DSAT extra practice Ch2 Lv2

A biologist is studying a specific type of bacteria. The bacteria, when introduced into a white rabbit’s body, doubles in quantity every 5 hours. The biologist implants 15 bacteria into a white rabbit. Which of the following functions best expresses the relationship between the quantity of bacteria [math]f(t)[/math] and time [math]t[/math] (in minutes)?

A pest control company analyzed the number of bedbug extermination requests received over the past 10 years. The company received 1,500 requests in the first year, and the number of requests doubled throughout the 10 years. Which of the following functions best represents the relationship between the year [math]t[/math] and the number of orders [math]y[/math]?

A man took his duck to ride a taxi. The following are his charge rate:
[math]\bullet[/math] If the distance is less than 1.5 km, the price is $2.5.
[math]\bullet[/math] Starting at 1.5 km, charge $0.8 every 0.5 km.
Let [math]f(x)[/math] represent the man s taxi fare where [math]x[/math] is the distance measured in kilometers, what is [math]f(3)[/math]?

The table above shows some values of [math]x[/math] and their corresponding values of the absolute value function [math]f(x)=a\cdot|x-1|+5[/math] where [math]a[/math] is a constant. What is the value of [math]a[/math]?

If [math]f(x)=2x^2+9[/math], what is the value of [math]-f(-3)[/math]?

If [math]f(n)=n^2-g(n)[/math] and [math]g(n)=2(n+1)[/math], what is the value of [math]f(-5)[/math]?

$$f(x)=2^{x+1}+1$$$$g(x)=k$$What is the value of [math]k[/math] such that [math]f(x)[/math] and [math]g(x)[/math] has one intersection?

Which of the following functions has no [math]x[/math]-intercepts?

The figure above shows the graph of [math]f(x)[/math] with domain [math]-6\leq x\leq6[/math]. If the equation [math]f(x)=k[/math] has only one solution, which of the following values could be [math]k[/math]?

The figure above shows the graph of [math]f(x)[/math]. What is the [math]x[/math]-coordinate of the intersection of [math]f(x)[/math] and [math]g(x)[/math] where [math]g(x)=-2x-2[/math]?

The figure above shows the graph of [math]f(x)[/math]. If function [math]g(x)=f(x)+k[/math] is always negative, what is the value of [math]k[/math]?

The figure above shows the graphs of three linear function [math]f(x)=m_1x+b_1, g(x)=m_2x+b_2[/math], and [math]h(x)=m_3x+b_3[/math]. Which of the following is true?

The figure above shows the graph of [math]f(x)[/math]. What is the multiplication of its [math]x[/math]-intercepts and [math]y[/math]-intercept?

What is the domain of the function [math]f(x)=\sqrt{2-x}[/math]?

Let [math]f(x)[/math] be a function. The domain of [math]f(x)[/math] is [math][1,4][/math] and the range of [math]f(x)[/math] is [math][-2,6][/math]. If [math]g(x)=f(x)-3[/math], which of the following statements must be true?

If [math]f(x)=\dfrac{1}{\sqrt{3-x}}[/math], what is the domain of [math]f(x)[/math]?

$$f(x)=\sqrt{x+1}+\sqrt{4-x}$$How many possible integers [math]a[/math] such that [math]f(a)[/math] is defined?

If [math]f(x)=3x-2[/math], which of the following expressions is equal to [math]f(a+2)[/math]?

The table above shows some values of [math]x[/math] and their corresponding values of [math]f(x)[/math]. Which of the following values is equal to [math]f(f(5))[/math]?

$$f(x)=(x-1)^2$$$$g(x)=\sqrt{3-x}$$Which of the following is [math]g(f(x))[/math]?

$$f(x)=\frac{1}{x}$$$$g(x)=x-7$$What is the domain of the function [math]h(x)=f(g(x))[/math]?

Environmental groups claim that from 2002 to 2022, Amazon rainforest has lost a total of 500 thousands square kilometers of forest area. If the function [math]f(t)=mt[/math] represents the relationship between time and forest area ([math]\text{km}^2[/math]) lost, where [math]t[/math] is the number of years after 2002, what is [math]m[/math]?

Which of the following lines has the largest [math]x[/math]-intercept?

If [math]f(x)=-3(x+b)[/math] where [math]b[/math] is a constant, what is the value of [math]\dfrac{f(2025)-f(1776)}{2025-1776}[/math]?

Let [math]f(x)=mx-3[/math] be a linear function where [math]m[/math] is a constant. If the equation [math]f(x)=6[/math] has one solution, which of the following numbers cannot be [math]m[/math]?

Let [math]R[/math] be the region bounded by line [math]\ell: y=3(x+6)[/math], the [math]x[/math]-axis and the [math]y[/math]-axis. What is the area of the region [math]R[/math]?

Linear function [math]f(x)[/math] passes through [math](-1,4)[/math] and [math](5,-8)[/math]. What is the [math]y[/math]-intercept of [math]f(x)[/math]?

If the slope of the linear function [math]f(x)[/math] is positive and the [math]x[/math]-intercept of [math]f(x)[/math] is negative , which quadrant does the graph of [math]f(x)[/math] not pass through?

Line [math]\ell[/math] passes through two points [math](3,-1)[/math] and [math](1,-5)[/math]. If [math]P[/math] is on [math]\ell[/math], which of the following coordinates could be [math]P[/math]?

$$\ell: 2x-5y=12$$Which of the following lines passes through [math](3,-2)[/math] and is perpendicular to line [math]\ell[/math] above?

If two lines [math]\ell_1: y=6x+3[/math] and [math]\ell_2: y=mx+3[/math] are perpendicular where [math]m[/math] is a constnat, what is the [math]x[/math]-intercept of [math]\ell_2[/math]?

$$3x+ay+11=0$$$$bx+2y-26=0$$If [math](x,y)=(3,4)[/math] is the solutions to the equations system above where [math]a[/math] and [math]b[/math] are constants, what is the value of [math]a+b[/math]?

$$5x+4y=20$$$$3x-18y=24$$What is the value of [math]x+11y[/math]?

$$3x+y=5$$$$x+3y=-1$$What is the solution to the system of equations?

A farmer has [math]x[/math] sheeps and [math]y[/math] ducks. If there is a total of 50 animals and 136 legs, how many ducks are there?

$$\begin{cases}y=\dfrac{2}{3}x-1\\2x-9y=13\end{cases}$$What is the solution of [math]x[/math] to the system of equations above?

$$3x+4y=12$$$$5x-3y=a$$If [math](x,y)=(-4,m)[/math] is a solution to the equations system above, what is the value of [math]a[/math]?

The exponential function [math]f(t)=5000-100\cdot\left(\dfrac{1}{3}\right)^t[/math] represents the population of zebras in Africa, where [math]t[/math] represents the number of years after 2020. What is the approximation number of zebras in Africa after “many” years?

$$f(t)=9\cdot1.5^t$$The function [math]f(t)[/math] above represents the relationship between the time [math]t[/math] (in years) and the number of fish in a lake. If the unit of [math]t[/math] is changed from years to months, what will be the new function?

$$f(t)=10\cdot(0.9)^t$$The function [math]f(t)[/math] above shows the relationship between the time [math]t[/math] (in days) and the amount of water (in liters) in the water tank of a machine. If the amount of water is less than 6 liters, the machine will overheat. How long will it take for the machine to start overheating if we never refill water?