7}\right)$. The product of $a$ and $b$ is $\frac{320}{7}$. What is the value of $a$?

Scientists recorded data about the ocean water levels at a certain location over a period of $6$ hours. The graph shown models the data, where $y=0$ represents sea level. Which table gives values of $x$ and their corresponding values of $y$ based on the model?

The function $f$ is defined by $f\left(x\right)=4+\sqrt{x}$. What is the value of $f\left(144\right)$?

A rectangular volleyball court has an area of 162 square meters. If the length of the court is twice the width, what is the width of the court, in meters?

A machine launches a softball from ground level. The softball reaches a maximum height of $51.84$ meters above the ground at $1.8$ seconds and hits the ground at $3.6$ seconds. Which equation represents the height above ground $h$, in meters, of the softball $t$ seconds after it is launched?

The 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 $y=f\left(x\right)$ has an $x$-intercept at $\left(2,0\right)$ and a $y$-intercept at $\left(0,-323\right)$. What is the value of $b$?

The function S above models the annual salary, in dollars, of an employee n years after starting a job, where a is a constant. If the employee’s salary increases by 4% each year, what is the value of a ?

The revenue , in dollars, that a company receives from sales of a product is given by the function f above, where x is the unit price, in dollars, of the product. The graph of in the xy-plane intersects the x-axis at 0 and a. What does a represent?

A culture of bacteria is growing at an exponential rate, as shown in the table above. At this rate, on which day would the number of bacteria per milliliter reach ?

The equation above estimates the global data traffic D, in terabytes, for the year that is t years after 2010. What is the best interpretation of the number 5,640 in this context?

$f\left(x\right)=a{x}^2+4x+c$

In the given quadratic function, $a$ and $c$ are constants. The graph of $y=f\left(x\right)$ in the xy-plane is a parabola that opens upward and has a vertex at the point $\left(h,k\right)$, where $h$ and $k$ are constants. If $k<0$ and $f\left(-9\right)=f\left(3\right)$, which of the following must be true?

1. $c<0$
2. $a\ge 1$

The x-intercept of the graph shown is $\left(x,0\right)$. What is the value of $x$?

Which of the following could be the equation of the graph shown in the xy-plane?

$f\left(x\right)=4x^2+64x+262$

The function $g$ is defined by $g\left(x\right)=f\left(x+5\right)$. For what value of $x$ does $g\left(x\right)$ reach its minimum?

The graph of $y=f\left(x\right)$ is shown, where the function $f$ is defined by $f\left(x\right)=a{x}^3+b{x}^2+cx+d$ and $a$, $b$, $c$, and $d$ are constants. For how many values of $x$ does $f\left(x\right)=0$?

The table shown includes some values of x and their corresponding values of y. Which of the following graphs in the xy-plane could represent the relationship between x and y ?

The function $f$ is defined by $f\left(x\right)=\left(x-6\right)\left(x-2\right)\left(x+6\right)$. In the xy-plane, the graph of $y=g\left(x\right)$ is the result of translating the graph of $y=f\left(x\right)$ up $4$ units. What is the value of $g\left(0\right)$?