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The exponential function $g$ is defined by $g\left(x\right)=19·a^x$, where $a$ is a positive constant. If $g\left(3\right)=\mathrm{2,375}$, what is the value of $g\left(4\right)$?

The total distance d, in meters, traveled by an object moving in a straight line can be modeled by a quadratic function that is defined in terms of t, where t is the time in seconds. At a time of 10.0 seconds, the total distance traveled by the object is 50.0 meters, and at a time of 20.0 seconds, the total distance traveled by the object is 200.0 meters. If the object was at a distance of 0 meters when , then what is the total distance traveled, in meters, by the object after 30.0 seconds?

The function $p$ is defined by $p\left(n\right)=7n^3$. What is the value of $n$ when $p\left(n\right)$ is equal to $56$?

The equation $E\left(t\right)=5{\left(1.8\right)}^t$ gives the estimated number of employees at a restaurant, where $t$ is the number of years since the restaurant opened. Which of the following is the best interpretation of the number $5$ in this context?

$f\left(x\right)=4x^2-50x+126$

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

The function h is defined above, where a, b, and c are integer constants. If the zeros of the function are 6, and 7, what is the value of c ?

The function $f$ is defined by $f\left(x\right)=8\sqrt{x}$. For what value of $x$ does $f\left(x\right)=48$?

$f\left(x\right)=9{\left(4\right)}^x$

The function $f$ is defined by the given equation. If $g\left(x\right)=f(x+2)$, which of the following equations defines the function $g$?

$f\left(x\right)={\left(x+7\right)}^2+4$

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

The function $f$ is defined by $f\left(x\right)=x^3+15$. What is the value of $f\left(2\right)$?

Kao measured the temperature of a cup of hot chocolate placed in a room with a constant temperature of 70 degrees Fahrenheit (°F). The temperature of the hot chocolate was 185°F at 6:00 p.m. when it started cooling. The temperature of the hot chocolate was 156°F at 6:05 p.m. and 135°F at 6:10 p.m. The hot chocolate’s temperature continued to decrease. Of the following functions, which best models the temperature , in degrees Fahrenheit, of Kao’s hot chocolate m minutes after it started cooling?

The graph of the polynomial function $f$, where $y=f\left(x\right)$, is shown. The y-intercept of the graph is $\left(0,y\right)$. What is the value of $y$?

The function f is defined above. Which of the following is NOT an x-intercept of the graph of the function in the xy-plane?

$p\left(t\right)=\mathrm{90,000}{\left(1.06\right)}^t$

The given function $p$ models the population of Lowell $t$ years after a census. Which of the following functions best models the population of Lowell $m$ months after the census?

The population of a town is currently 50,000, and the population is estimated to increase each year by 3% from the previous year. Which of the following equations can be used to estimate the number of years, t, it will take for the population of the town to reach 60,000 ?

For the exponential function $f$, the value of $f\left(1\right)$ is $k$, where $k$ is a constant. Which of the following equivalent forms of the function $f$ shows the value of $k$ as the coefficient or the base?

An object is kicked from a platform. The equation $h=-4.9t^2+7t+9$ represents this situation, where $h$ is the height of the object above the ground, in meters, $t$ seconds after it is kicked. Which number represents the height, in meters, from which the object was kicked?

The quadratic function above models the height above the ground h, in feet, of a projectile x seconds after it had been launched vertically. If is graphed in the xy-plane, which of the following represents the real-life meaning of the positive x-intercept of the graph?

The function $f$ is defined by $f\left(x\right)=5x^2$. What is the value of $f\left(8\right)$?

$h\left(x\right)=x^2-3$

Which table gives three values of $x$ and their corresponding values of $h\left(x\right)$ for the given function $h$?

Bacteria are growing in a liquid growth medium. There were $\mathrm{300,000}$ cells per milliliter during an initial observation. The number of cells per milliliter doubles every $3$ hours. How many cells per milliliter will there be $15$ hours after the initial observation?

The rational function $f$ is defined by an equation in the form $f\left(x\right)=\frac{a}{x+b}$, where $a$ and $b$ are constants. The partial graph of $y=f\left(x\right)$ is shown. If  $g\left(x\right)=f\left(x+4\right)$, which equation could define function $g$?

$f\left(x\right)=\left(x-10\right)\left(x+13\right)$

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

The area $A$, in square centimeters, of a rectangular cutting board can be represented by the expression $w\left(w+9\right)$, where $w$ is the width, in centimeters, of the cutting board. Which expression represents the length, in centimeters, of the cutting board?